The 8th Victor de Mello lecture: role played by viscosity on the undrained behaviour of normally consolidated clays

Differently from those who have preceded the author towards the honourable task of writing the eighth Victor de Mello Lecture, he belongs to a subsequent generation, the same of his son, his friend Luiz Guilherme de Mello. Our fathers were born in the very year of 1926, with a difference of a month and a half. For this reason, he thinks his way of perceiving Professor Victor F. B. de Mello may be different and more distant from those ways posed by the previous de Mello lecturers. Such a distance should be taken as a measure of the author’s respect and admiration since the time he was a student at the Polytechnic School of the Federal University of Rio de Janeiro and trainee at the Geotechnical Laboratory of COPPE/UFRJ at the end of the seventies. The author perceived Professor Victor Froilano Bachmann de Mello as a live legend, as a shining and unreachable sun of knowledge rising from the horizon... The author has heard about his critical mind several times. In fact, the author has been introduced to his critical way of behaving even before meeting him in person. This happened when the author read the preface of the book Soil Testing for Engineers (Lambe, 1951), in which the acknowledgements end with: “To Dr. Victor F. B. de Mello, a former member of the soil mechanics staff at the Massachusetts Institute of Technology, especial thanks are due for his sharp but constructive criticisms based on a careful study of the manuscript.” (Lambe, 1951, pp. v-vi). The practice of criticism is usually taken with reservation among Latins. Many times the Latin spirit takes criticism as a personal attack. Perhaps, for this reason, when practicing criticism, Victor de Mello may often have been misunderstood in the country he chose to live in. The biographical notes posed by Moreira & Décourt (1989) for the de Mello Volume suggest that, as regards Victor de Mello, who was born in a family in which education was always taken into high account, the practice of criticism used to be a natural consequence of the act of thinking, with ideas fighting against each other. Criticism as the exercise of ever trying to improve what is being criticized. Criticism in the very analytical meaning of the word. Criticism addressed to opinions and ideas, never to persons. Perhaps this gift to criticism has even more been developed in the soul of the young man who, having left Goa, an old Portuguese province on the west coast of India, had to triumph by using merit as the main weapon within the competitive environment of the Massachusetts Institute of Technology (MIT), as Christian & Baecher (2015) suggest. If he had not imposed himself, neither would he have become Abstract Phenomena that do not obey Terzaghi’s principle of effective stress (PES) are related to strain rate and time effects. This issue led the author to refer to early articles in soil mechanics, which used to consider the shear resistance of clays as a combination of two components: a frictional and a viscous one. In these articles the viscous component was assigned to the distortion of highly viscous adsorbed water layer in the contact points between grains along the plane where shearing takes place. Assuming the shear resistance of plastic soils comprises frictional and viscous resistance components, a shear stress equation can be added to the PES. It is shown that Mohr’s circle of effective stress is the sum of two ellipses: the viscosity and the friction ellipses. The ordinates of the viscosity and the friction ellipses represent the viscous and the frictional components of shear resistance in different planes, respectively. This approach leads to a failure criterion considering strain rate, according to which failure takes place whenever the friction ellipse touches the strength envelope, which is the ' e φ sloped straight line passing through the origin, ' e φ being the Hvorslev’s true angle of friction. By adding such shear stress equation to the PES, a model that explains strain rate and time effects is developed. Predictions of the proposed model are compared to results from tests carried out on San Francisco Bay Mud specimens.

the eventual substitute of Professor Taylor [de Mello, L.G. (2021). Personal communication.] nor would he have deserved the comment made by Moreira & Décourt (1989) in his biographical notes: "Back at MIT his academic past had left one mark. It has been heard that Taylor often mentioned him as the best student to have gone through the department, and that for a couple of decades the challenge to the new staff was to hear from the older faculty "how de Mello would have handled the problem" (Moreira & Décourt, 1989, p. xiii). The Italians would say: "se non è vero è bene trovato", because vestiges of this admiration appear at Taylor's (1955) acknowledgements in his ultimate report: "Review of Research on Shearing Strength of Clay". Part of the acknowledgements says: "Especially valuable contributions were made by V.F.B. de Mello and R.H.Clough." (Taylor, 1955, p. 2). This happened about 6 years after Victor de Mello had left MIT on his way to Brazil, showing that Victor and Don Taylor were still connected.
The author, who was also educated within an environment in which the practice of criticism was always carried out, deeply understood that way of behaving because he apprehended its aims. An illustrative example of Victor de Mello's critical attitude appears in the outline of his potential book (de Mello, 2014), where he presented a list of items which should be reviewed. One of these items is, for instance, the void ratio (e ) versus vertical effective stress ( ' v σ , log scale) relationship in the one-dimensional compression, which, if represented by a straight line, leads to the mistake of obtaining a void ratio equal to zero (and even negative ones). By the way, the author (Martins, 1983;Martins & Lacerda, 1994) also discussed such subject.
Despite the author had maintained brief contacts with Professor Victor de Mello, usually during conferences and meetings' intervals, he always tried to draw closer to him to listen to the soil mechanics stories he witnessed. These stories, which were always told in a picturesque way and with a special pleasure, were usually "painted" with the colours of his vernacular palette. Marzionna (2014), a close friend and colleague of his son Luiz Guilherme at the Polytechnic School of the University of São Paulo, managed, in the author's opinion, to capture by the adjectives passionate, unresigned and perfectionist the essence of the man who, even being aware that many things inside his soul were utopian, knew that dreams, although unreachable, have just one purpose in life: to keep everyone walking forward. Nevertheless, according to Burland (2008) his way of saying that was more poetical: "Choose your love and love your choice" (Burland, 2008, p. 116). That was what he did throughout his life.

Philosophical spirit of this lecture
As regards science, the soul of things is in the fundamentals. The birth of any science is in man's creative ability to observe and imagine how things work.
To make science means to explain how things operate in our universe and to establish links between causes and effects, thus following the so-called scientific method. Several texts have been written about the scientific method, but none of them teaches neither how to observe nor how to proceed in order to make ideas spring out concerning a given phenomenon. Such ideas are "creation blows" and nobody knows where they come from … they are the "soul of science". Costa (2005) quotes the following passage from Lobo Carneiro's study about Galileu's investigation method: "his scientific investigation method consists in a suitable combination of experiment with mathematics, a deductive logical tool. Considering some experimental facts, a first hypothesis or theory is built in order to interpret them. Certain conclusions are deductively drawn from that theory; then the validity of those conclusions is submitted to experiment, which the last word always correspond to. The hypothesis should be replaced or improved if the tests do not corroborate it. The final verdict is based on the truth criterion, which is always given by the experimental results." (Costa, 2005, p. 139).
Philosophically speaking, the first step of that method consists in something that cannot be taught: in the observation of a phenomenon and of ideas concerning why and how that phenomenon occurs. (Where do the ideas come from and how do they spring into our thoughts?) That is a mystery, which is in the birth of all sciences. The idea becomes a working hypothesis regardless of how it has appeared. By means of sequential reasoning or deductive logic, that working hypothesis leads to forecasts regarding the studied phenomenon. If forecasts are confirmed by means of tests whose results are repeated, then the hypothesis becomes a principle, a postulate, an axiom or a law. So to speak, theories that allow predicting phenomena concerning that science are developed based on those laws. Therefore, every science is supported by a principle or a set of principles. The word principle is used because it means the beginning of things. As regards soil mechanics, it is not different; it is built upon the Principle of Effective Stress (Terzaghi, 1936).
Being a postulate, a principle cannot be demonstrated. After being accepted as a truth, it is strengthened every time its validity is checked by an experimental result. However, despite a principle may many times have its validity confirmed, the repeatability of experimental results indicating the principle's validity does not turn such repeatability into proof. On the contrary, just one example that does not follow a principle (called a counterexample) is enough to show the validity of that principle is restricted.
Irrespective of a principle having a chance of being of restricted validity (a common thing in science), "to make science" follows no other path than that of the idea that evolves into a working hypothesis, which, after confirming experimental results, reaches the status of a principle.
Understanding, examining, reexamining and pondering about what a principle establishes is also a role of science. For this reason, it is necessary to deeply understand the statements of the established principles to correctly apply them but also to adequately check their validity.
If the process of managing to have an idea cannot be taught, perhaps to exercise thinking may be a way of opening the doors of mind to let the ideas come in. [Saramago, R.P. (2021). Personal communication.] reminded that Lobo Carneiro, the creator of the "Brazilian Test" (used to measure tensile strength of concrete), of whom the author is also proud of having been a pupil, used to say that, before writing any mathematical equation to describe a phenomenon, "it is necessary to conceive a mental model explaining how and why the phenomenon occurs, no matter how rudimentary the model can be". Another important task is to identify the variables on which the studied phenomenon depends and to identify any other already known phenomenon with which an analogy may be established, a parallel may be drawn. We must think about the subject and let ideas flow. [Santa Maria, P.E.L.(2000). Personal communication.] posed to the author the following thought about the matter: "… so that ideas may arise from our minds, time is necessary to think about them, to appraise them…and thus brain must be "idle" and free from daily tasks, otherwise ideas shall take another way…".
In these modern times, when lack of time predominates, the profusion of published papers leads to the reflection that much more time has been spent in writing rather than in thinking about things that would be worth writing. In short: producing papers has become more important than producing knowledge. One of the reasons for that can be found in a statement made by Lambe (1981) when he referred to one aspect of the geotechnical engineering history of MIT: "One outstanding paper can contribute far more than five mediocre papers; unfortunately five mediocre papers can carry more weight in the [university] promotion process than one outstanding paper." (Lambe, 1981, p. 56).
Similarly, de Mello's thought "We professionals beg less rapid novelties, more renewed reviewing of what is already there" also seems to express his concern about the rapid and abundant way by which most new papers have been written, without taking into consideration a deeper analysis of the subjects. Since Taylor was the sole soil mechanics professor at MIT from the mid thirties up to 1945 (Christian & Baecher, 2015), it is not difficult to imagine how much de Mello and Lambe, both Taylor's pupils at that period, have been influenced by his careful way of thinking, rethinking and understanding the phenomena, mainly as regards the fundamental concepts. Christian & Baecher (2015) realized that part of the cause for the bad treatment dispensed to Taylor by the group led by Terzaghi was related to Taylor's way of being. The following quotation illustrates this point of view: "Neither MIT nor his Professional colleagues treated Taylor well. The reasons are hard to grasp at this remove, but part of the problem seems to be that he often worked on problems that were supposed to have already been solved and he discovered previously unappreciated complexities. He was a careful and thorough experimentalist, a strength that lay behind many of his successes. He had actually looked at the data and understood mechanics." (Christian & Baecher, 2015, p. 16).
The author heard from Professor Victor F. B. de Mello that "Fundamentals of Soil Mechanics" could be considered one of the five major books ever written about soil mechanics. The author also shares this opinion. Christian & Baecher (2015) still went further and added: "Fundamentals of Soil Mechanics remains today a seminal text on soil mechanics and influenced generations of geotechnical engineers. In many ways, it is as contemporary as texts written fifty years later, and it may be as influential to the modern field of soil Mechanics as the books of Terzaghi. The presentation is clear and reflects careful thought.".
Again, the author not only agrees with the above mentioned comments but also intends to show the ideas presented herein came from Terzaghi (1936) and Terzaghi & Frölich (1936). Those ideas grew up with the special care Taylor (1942Taylor ( , 1948 used to carry out research: observing phenomena, creating a mechanism to explain them, translating them into a mathematical language, solving the equations assumed as representative of the phenomena and comparing their results to the experimental data obtained. Just the same path followed by Galileu. As the name suggests, "Fundamentals of Soil Mechanics" was written with a focus on fundamentals. The author learned from Carneiro & Battista (1975) and studying Taylor (1948) that the soul of science is in the fundamentals. This lecture also concerns fundamentals and was written inspired by de Mello's spirit of thought: "We professionals beg less rapid novelties, more renewed reviewing of what is already there" (Jamiolkowski, 2012, p. 117) (or pursuant to the author's perception). That is why the number of references is not so large. After all, the task of reviewing already settled issues in a renewed way requires deeper and more intensive work rather than extensive. That is what the author tried to do. are filled with water under a stress u, the total principal stresses consist of two parts. One part u acts in the water and in the solid in every direction with equal intensity. It is called the neutral stress (or the pore pressure). The balance   1  1  2  2  3  3 , ' ' ' u u and u σ σ σ σ σ σ =− =− =− represents an excess over the neutral stress u and it has its seat exclusively in the solid phase of the soil. This fraction of the total principal stress will be called the effective principal stress. (Atkinson & Bransby, 1978, p. 21).
Hence, the fundamental effective stress equation is given by Equation 1.
The second part of the PES statement gives the role played by effective stresses on the behaviour of soils: All measurable effects of a change of stress, such as compression, distortion and a change of shearing resistance, are exclusively due to changes in the effective stresses. (Atkinson & Bransby, 1978, p. 21).

Role played by effective stresses on the behaviour of soils
Considering the way the PES was stated, the second part only assures that volume change, distortion and a change of shearing resistance are effects caused by a change in the effective stress state. Nevertheless, rigorously speaking, according to the way it was stated, the second part of the PES does not ensure that changes in the effective stress state necessarily cause volume variation, distortion or change of shearing resistance. However, that is the way how soil mechanics interprets and uses the PES. Thus, as far as volume change and distortion are concerned, the second part of the PES might be summarized, without loss of its essence, in the following bidirectional mathematical sentence:

change in effective stress ↔ volume change or distortion
The above mathematical sentence is then interpreted as follows

→ the "going"
Whenever there is a change in the state of effective stress, there will be either a change of volume or distortion (or both).
The connective or in the right side of the PES second part sentence makes the sentence true when at least one of the two statements (volume change or distortion) is true and false only when both are false.

← the "converse"
Whenever there is a change of volume or distortion (it is enough that one of them occurs) or both, the change(s) was (were) caused by a change in the state of effective stress.
To illustrate the PES meaning according to classical soil mechanics, Atkinson & Bransby (1978) state the three following corollaries: Corollary 1: The engineering behaviour of two soils with the same structure and mineralogy will be the same if they have the same effective stress.
Corollary 2: If a soil is loaded or unloaded without any change of volume and without any distortion there will be no change of effective stress.
The above-mentioned corollaries are illustrations of how the PES is interpreted and used in classical soil mechanics. Nevertheless, it is possible to present counterexamples which show that these corollaries have no general validity.
As regards corollary 1, one knows that two specimens of the same soil subjected to CIU (isotropically consolidated, undrained) triaxial tests starting from the same state of effective stress, but sheared with different axial strain rates ( ) , show different behaviour. This effect was identified a long time ago [see, for instance, Taylor (1948)]. Such effect is illustrated in Figure 1 by CIU test results carried out by Lacerda (1976) on San Francisco Bay Mud samples.
It is possible to present counterexamples which show that the second corollary also has no general validity. In this case, it is enough to observe what happens during an undrained stress relaxation test. As far as this kind of test is concerned, the procedure is almost the same followed during a conventional CIU triaxial test. The specimen is subjected to a constant axial strain rate ( ) a ε and led up to a determined deviator stress without necessarily being led to failure. Then, at a given axial strain, the load frame motor is switched off and the specimen behaviour is observed over time. It is the so-called stress relaxation test (or stage).
Provided the soil is saturated, there will be no volume change in a CIU triaxial test during the shearing phase but only distortion. When the load frame motor is switched off, there will be no variation of distortion at all. However, even with no change in volume and distortion, there is a substantial variation of the effective stress state (see Figure 2).
Finally, it is possible to present counterexamples showing that the third corollary does not have general validity. Suppose that a soil specimen has been isotropically consolidated to some stress in the normally consolidated range. If after dissipation of the excess pore pressure drainage is closed and the total stress is kept constant, it is observed that pore pressure increases over time ( Figure 3). According to corollary 3, if a soil specimen is kept under a constant isotropic state of total stress and pore pressure increases over time, the effective stress decrease should make the specimen to expand, but this cannot occur since drainage is closed.
The counterexamples relating to the three aforementioned corollaries serve to raise important issues regarding the PES validity. After the advent of critical state soil mechanics, a relevant evolution towards theoretical soil mechanics approach took place, mainly as regards the introduction of plasticity theory concepts. As far as the above-mentioned counterexamples are concerned, time and strain rate effects are present in all of them. Thus, it is natural the attempt to create behavioural models into which concepts that deal with such effects may be introduced. Nevertheless, in view of the theoretical difficulties to deal with phenomena such as creep, stress relaxation and secondary consolidation, the usual approach is to preserve the PES essence and develop tools to tackle one of these specific phenomena, considering each one out of the PES validity domain. A typical example of such an approach is the assumption / constant c C C α = (Mesri & Godlewski, 1977) to handle secondary consolidation.
Computer-aided numerical analyses have made sophisticated stress-strain-strength models feasible. However, those approaches often become so tricky that the feeling of the physical phenomenon sometimes is lost in the midst of the mathematical approach.
As the main purpose of this paper is to study the causes and effects of strain rate on the undrained behaviour of clays, the focus will be on fundamentals. Thus, one will only study here saturated isotropic normally consolidated clays, without cementation among grains, subjected to undrained axi-symmetric stress states, similar to those found in CIU triaxial tests. This paper follows a different approach from those usually found. The original PES is extended so that phenomena which escape from its validity domain, such as strain rate effects, undrained creep and stress relaxation, may naturally result from the extended PES version. Concepts that allow such PES extension are already presented in classic texts. Many of these concepts can be found in Terzaghi & Frölich (1936),   . Pore pressure increase after closing drainage after isotropic consolidation (Thomasi, 2000). Terzaghi (1941), Taylor (1942), Taylor (1948), Hvorslev (1960), Bjerrum (1973) and Leroueil et al. (1985), once more illustrating de Mello's thought: "We professionals beg less rapid novelties, more renewed reviewing of what is already there." (Jamiolkowski, 2012, p. 117).

Strain rate effects on the undrained strength of claysa brief discussion
The expression strain rate effects as used in this article means the effects of speed of shear as defined by Taylor (1948, p. 377). In his own words: "…all plastic materials exhibit a resistance to shearing strain that varies with the speed at which the shearing strain occurs. The plastic structural resistance to distortion in clays, called herein the plastic resistance, is an example.".
From now on the acronym CIUCL (consolidated isotropically undrained compression loading) will be used to denote CIU triaxial tests carried out keeping the radial stress r σ constant and increasing the axial stress a σ . This is to say that during the undrained shear stage of a CIUCL test, The shear strain rate can be defined by Equation 2 ( ) where γ is the distortion ( ) where ' af σ and ' rf σ are respectively the axial and radial effective stresses at failure (condition indicated by the use of the subscript f ).
The strain rate effect on the undrained strength of clays may be illustrated by the results of a CIUCL test carried out in a normally consolidated specimen of Sarapuí II Clay [for a detailed description of this clay, see Danziger et al. (2019)]. Such a test has been carried out using an intact sample and lubricated ends technique so that the specimen could be led to a high axial strain, maintaining the cylindrical format.  Figure 4. Figure 5 shows the ( ) / 2 ' ' a r a σ σ ε − × plot for the CIUCL test carried out on the specimen shown in Figure 4. Initially, the specimen was sheared with the strain rate 0.02 % / min.
, when failure occurred with 68.5 kPa u S ≅ . Then, the strain rate was increased to 0.2 % / min. causing u S to increase to 76.0 kPa. The strain rate was then reduced to 0.002 % / min. obtaining 62.0 kPa u S ≅ . Finally, the strain rate was reduced to 0.0002 % / min., showing 56.5 kPa u S ≅ . The deviator stress drops observed in Figure 5 are due to the stress relaxation stages carried out before the strain rate was changed.    , a 0.10 µ ≅ is obtained. The fitted curve is also shown in Figure 6. Figures similar to Figure 6 were firstly presented by Taylor (1948, p. 378) and afterwards by several authors [as for instance Berre & Bjerrum (1973) and Sheahan et al. (1996)   not be considered a clay property. This idea was qualitatively presented by Leroueil et al. cited by Jamiolkowski et al. (1991) and is reproduced in Figure 7.
As concerns the existence of multiple state boundary surfaces, Figure 7 would also indicate the dependence of the virgin oedometric compression line on the axial strain rate ( ) a ε . This would be in full accordance with the results of Leroueil et al. (1985), showing that in onedimensional compression there is a unique relationship between effective vertical stress ( ) K . This question, raised by Schmertmann (1983) and discussed by several The 8th Victor de Mello lecture: role played by viscosity on the undrained behaviour of normally consolidated clays authors (Lacerda, 1977;Kavazanjian Junior & Mitchell, 1984;Holtz & Jamiolkowski, 1985;Lacerda & Martins, 1985;Leonards, 1985;Kavazanjian Junior & Mitchell, 1985;Mesri & Castro, 1987, has also remained without a final verdict up to now. Nevertheless, this is a discussion that is beyond the scope of this paper. According to Bjerrum (1973), who refers to the strain rate effect on the shear strength of clays as "effect of time" (the shorter the time to failure, the greater the strain rate), the referred effect aroused interest from Terzaghi, who discussed it in deep detail in a paper from 1931. According to Bjerrum (1973), the mentioned paper would led Hvorslev to include in his test program the "effect of time" on shear strength of Little Belt plastic remoulded clay.
Henceforth, instead of using the expression "effect of time", it will be used the expression "strain rate effects" since it is an expression which better translates the mechanics of the phenomenon. According to Bjerrum (1973), who was one of the authors that have most deeply studied strain rate effects on the shear strength of clays, there are many evidences which show that strain rate effects are associated with the cohesive component of shear strength, as defined by Hvorslev (1960). Notwithstanding, as discussed by Schofield (1999Schofield ( , 2001 and assumed in critical state soil mechanics, soils do not possess cohesion in the sense used by Coulomb, or rather, they do not resist to effective tensile stresses. How can this impasse be solved? After all, what is cohesion? Do soils have or do not have cohesion? That is what will be discussed in the next section. This seems to be the case of the word cohesion, which in soil mechanics has assumed different meanings, thereby bringing about a lot of confusion [see, for instance, Schofield (1999)]. In order to discuss this subject, it will be necessary to make a brief review of the Mohr failure criterion.

What is cohesion?
Mohr's failure criterion, for a given material, can be stated as follows: there is a shear stress expressed as a function f of the normal stress σ with the following property: if a couple ( ) , σ τ which satisfies the function ( ) f τ σ = is acting on a plane passing through a point P of the material, then there will be failure at that point P along the referred plane.
One of the functions used to express the failure criterion in rocks and natural materials is the so-called Mohr-Coulomb envelope, gathering Mohr criterion and Coulomb law. The Mohr-Coulomb envelope can be written as: where ff τ and ' ff σ are respectively the shear stress and the normal effective stress on the failure plane at failure, φ′ is the angle of internal friction and c′ is the cohesion. Plotting Equation 7, taking into account just the positive values of ff τ , Figure 8 is obtained.
Solid materials such as concrete and rocks have a strength which cannot be assigned to any applied stress state which can be perceived by human eyes. This kind of strength can be described as a consequence of an "imaginary pressure", called "intrinsic pressure" (Taylor, 1948), denoted by ' i σ , which remains from the formation of those materials and which awards a certain tensile strength to those materials. This "intrinsic pressure" corresponds to the segment ′ P O O in Figure 8. This occurs, for example, in the case of an igneous rock that, after being formed by magma cooling, presents  Leroueil et al. cited by Jamiolkowski et al. (1991)].
subjected to tensile effective stresses. This type of strength can be quantified by segment , as shown in Figure 8. Such strength is denoted by c′ and defined as true cohesion or Coulomb cohesion.
An alternative way of writing the envelope in Figure 8 would be to introduce the "intrinsic pressure", denoted by ' i σ , shifting the origin of the graph in Figure 8 According to Figure 8, being O p the pole of Mohr circles at failure under unconfined compression and simple tension tests, the angles of failure planes in compression and in simple tension would be 45 / 2 φ°+ ′ and 45 / 2 φ°− ′ respectively (see Figure 8). Nevertheless, in a homogeneous and isotropic material subjected to a simple tension test, failure planes occur orthogonally to the tensile stress direction, as shown in Figure 9. It is the failure by separation. So, there are two failure modes: by shear and by separation [Carneiro, F.L.L.B.(2021). Private communication].
As in the separation failure mode the failure plane is orthogonal to the tensile stress direction, the strength envelope must necessarily be a vertical tangent to the Mohr circle at failure under simple tension at its leftmost point, or rather, at the point of abscissae ' t σ , on the left side of the effective stresses axis, as shown in Figure 10a. This kind of strength envelope is illustrated in Figure 10b for a residual soil. In this case, the true cohesion given by c' in Figure 10b can be assigned to grain cementation remaining from the mother rock, which have not yet been destroyed by the weathering process in its inexorable march of transforming rocks into soils. A way of evaluating c' of a residual soil was used by Rodriguez (2005) carrying out a drained Brazilian Test on a submerged specimen, as shown in Figure 10c.
One can say that weathering, a process by means of which rocks are transformed into residual soils, occurs due to loss of true cohesion (grain cementation) existing in the mother rock. Concerning the inverse process, called diagenesis, in which sedimentary soils suffer a litification process and have their grains cemented, there is a gain in true cohesion. This process is illustrated in Figure 11. The assumption that during weathering/litification the strength envelope suffers a displacement keeping the friction angle φ′ constant and reducing/increasing the true cohesion is admittedly an oversimplification to better explain the phenomenon.

Hvorslev's "true cohesion", cohesive soils, plasticity and viscosity
Figure 12 gathers figures from Terzaghi (1938) and Gibson (1953), summing up the results obtained by Hvorslev (1960) as regards a set of drained direct shear tests carried out on saturated remoulded clay specimens.  this type of strength. Similar thing happens in the formation of a sedimentary rock, when a cementation agent by means of a process called diagenesis gradually links grains of a sedimentary soil. A similar phenomenon happens as regards concrete, when cement connects the aggregates. Cementation makes such materials present a tensile strength ( ) ' t when The 8th Victor de Mello lecture: role played by viscosity on the undrained behaviour of normally consolidated clays In Figure 12, A 0 B 0 C 0 D 0 represents the virgin one-dimensional (oedometric) compression line followed by a rebound D 0 E 0 F 0 G 0 H 0 I 0 . When the normally consolidated specimens represented by A 0 , B 0 , C 0 and D 0 are subjected to a drained direct shear test, they decrease in volume during shear and fail respectively with the void ratios of points A, B, C and D. At the lower part of Figure 12, it is shown the strength envelope OABCD, corresponding to the normally consolidated condition: a straight line with slope ' tanφ passing through the origin. This means that, under the normally consolidated condition, the clay does not have true cohesion in the physical sense given by Coulomb, or rather, it does not have shear strength under effective stress minor than or equal to zero or tensile strength conferred by cementation, as discussed in section 4.1.
When testing the specimens represented by D 0 , E 0 , F 0 , G 0 and H 0 , the last four ones being overconsolidated, the void ratios at failure are given by D, E, F, G and H. In the lower part of Figure 12 it is shown the corresponding overconsolidated strength envelope DEFGH. The strength envelope DEFGH depends upon two variables: the normal effective stress on the failure plane at failure ' ff σ (which is equal to ' v σ in a drained direct shear test) and the void ratio at failure. However, Hvorslev (1937) observed that a straight line strength envelope of equation ' ff e ff e c e tan τ σ φ = + could be drawn provided the specimens had the same void ratio at failure. Hvorslev (1937) also noted that the linear coefficient e c of these Figure 11. Weathering/litification as a loss/gain in true cohesion of rocks/soils. straight lines was a function of the void ratio at failure and that the slope ' e tan was a constant. One of these straight lines, as shown at the lower part of Figure 12, is the line XHB, whose ff τ axis intercept is ( ) 1 e c e , associated with the void ratio 1 e at failure. All points of straight line XHB have the same void ratio at failure equal to 1 e . Another straight line, which represents failure of specimens with void ratios at failure equal to 2 e , is the straight line YFC, whose ff τ axis intercept is [adapted from Rodriguez (2005)]; (c) Sketch of a Brazilian test carried out on a submerged specimen of residual soil.

Martins
In Equation 9, ff τ is the shear stress on the failure plane at failure, is denominated "effective cohesion" or "true cohesion", a function of the void ratio and soil structure at failure, ' ff σ is the effective normal stress on the failure plane at failure, and ' e φ is called "effective angle of internal friction" or "true angle of internal friction".
If the clay is saturated, e G w = ⋅ , being e the void ratio, G the specific gravity and w the water content.
As constant G = for a given soil, there is a one-to-one correspondence between void ratio and water content. Thus, the parameter e c can be expressed as a function of either the void ratio or the water content, provided that both correspond to the failure condition.
In order that Equation 9 can be dimensionally homogeneous, ( ) e c e must have the physical dimension of a stress. To write ( ) c e expressing it as a stress [see Terzaghi (1938)], the equivalent stress ' e σ has been used. As for direct shear tests, ' e σ is defined as the effective vertical stress, taken on the one-dimensional (oedometric) virgin compression line (see Figure 13), corresponding to the void ratio at failure.
Tests carried out by Hvorslev (1937) where K is a non-dimensional constant. Then, the shear strength of a saturated clay would be given by According to Terzaghi (1938), if the results of direct shear tests are plotted in a ( ) ( ) σ σ τ σ × graph, the straight line shown in Figure 14 will be obtained.
As previously told, Terzaghi (1938) and Hvorslev (1937Hvorslev ( , 1960 K c e σ = as "cohesion", "true    Schofield (1999Schofield ( , 2001], as discussed in section 4.1, none of the three terms (cohesion, true cohesion and effective cohesion) would be adequate in this case. Then, what would be the physical meaning of the term ( ) e c e in Equation 9? This is the major discussion posed in this section.
Going ahead on the discussion, all the points on the straight line segment HB in Figure 12 have the same void ratio 1 e at failure. Therefore, in a with e e < . Thus, points F and C define another strength envelope, with the same slope ' e tanφ , but with a Hvorslev "true cohesion" of magnitude OY. Now, it is worth comparing a strength envelope of the type obtained by Hvorslev (1937) for an overconsolidated clay with the envelope obtained from normally consolidated specimens of the same clay. This is presented in Figure 15.
The straight line OAJBCD, at the lower part of Figure 15, is the strength envelope corresponding to the normally consolidated condition, where the shear stress at failure On the other hand, the same strength envelope can be written as However, in this case, ( ) e c e varies along the envelope OAJBCD because the void ratio also varies. The difference between the ordinates of the straight lines OAJBCD and OLN is a linear function of ' ff σ (or ' v σ ), that is: where C is a constant. This means that the shear strength ff τ of a normally consolidated clay can be written as: ( Equation 15 reveals that the friction angle φ′ of a normally consolidated clay is "contamined" by a portion C. In other words, within the shear strength of a normally consolidated clay, which does not have cohesion in the physical sense used by Coulomb, there is a portion C which is not due to friction. Shearing of a normally consolidated clay produces decrease in volume. Being so, C cannot be assigned to the work done to dilate the specimen since, being normally consolidated, the specimen presents a contractile behaviour. Then, once more, a question is asked: which physical phenomenon does the portion ( ) ' e ff c e Cσ = come from, since it cannot be attributed neither to cohesion (cementation), as conceived by Coulomb, nor to additional dilating work? After all, what does exist behind the "effective cohesion" as inappropriately defined by Hvorslev and Terzaghi? This is the discussion that follows.
What the author believes that exists behind Hvorslev's (1937) "effective cohesion" is the "softness" sensation when one rubs between the fingers an amount of clay with a water content between the liquid limit and the plastic limit. It is also the sensation of something "sticky" which is found in clays, because of its plasticity. Possibly, owing to such sensation, clays have begun to be improperly called "cohesive soils".
According to the author's understanding, the expression "cohesive soil" leads to plastic soils. As regards soil mechanics, plastic soils are those soils that present liquid and plastic limits. After all, where does the "sticky" sensation come from when a moist clayey soil is rubbed between the fingers? A mechanistic picture given by Terzaghi (1941) throws some light on this question.
According to Terzaghi (1941), clay particles are surrounded by an adsorbed water layer. On the clay particles surface, adsorbed water is in the solid state and is strongly adhered to it. As the distance from the particle surface increases, the adsorbed water viscosity decreases. For distances greater than a limiting value, viscous water becomes free water. This means that in a clay the interactions among grains are influenced by the adsorbed water layer that involves them. Since the viscosity of the adsorbed water decreases as the distance from the particle surface increases, it is expected that in a saturated clay the greater the water content (or the void ratio) the smaller the relative displacement resistance between neighbouring particles. In this case, "true cohesion" or "effective cohesion" to which Hvorslev (1937Hvorslev ( , 1960 and Terzaghi (1938) refer should be called viscous resistance, as explicitly written in a passage by Terzaghi & Frölich (1936). To avoid loss of fidelity, this passage is transcribed below: "Les résultats des expériences entreprises pour trouver la relation entre l'indice des vides et le coefficient de perméabilité des argiles, imposaient déjà il y a quelques années, l'hipothése que chaque particule d'argile est séparée de l'eau interstitielle par une couche séparatrice dont la constitution diffère de celle de l'eau ordinaire. L' épaisseur de cette couche est une fraction d'un micron (1/1000 mm). A l'intérieur de cette couche séparatrice, la viscosité de l'eau tombe d'une valeur élevée (surface de la particule solide) à sa valeur normale (surface extérieure de la couche séparatrice). Les avis relatifs aux forces attractives qui provoquent la couche séparatrice sont trés partagés. La Figure 7 représente trois coupes à travers deux particules voisines. A l'intérieur de la zone hachurée, la viscosité augmente beaucoup à mesure que l'on s'approche de la surface solide. Par . 7c), les particules sont de nouveau séparées par une couche de fluide visqueux. La mobilité des particules augmente avec l' épaissseur de cette couche; le coefficient de compressibilité, par contre diminue." (Terzaghi & Frölich, 1936, pp. 18-19).
An adaptation of Figures 7a, 7b and 7c as mentioned by Terzaghi & Frölich (1936) in the above quotation is reproduced in this article as Figure 16a, 16b and 16c, as follows: From the passage transcribed above, it seems clear that the "cohesion" to which Terzaghi (1938) refers and the "effective cohesion"and "true cohesion" referred by Hvorslev (1937Hvorslev ( , 1960 and Gibson (1953) are all of them from viscous nature. This seems to be Bjerrum's (1973) understanding as well. As a matter of fact, it is the viscous nature of "cohesion" which is behind the Bjerrum's (1973) correction factor to be applied to the undrained shear strength ( ) u S measured in the vane test ( measured in a vane test is higher because it is obtained with higher shear speed). It is believable that, viewing "cohesion" as being of a viscous nature, Bjerrum (1973) proposed the correction factor as a function of the plasticity index. After all, the more plastic the clay the greater its "cohesion" (or viscous resistance). Therefore, the higher the plasticity index the higher the influence of viscous resistance on the measured undrained shear strength. What is not appropriate is the use of the expression "time effect" to describe the phenomenon. Although Bjerrum (1973) had used the expression "time effect", it is clear that, according to his own understanding, the effect in question can be more properly called "strain rate effect".
In a re-appraisal of his 1937 work, Hvorslev (1960) highlights three components of shear strength ff τ of a In a normally consolidated clay, which has a contractile behaviour, 0 d τ = . The component is a function of the effective stress and is expressed by Yet, according to Hvorslev (1960), "cohesive soils" (which, due to the confusion created by the term "cohesive", the author prefers to call plastic soils) are those which have a strength component e c . Instead of commenting, it is better to quote how Hvorslev (1960) (3) there is no significant difference in the geometric structure of the clays during a given test series." (Hvorslev, 1960, p. 183).
It is worth observing the reference that Hvorslev (1960) made to the strain rate influence. Nevertheless, the approach given to the subject does not explicitly translate the strain rate influence by means of a mathematical expression that quantifies the physical phenomenon. This issue has only become to be coherently approached by Leroueil et al. (1985), showing that, as concerns one-dimensional consolidation, there is a unique relationship among the axial (vertical) strain ( ) a ε , the effective vertical stress ( ) ' v σ and the axial (vertical) strain rate ( ) a ε . However, as far as the author's knowledge is concerned, Taylor (1948) was the first researcher not only to physically explain the "effective cohesion" as being of a viscous origin but also to physically quantify it by means of a mathematical expression.
According to Taylor (1948, pp. 377-378), all viscous materials and all plastic materials exhibit a resistance to shearing strain that varies with the speed at which the shearing strain occurs (see section 3.3). Taylor (1948) called such a kind of resistance in clays as "plastic resistance". Figure 17 shows the dependence of the deviator stress at failure ( ) ( ) on the axial strain rate of CIUCL tests. The test results shown in Figure 17 were carried out on remoulded specimens of Boston Blue Clay with the same water content, but subjected to different axial strain rates ( ) a ε (corresponding to different speeds of shear or different shear strain rates).
Also, according to Taylor (1942), experimental results indicated that "plastic resistance" under any speed of shear in a given clay with different void ratios is proportional to the effective stress. Assuming that "plastic resistance" depends on effective stress and shear strain rate, Taylor (1948) wrote the following equation for the shear strength ff τ of a clay: where ff τ and ' ff σ are, respectively, the shear stress and the effective normal stress on the failure plane at failure, ' i σ is the "intrinsic pressure", as defined in section 4.1, φ′ is the angle of internal friction (to be discussed further again) and ( ) / s t ε ∂ ∂ is the shear strain rate on the failure plane. The following passage quoted from Taylor (1948) summarizes the conception of the above-mentioned mechanism. In order to avoid loss of fidelity, it is suitable to quote the referred passage: "The effect of speed of shear on the strength is believed to be caused by the viscous or plastic characteristics of material in the adsorption zones in the vicinity of points of contact or near contact of clay particles. Thus this effect is a colloidal phenomenon, and it is of sufficient importance to justify a detailed discussion. The following hypothetical explanation of plastic resistance and of time relationships was first presented (Taylor, 1942) for one-dimensional compressions, but it may be extended Figure 17. Effect of speed of shear on the compressive strength of clay (Taylor, 1948).
to the action of clays in shear. If a drained clay sample is maintained under any given system of constant applied direct and shearing stresses that do not cause failure, it gradually approaches an ultimate shape and an ultimate void ratio at which there is static equilibrium. Ages may be required to reach this state of equilibrium, but when it is reached the applied stresses are equal to static internal resistances and they have values that are free of plastic resistance and all other time effects. During the approach to equilibrium, however, the applied stresses are made up in part of the stresses required to overcome the plastic resistance. The plastic resistance is usually considered to depend mainly on the speed of strain although possibly it depends also on such factors as changes in type or degree of adsorption. As the clay specimen approaches the static case, the strains continuously decrease in speed and the plastic resistance decreases in magnitude; however, the speed becomes almost imperceptibly small when the plastic resistance is still quite large and the strains and the void ratio still have a considerable change to undergo before they reach the static case. Secondary compression, as it occurs in consolidation tests, is a good illustration of this condition. From these concepts it appears that a clay that has reached static equilibrium in nature after the lapse of many centuries and is suddenly subjected to stress increases of relatively small magnitude may be expect immediately to exert a plastic resistance that is equal to the stress increase, and it is possible that the speed of distortion required for the exerting of this amount of plastic resistance may be too small to be noticeable. In such a case the plastic resistance cannot be distinguished from a bond, and the occurrence of bonds of this type is possible both when the shearing stresses are small and when they are relatively large." (Taylor, 1948, pp. 379-380).
From now on the expression "plastic resistance" used by Taylor (1948) will be called viscous resistance.

The viscosity concept
As the approach of strain rate effects on plastic soils strength is concerned, it is usual to make use of the term viscosity without defining, however, what is understood by soil viscosity. In soil mechanics, the term is generically used without a clear definition (Schnaid et al., 2021). The viscosity concept was introduced by Newton via Newton's law of viscosity: The tangential stress between neighbouring layers of a fluid in a laminar flow is proportional to the ratio / dv dy with which speed v varies in the transverse direction of flow y (see Figure 18). Newton's law of viscosity is written as: which can be written alternatively as: The coefficient µ is called coefficient of viscosity or simply viscosity and / d dt γ γ =  is called distortion rate. Every fluid which obeys Equations 19 or 20 is said to be considered a newtonian fluid.

Shearing of clayey soils -a working hypothesis
The approach presented next is only based on mechanical interactions, which greatly simplify the interaction among clay particles. However, as argued by Bjerrum (1973), in spite of admittedly being an oversimplification, this approach gathers the essential characteristics of the behaviour of plastic soils as far as strain rate effects are concerned.
According to Terzaghi (1941), clay particles are involved by a viscous adsorbed water layer. In the particles surface vicinity, adsorbed water is in a solid state and strongly adhered to grains surface. As the distance from particles surface increases, the adsorbed water viscosity decreases until water becomes free water beyond a certain distance "d " (Figure 19). Distance d depends on the physico-chemical properties of the minerals of the clay particles and on other substances in the adsorption region.
Also, according to Terzaghi (1941), contacts between grains can occur through solid water (solid to solid contacts) or through viscous water (viscous contacts) and both types of contact transmit effective stresses.  Starting from the conception of Terzaghi & Frölich (1936) to explain clay shear strength and assuming some additional hypotheses, Martins (1992) obtained the results whose essence is presented as follows.
Considering an imaginary plane P -P passing through a plastic soil mass, it will pass by solid to solid and viscous contacts ( Figure 20). Consider now a region of area A ( 1 A A u c = × ⋅ , where 1 u c ⋅ is a unitary length in the normal direction to the plane of Figure 20). Also consider that the normal force N and the tangential force T are acting on the area A.
Assuming that only solid contacts can transmit effective normal stresses, the balance of forces in the normal direction of the plane P -P leads to the PES equation, u σ σ = − . A more general hypothesis according to which viscous contacts can also transmit effective stresses is being developed but this approach will not be discussed herein.
The tangential force T acting on area A divided by is by definition the shear stress on the area A along plane P -P. Force T can be expressed by the sum of tangential forces, which causes the relative displacement between the particles from the upper side and the lower side of the plane P -P (see Figure 20). According to the mechanism posed by Terzaghi & Frölich (1936), force T consists in summing up the friction resistance component s T , which exists in solid contacts, and the viscous resistance component v T , due to the distortion of the adsorbed water.
Suppose there are m solid to solid contacts within the area A in Figure 20. The friction force si T acts at the solid to solid contact of order i as a local reaction to the applied force T. Therefore, the friction resistance component s T mobilized as a partial reaction to force T can be written as: where ' i φ is the friction angle of the solid to solid contact of order i and i ξ is the degree or percentage of the friction strength mobilized at the solid to solid contact of order i.
Finally, denoting by ξ the average value of all * i ξ values taken over area A, one obtains:

Martins
Suppose now that the total number of contacts within area A is n. In all contacts, irrespective of their type, there will be viscous resistance. For instance, at the contact between the intermediate couple of grains in Figure 20, viscous resistance comes from the shear strain rate of the adsorbed water element ijkl. Such viscous resistance is also present in the solid to solid contacts. This is illustrated in Figure 20 by the shearing strain of the ring shaped element whose transversal section is abcd -efgh.
The viscous resistance existing in a viscous contact caused by the shear strain rate of an element of section ijkl or in a solid to solid contact by the shear strain rate of a ring shaped element whose section is abcd -efgh varies along the contact. This occurs because the viscosity coefficient µ of the adsorbed water at points within the contact zones along the plane P -P depends on the distances from these points to the particles surface (see Figure 21).
There is also an extremely important issue concerning the behaviour of viscous fluids, as highlighted by Rouse & Howe (1953). As presented in Figure 18, the concept of individual layers or fluid laminae flowing side by side is merely a question of convenience in order to model the phenomenon mathematically. Such a model can lead to the false idea that in a laminar flow fluid laminae can literally slide one over the others producing a kind of mechanical drag measured in terms of the viscous resistance τ , as expressed by Equation 19. In fact, in a submicroscopic scale, viscous resistance results from the interaction of fluid molecules whenever any portion of fluid, no matter how small it is, is subjected to shear strains. A fundamental feature of a viscous fluid is the fact that a slip along a surface between two neighbouring layers of the fluid (inside a fluid mass) or between a viscous fluid and a solid contour cannot occur because this would result in an infinite value for the ratio / dv dy in Equations 19 and 20. Thus, regardless the fluid nature, molecular interactions compel to the condition of identical velocities along both sides of any fluid surface, real or imaginary. For this reason, the velocity of a moving fluid at the surface of contact with a solid contour will be exactly the same as the velocity of the contour itself. If the contour is at rest, the fluid in contact with this contour will also be at rest, irrespective of how great its velocity may be a short distance away. This means that, during shear, relative displacements between soil grains occur without slippage along the surface of contact between viscous adsorbed water and solid grains contours. This also means that during relative displacements, for instance, along the plane P -P in Figure 20, soil grains are subjected to drag forces due to shear strain of their viscous adsorbed water layers. The resultant of these viscous forces, denoted by v T , is the viscous component proposed by Terzaghi & Frölich (1936), which, added to the friction resistance component s T , gives the internal reaction to the applied tangential force T .
As the viscous resistance is present in all n contacts within the area A, irrespective of the type of contacts, v T can be written as: being vj T the local viscous resistance acting at the contact of order j. In its turn, vj T can be written as: Considering the viscosity of the free water as being negligible if compared to the viscosity of the adsorbed water, the integral in Equation 25 should be taken all over the viscous contact area taking into account that the distortion P P γ − of a clay along the plane P -P in Figure 20 is the result of the gathered relative displacements of particles from both sides of plane P -P, Equation 27 can be rewritten as: The left hand side of Equation 29 ( ) being s T the mobilized friction resistance, which is a part of the internal reaction to the applied horizontal force T (see Figure 20). As / T A is the shear stress τ acting over the area A, the ratio / s T A, denoted by φ τ , is the part of the shear resistance due to friction mobilized on the area A along the plane P -P.
In the second part of the right hand side of Equation 29, µ is a function of the distance between neighbouring particles and, therefore, of the void ratio ( ) e . However, µ is also a function of the relative position according to which clay particles are arranged along the plane P -P, that is to say, a function of the structure. Nevertheless, the ratio is an exclusive function of the void ratio. Thus, the product can be rewritten as a function ( ) e η , being ( ) e η a function of the void ratio and the structure. Thereby, the second part of the right hand side of Equation 29, denoted by η τ , can be rewritten as: being ( ) e η here defined as the viscosity of a plastic soil. Thus, the expression for the shear stress α τ of a plastic soil, at any instant, acting on plane P -P whose normal makes an angle α with the principal direction 1 σ , being the soil at failure or not, can be written as: If the simplifying assumptions from which Equation 32 has been derived are accepted as valid, such equation will reveal that, at any moment, the shear stress α τ on a plane whose normal makes an angle α with the direction of 1 σ will be internally resisted by the sum of a friction Equation 32 leads to the following immediate consequences: 1. It translates mathematically the mechanism conceived by Terzaghi & Frölich (1936) and by Taylor (1948) 2. Part of the shear resistance existing in plastic soils is of a viscous origin. It is worth observing that the viscous component becomes zero when strain rate is zero, which does not correspond to the Coulomb's cohesion concept (Schofield, 1999), but corresponds to the viscous resistance concept introduced by Newton.
3. The viscous component ( ) ηα τ would correspond to the "true cohesion" of Hvorslev (1960), an inappropriate name (in the author's opinion), since according to Hvorslev (1960)  α σ is zero, friction strength will be zero and the resistance to shearing strain will only reside in viscosity, which is a feature of fluids. 6. Finally, Equation 32 explicitly shows the influence of strain rate on the shear strength [see for instance Taylor (1948), Bjerrum (1973), Berre & Bjerrum (1973), Lacerda & Houston (1973), Graham et al. (1983), Sheahan et al. (1996), Tatsuoka et al. (2002), and Aguiar (2014)] and on consolidation (Taylor, 1942;Graham et al., 1983;Leroueil et al., 1985;Andrade, 2014). As previously discussed, being the "effective cohesion" or "true cohesion", as defined by Terzaghi (1938) and Hvorslev (1937Hvorslev ( , 1960, of a viscous nature, it is expected that the greater the plasticity of a soil (given by its plasticity index I P ) the greater its viscosity ( ) e η . In the author's opinion, this might have been the main reason for Bjerrum (1973) having expressed the influence of strain rate on shear strength of plastic soils as a function of the plasticity index (I P ).
Last but not least, to avoid the confusion created by the inappropriate use of the term "cohesion", instead of using the words "cohesive" and "non-cohesive", it is suggested the use of the words "plastic" and "non-plastic" soils. By a plastic soil is to be meant a soil on which one can carry out plastic and liquid limit tests.

Mohr's circle of strain in a CIUCL test
The state of stress found in a CIUCL test is shown in Figure 22a. In this case, 1 a σ σ = and, due to the axisymmetry, In such a case, there will be no shearing strains on horizontal planes.
In a similar way to which has been done for stresses, it can be written: It is the Mohr's circle of strain, shown in Figure 23.
In soil mechanics it is usual to take a normal linear strain as positive when the element suffers a reduction in length (shortening). On the contrary, an elongation is considered negative. In the case of the specimen shown in Figure 22, the axial strain Being f V and 0 V , respectively, the final and the initial specimen volumes, the volumetric strain, denoted by V ε , is by definition: In soil mechanics it is usual to consider a compression (decrease of volume) as being positive. Thus, in the case of a triaxial test specimen (see Figure 22), V ε , defined by Equation 35, is accurately given by: ε ε = − and the specimen is distorted on planes which are not horizontal (see Figure 22b). Figure 22b shows the section 1234 made by a vertical plane that contains the axis of the specimen of Figure 22a. Consider now the square region ABCD on the section 1234 before deformation. Taking 45 α =° in Figure 22b, the square ABCD of side l , shown in Figure 24, is deformed into the rectangle A'B'C'D'. In a similar way, the square EFGH of side 2 / 2 l is deformed into the rhombus E'F'G'H'. According to Figure 24 The value of Equation 39 can also be obtained using 45 α =° in Equation 34, that is: Finally, the distortion, denoted by α γ , is the angular change between two fibres of the vertical plane of Figure 22b, which were originally at right angles one to another and whose normal directions make the angles α and ( ) 2 π α − with the direction of 1 ε (see Figure 22b).
Thus, the distortion α γ can be determined via Equation 34 as ( ) The maximum distortion 45 γ°, or simply the distortion γ , is the angular change between two fibres of the vertical plane of Figure 22b, which were originally at right angles one to another and whose normal directions make the angles 45 +° and 45 −° with the direction of 1 ε (see Figure 25). This distortion γ , during the undrained shear stage of a CIUCL test, can be obtained using 45 α =° in Equation 41 to obtain:

The Mohr's circle, the viscosity ellipse and the friction ellipse
Considering Equation 31 and assuming ( ) e η does not vary with direction (soil is assumed to be isotropic) and also recalling that distortion α γ is twice the shear strain sα ε , the viscous component of the shear stress ηα τ along a plane whose normal makes an angle α with the 1 σ or 1 ε direction can be written as: Recalling that At a given instant of a triaxial compression test, whether it is drained or undrained, provided that accelerations are negligible (so that equilibrium equations can be written), the state of mobilized viscosity is given by: Equations 45 and 46 are the parametric equations of an ellipse whose centre has coordinates ( )  and whose major and minor axes are respectively ( ) . This ellipse, as shown in Figure 26, will be called viscosity ellipse or Taylor's ellipse, in honour of Donald Wood Taylor, since, in fact, all these concepts are expressed in several of his writings, though not in detail.  From now on, the maximum ordinate of the viscosity ellipse will be denoted by  and expressed by: From the above exposed, the friction component of the shear stress φα τ , acting on the same plane on which the viscous portion ηα τ acts, is given by: Based on Equations 45 and 48, the state of mobilized friction is defined. One can observe that Equations 45 and 48 are the equations of another ellipse whose centre has  and whose major and minor axes are, respectively, ( ) This ellipse, as shown in Figure 27, will be called friction ellipse or Coulomb's ellipse.
It is noteworthy that the Mohr's circle of effective stresses is the result of summing up the viscosity and the friction ellipses. However, the ellipses cannot exist separately since equilibrium conditions are only fulfilled by the Mohr's circle of stress. Thus, the shear stress α τ , which acts on a plane whose normal makes an angle α with the 1 σ direction, consists of two parts: a friction part φα τ and a viscous part ηα τ .

A failure criterion for soils taking into account the strain rate effect
The ideas herein exposed can be generalized for any stress and strain states. Nevertheless, as this text deals with fundamentals, only CIUCL triaxial tests on normally consolidated specimens will be discussed. In this type of test, 1 ' Figure 22a).
When carrying out a CIUCL triaxial test in a saturated soil, since the water compressibility is negligible, the volumetric strain v ε is assumed to be zero during the shearing stage.
, and the viscous component of the shear stress ηα τ corresponds to: fixed plane, up to the end of shear. Notwithstanding, although the viscous resistance will be fully mobilized immediately and remaining constant along the whole shear, the deviator stress will increase as the specimen strains up to failure. This means that during shear the frictional resistance will be mobilized as the test takes place, contrarily to the viscous resistance mobilization, which occurs instantaneously. The immediate consequences of such mechanism are listed as follows: 1. To mobilize the frictional resistance, it is necessary to strain the specimen and, as it begins to be strained, the deviator stress will begin to increase up to the specimen reaches failure. As during the shear stage of a CIUCL test there are no volume changes, only shear strains occur. Thus, the mobilization of the frictional component is intimately related to shear strains and, therefore, failure will occur when the frictional component is fully mobilized. The conclusion is that shear strains and failure are governed by the mobilization of the frictional component. In the very beginning of shear, there is immediate viscous resistance mobilization, whatever the plane may be. On a fixed plane, viscous resistance will be acting with a value that will be kept constant up to failure (provided that a ε and soil structure remain the same). As shear strains take place, deviator stress will increase due to the mobilization of the frictional resistance component. When the frictional resistance component is entirely mobilized, failure occurs. 2. As regards specimens with the same void ratio and the same structure, the viscous resistance component at failure, i.e., the viscous part of the undrained shear strength, only depends on the strain rate. Thus, the shear strain rate only affects the shear strength value but does not affect strains. This is illustrated by the test results shown in Figure 5 (see also Figure 6). As the field vane test is usually carried out with a higher speed of shear than those observed in real failures in the field, the results of Figures 5 and 6 also explain the need for Bjerrum (1973) having proposed the correction factor to be applied to undrained shear strength results obtained via field vane tests. 3. If failure is commanded by the mobilization of the frictional component of the shear strength and if the frictional part of the shear stress is given by the friction ellipse ordinates, then, if the failure criterion established by Hvorslev (1937) holds valid, failure must occur whenever the friction ellipse touches the strength envelope. Remembering that the approach in this article is limited to the normally consolidated specimens, the strength envelope to be considered is that one which passes through the origin and has slope tan ' e φ (see Figure 28).
Denoting by ff τ the shear stress on the failure plane at failure, where ff φ τ and ff η τ are, respectively, the friction and viscosity parts of the shear stress on the failure plane at failure. As friction is what commands failure, failure occurs according to Mohr-Coulomb-Hvorslev's envelope, which is the straight line that passes through the origin and has slope ' e tanφ (see Figure 28). Thus, failure occurs in the maximum obliquity plane, taking into account only the frictional part of the shear stress, given by: Being 2 cos 2 cos 2 cos 2 2 sin 2 0 cos 2 Solving Equation 54, one obtains: Replacing the result of Equation 55 into Equation 51, one finally obtains: The 8th Victor de Mello lecture: role played by viscosity on the undrained behaviour of normally consolidated clays 6. CIUCL tests under the light of the concepts presented in the previous section

Introduction and summary of the main points of previous section
Although the concepts presented in section 5 can be extended to more general cases, the approach herein presented is restricted to normally consolidated saturated plastic soils subjected to CIUCL tests. Such approach describes and considers the effect of strain rate on clays behaviour based on a mechanical view, via viscosity. Considering the strain rate effect via viscosity greatly simplifies the phenomenon of interaction between clay particles. Nevertheless, this kind of approach captures the essence of the strain rate effects on plastic soils behaviour, making its understanding easier.
The assumptions used in this approach are the following: 1. Soil is seen as a set of grains, each one involved by a highly viscous adsorbed water. The closer the adsorbed water is to the grain surface, the higher its viscosity. 2. Contacts between grains are of two types: solid to solid and viscous (Figures 20 and 21). 3. In a plane passing through a "point" of a soil mass in equilibrium whose normal makes an angle α    Such "initial jump" or "viscosity jump" corresponds to the instantaneous mobilization of the viscous resistance given by . Since the viscous part of the shear resistance is a function of the shear strain rate (and not of the shear strain), when the load frame motor is turned on, the viscous resistance will start to act immediately, when both shear strain ( ) t and excess pore-pressure ( ) u ∆ are still zero. Thereafter, if the shear stage continues running with the same strain rate / 2 t ε γ =   , this viscous resistance will remain constant for the rest of the test.
The "viscosity jump" appears in both s t ′× ′ effective stress path (from now on called ESP) and s t × total stress path (from now on called TSP), as shown in Figure 30. From point B in Figures 29 and 30, friction resistance begins to be mobilized gradually, pore pressure begins to increase and the specimen begins to undergo shear strains until reaching point C, where all the available friction resistance is mobilized. It is when failure takes place.
In Figure 30, along the "viscosity jump", which goes from A to B instantaneously, the ESP and TSP are coincident. This "viscosity jump" causes the ESPs of normally consolidated clays to move to the right afterwards changing their direction moving to the left, as shown in Figure 30. It is important to note that the frictional resistance mobilized at point B is zero and, therefore, at point B there is only mobilization of viscous resistance.
This shape of ESPs in CIUCL tests, as shown in Figure 30, seems to have been originally presented by Leroueil et al. cited by Jamiolkowski et al. (1991) and is reproduced in Figure 7. Such a feature suggests that both the critical state line (CSL) and the state boundary surface are not unique but dependent on the strain rate / t t d dt ε ε =  , or rather one CSL and one state boundary surface exist for each t ε value. There are several experimental evidences supporting this idea. One of them is found in the following passage from Bishop & Henkel (1962), which refers to strain rate (although the phenomenon has been described as duration of test): [IV] Duration of Test. The duration of test commonly used in the triaxial apparatus and the parameters by which the results are expressed are open to criticism on the grounds that they take no account of the phenomena of creep in soils [for example, Geuze, 1953]. As the criticism is usually based on the results of undrained tests, it is necessary to separate the factors involved. The application of a shear stress to a saturated sample will result, under undrained conditions, in an excess pore pressure. Failure conditions in a consolidated-undrained test on a normally consolidated clay are represented in Figure 1a (an adaptation is presented in Figure 31a   at a much lower rate of testing, it is found that the undrained strength ( ) 1 3 σ σ − is lower and that φ′ has also decreased a little (Figure 1b) (an adaptation is presented in Figure 31b of this article). The drop in φ′ is negligible for sands but may amount in some clays to about 5% decrease in tan φ′ for each increase of ×10 in the duration of the test. (Bishop & Henkel, 1962, pp. 30-31).
Taking into account that in a normally consolidated clay failure conditions ind icate that CSL is written as ' tanφ increases with a ε , M must also increase with a ε , or rather the CSL is dependent on the strain rate a ε . In this case, the CSL cannot be a clay property in the sense of being something intrinsic to the clay, a sense used by Burland (1990) for the word intrinsic. The same fact holds for Roscoe's surface, which would depend on strain rate. These two aspects are illustrated in Figure 7 (Leroueil et al. cited by Jamiolkowski et al., 1991). According to Figure 31, strain rate would not affect sands since they do not present the viscous effects because they do not have plasticity. Evidence that Bjerrum (1973) grasped the essence of the phenomenon mechanism as being of a viscous nature is the fact that he related its importance and magnitude to plasticity (evaluated by the plasticity index I P ).

A set of ideal CIUCL tests
The advantage of working with the mean effective stress  Figure 32: the curves are proportional to ' e p . The effective stress paths on the s t ′× ′ plane of these tests are presented in Figure 33 together with their curves s e ′× .
The ESPs in the upper part of Figure 33 are homothetic with point O being the centre of homothety. Thus, the generated pore  . Paths on plane s e ′× start from points A 1 , A 2 and A 3 and instantaneously move to the right to points B 1 , B 2 and B 3 , respectively, forming the viscosity jumps A 1 B 1, A 2 B 2  and A 3 B 3 . Along the segments A 1 B 1, A 2 B 2 and A 3 B 3 there is neither shear strain nor pore pressure generation. From points B 1 , B 2 and B 3 on, shear strains begin to be developed, the frictional resistance begins to be mobilized and there is pore pressure generation. Specimens fail when points C 1 , C 2 and C 3 are reached, on the failure envelope. In the space p q v ′× × ′ (where v is the specific volume, 1 v e = + ), points C 1 , C 2 and C 3 are on a critical state line corresponding to the same strain rate t ε used in the three tests. According to Equation 47, for a given clay and for a given point ( ) , ' e e p on the VICL, the "viscosity jump"  would be proportional to the distortion rate γ. Nevertheless, experimental results have been shown that viscous resistance is not proportional to γ. Thus, it is more correct to rewrite the viscous resistance parameter  as a non-linear function f of the distortion rate, or rather being f an exclusive function of the distortion rate ( ) γ and not of the angle α , which indicates the plane considered. Then, for e and γ as constants, is also a constant. Thus, Equation 46 can be rewritten as:    Lira (1988)].
The 8th Victor de Mello lecture: role played by viscosity on the undrained behaviour of normally consolidated clays Regardless of function type, the viscous resistance component  must have the physical dimension of stress. Experimental data suggest that for normally consolidated clays the "viscosity jump"  is proportional to the isotropic consolidation stress ' e p , a feature that had already been identified by Taylor (1948, pp. 377-378). Such a feature can be observed for two clays in Figures 34 and 35.
Based on these experimental evidences, it can be written as Thus, viscous resistance , geometrically identified by the "viscosity jump", can be written as a linear function of ' e p , whose coefficient C η is a non -linear function of the distortion rate γ (and also of the soil structure).
The viscosity jumps A 1 B 1 , A 2 B 2 and A 3 B 3 in Figures 33 to 35 do not always appear clearly. The author does not know how to explain precisely the reason for that. The author believes that some of the possible reasons are the filter paper and porous stones adjustments, the non-coaxiality between the piston and the specimen axes, the silicone grease when lubricated ends are used, etc. Even when the same equipment, the same soil, the same specimen preparation and the same test procedures are used, sometimes the viscosity jump clearly appears and other times it does not. Although this issue will not be discussed here, it is a practical aspect that deserves more investigation.

A model of behaviour for saturated
normally consolidated clays taking into account strain rate in CIUCL tests 7.1 Normalization of × ′ ′ s t , ′× t t ε and ∆ × t u ε curves This work is supported by experimental evidences and basic hypotheses.
The experimental evidences, which are also considered as hypotheses, are as follows:  define the state of mobilized friction, which is represented by the friction ellipse. The sum of these two ellipses corresponds to the Mohr's circle of effective stress and, therefore, they cannot exist separately since only the stresses given by the Mohr's circle meet equilibrium. 9. As a consequence of hypotheses (5) and (6), during the undrained shear stage of a CIUCL test carried out with constant t ε =  , ηα τ is instantaneously mobilized and remains constant up to the end of shear. During the undrained shear of a CIUCL test there is no volume change but only shear strains. Thus, the increase of the deviator stress along the undrained shear is due to the frictional resistance mobilization, which occurs due to the development of shear strains. Therefore, the failure process is ruled by the frictional resistance mobilization. For a given distortion γ , the frictional resistance is fully mobilized and failure occurs. This means that, in a normally consolidated clay, failure occurs when the friction ellipse touches the strength envelope, which is the straight line with slope ' e tanφ , as illustrated in Figure 28. In other words, failure occurs when ( ) ' ' Martins where subscript f indicates failure and ' e φ is the Hvorslev's "true angle of internal friction".
10. Finally, another hypothesis concerning viscous resistance , which comes from experimental evidences, is that  is proportional to isotropic consolidation stress ' e p . Thus, Equation 61 and Figures 34 and 35), being ( ) C η γ a non-linear function of distortion rate γ and of soil structure.
Although this article is limited to normally consolidated clays subjected to CIUCL tests, it is possible to extend the model presented herein to overconsolidated clays. Part of the ten items listed above can be viewed as an extension of Terzaghi's PES and make it possible to consider the influence of strain rate on a failure criterion which gathers concepts from Newton, Mohr, Coulomb, Terzaghi, Hvorslev, Taylor and Bjerrum. Such influence of strain rate occurs by means of Newton's viscosity concept, despite soils viscous resistance does not obey Newton's law of viscosity. In plastic soils the viscous resistance to shear comes from the distortion of viscous adsorbed water whenever two clay particles in contact are moving relative to each other (Terzaghi & Frölich, 1936;Terzaghi, 1941;Taylor, 1942;Taylor, 1948). Such viscous adsorbed water provides clayey soils with plasticity. It is for that reason that Bjerrum (1973) associates strain rate effects with plasticity index. Unfortunately, many times the viscous component of shear resistance is inadequately called "cohesion". As understood by Coulomb and explained by Schofield (1999Schofield ( , 2001, cohesion originates from cementation between grains, like in rocks and saprolites, providing materials with a tensile strength, which is a consequence of true cohesion, as discussed in section 4.1. Therefore, cohesion as defined by Coulomb has a different physical meaning from the "true cohesion" as defined by Hvorslev. Unfortunately, the expression "true cohesion" was used by Hvorslev (1937Hvorslev ( , 1960 and Terzaghi (1938) improperly, bringing the conceptual confusion raised up by Schofield (1999Schofield ( , 2001. In this article, the strain rate effect on the undrained shear strength is evaluated via viscous resistance originating from the action of adsorbed water on the behaviour of plastic soils.
Back to the geometric similarity in Figure 32 and to the homothety of the ESPs in Figure 33, the curves in Figure 36 are obtained, provided the strain rate  t ε is the same and kept constant for all tests.
The straight line with slope tanφ′ passing through the origin, shown in Figures 15 and 28, is the strength envelope for a normally consolidated clay on the τ σ × ′ plane. According to the approach herein developed, such an envelope includes two strength components: the frictional component and the viscous component. Moreover, as stated in experimental evidence (1) of this section, for a fixed strain rate t ε , all ESPs on the ′ ′ × s t plane are homothetic with the origin as the centre of homothety. However, according to hypothesis (9), failure is not determined when the Mohr's circle of effective stresses touches the envelope with slope tanφ′, but when the friction ellipse touches the straight line whose slope is ' e tanφ , being ' e φ the Hvorslev's true angle of internal friction, which is a property of the soil. Thus, the question to be answered is: how can one explain and conciliate the envelope with slope tanφ′, which gives the real strength of the soil, and the envelope whose slope is ' e tanφ , by which failure is ruled? To answer this question, one must take into account the experimental evidences and basic hypotheses listed in the beginning of this section as well as the following discussion based on Figure 37.
From Figure 37 it immediately follows that points D and F lie on the same vertical straight line since ellipse AFGB can be obtained from a rotation of Mohr's circle Owing to the homothety of tests results carried out with constant γ =


, one comes to the conclusion that, for a given normally consolidated clay, when γ is fixed, the / Equation 67 leads to the conclusion that, assuming shear resistance consists of a frictional component and a viscous component, whenever a given normally consolidated clay, sheared with constant γ =  in a CIUCL test, presents homothetic ESPs, friction ellipses at failure will be homothetic, or rather they will have the same eccentricity, as shown in Figure 38.
When two or more specimens of the same clay are normally consolidated to the same isotropic stress in CIUCL tests, but sheared with different distortion rates, for instance,  Figure 39). In this case, the friction ellipse at failure AGHI will present a greater eccentricity than that of the friction ellipse at failure ABCD. The Mohr's circle of effective stresses at failure corresponding to the test carried out with 2 γ will be larger than that obtained from the test carried out with 1 γ . However, both friction ellipses at failure will be tangent to the friction envelope at points F 1 and F 2 . This friction envelope, which is unique for a given normally consolidated clay, is the straight line passing through the origin with slope ' e tanφ . Thus, any CIUCL test carried out on the same normally consolidated clay, irrespective of the distortion rate γ and irrespective of ' e p , will present at failure a friction ellipse which will be tangent to the straight line envelope whose slope is ' e tanφ .

Strain rate effects -additional experimental evidences
In order to quantify the strain rate in the shear stage of a CIUCL test, the variable t ε will be used from now on. Recalling that as    Figure 40). Such stress relaxation stages consist in turning off the load frame motor during the undrained shear phase, for a given time interval, monitoring deviator stress and pore pressure over time.
With the load frame motor turned off, t ε becomes zero and, therefore, during a stress relaxation stage carried out in the undrained shear phase of a CIUCL test, both volume and shear strains changes are zero. This kind of test, usually called stress relaxation test, would more properly be called CIUCL test with stress relaxation stages. Lacerda (1976) investigated strain rate effects by turning on the load frame motor after the end of the stress relaxation stages at different speeds. A typical result of such a test is shown in Figure 40.
The main features observed by Lacerda (1976), common to all CIUCL tests with stress relaxation stages carried out with different t ε values on normally consolidated specimens from San Francisco Bay Mud, were the following: d) The pore pressure decrease observed during stress relaxation stages are very small if compared to the deviator stress decrease.
Features b) and d) allow to assume, as an additional hypothesis, that pore pressure does not depend on the shear strain rate t ε , being only dependent on the shear strain t ε and on the isotropic effective stress ' e p to which the specimen was consolidated. The assumption that pore pressure does  The 8th Victor de Mello lecture: role played by viscosity on the undrained behaviour of normally consolidated clays not depend on t ε means that pore pressure will remain constant even during a stress relaxation stage, when 0 t ε =  . This additional assumption, based on such experimental evidences, allows Figure 41 to be drawn. Figure 41 shows that tests starting from the same isotropic effective stress ' e p , but carried out with different t ε values, will present, after the viscosity jumps, ESPs which change their directions to the left, until they attain envelopes with different α ′ values. Nevertheless, as previously explained, all the states of fully mobilized friction are represented by their respective friction ellipses at failure, which are tangent to the same friction strength envelope whose slope is ' e tanφ (see Figure 39).
Taking into account that Besides, experimental evidences indicate that, during CIUCL tests on two normally consolidated specimens of the same clay starting from the same ' e p , the following features are observed: a) Pore pressure u ∆ does not depend on the shear strain rate t ε . b) Pore pressure u ∆ does depend on the strain t ε .
Thus, it is expected that points like B 1 and B 2 in Figure 41 have the same values of t ε , u ∆ and ' emob tanφ , irrespective of the shear strain rate t ε . This working hypothesis, whose validity must be checked experimentally, may be presented in the complementary principle 1, as stated below: Complementary principle 1: All CIUCL tests carried out on a given normally consolidated clay compressed to the same isotropic effective stress ' e p will present, for any fixed shear strain t ε , the same pore pressure ∆u and the same ' φ emob , provided the points taken from the several

ESPs (each ESP corresponding to a different  t ε ) lie on the same 45º sloped straight line. In other words: points of intersection between a 45º sloped straight line and ESPs corresponding to different shear strain rates  t
ε have the same t ε , ∆u and ' φ emob (see points B 1 and B 2 in Figure 41).
' e t p will also be unique. However, if the pore pressure during CIUCL tests is not affected by the shear strain rate t ε , the curves / ' e t u p ε ∆ × will be unique, irrespective of the t ε value. Thus, Figure 41 can be redrawn ' e t p plane and pore pressure can also be normalized with respect to ' e p , as shown in Figure 42.

Strain rate effects -basic curves
In order to generalize the concepts presented in section 7.2, two CIUCL tests carried out on a normally consolidated clay will now be considered, both starting from the same isotropic effective stress ' e p . In one of these tests 0 That is what will be explained next.
The name basic curves (denoted by the subscript b in the parameters ' s and ' t as ' b s and ' b t ) will be given to all curves corresponding to 0 t ε =  . Such basic curves can be drawn from the tests carried out with 0 t ε ≠  subtracting the viscous resistance effects.
The main advantage of plotting basic curves is that they are free from viscous effects and, therefore, they are not dependent on the shear strain rate t ε . Thus, such basic curves only give the effects of the frictional resistance. Figure 43 shows the curves , there is only friction mobilization, which occurs as soil is deformed in shear along the curves AXM.
Another feature which is worth noting in Figure 43 is that for a given ' e p the curve t u ε ∆ × is unique since pore pressure is assumed to be not dependent on t ε . Recalling that this is an assumption based on experimental evidences, as shown in Figure 40.
The relationship between the coordinates of point Y which lies on the ESP associated with a fixed 0 t ε ≠  and the coordinates of point X which lies on the bESP (associated with 0) t ε =  , both points lying on the same 45º sloped straight line, can now be derived considering Figure 44.
In Figure 44 the ESP defined by points BYN corresponds to the shear stage of a CIUCL test carried out with a fixed On the other hand, the bESP, corresponding to a CIUCL test carried out with 0 =  t ε , is the curve defined by points A, X and M, whose coordinates are, respectively, M . According to the complementary principle 1, points Y and X which lie on the same 45º sloped straight line have the same values of ' emob tanφ , that is:  Besides, Particularly, for points A and B, and for points N and M, corresponding to failure, From the coordinates of points Y that define the ESP of a real CIUCL test carried out with a fixed 0 t ε ≠  , the coordinates of points X that define the bESP can be determined (see Figures 44 and 45).
Conversely, from the coordinates ( ) s t of points X of a bESP, one can determine the coordinates ( ) , s t ′ ′ of the corresponding points Y of an ESP of a CIUCL test whose viscous resistance  is known. This can be done by solving Equations 68 and 69 for s′ and t′, which gives: In order to check Equations 76 and 77, one can compute s′ and t′ for point B in Figure 44 t t ′ = ′. The discussion above leads to the conclusion that, from the results of a CIUCL test carried out on a specimen of a given plastic soil isotropically consolidated to ' e p and sheared with a strain rate t ε there is a viscous resistance featured by the parameter . With a  value obtained from a CIUCL test carried out with a given 0 t ε ≠  and starting from an isotropic effective stress ' e p , it is possible to draw the corresponding basic curve ' b t t ε × and the bESP (see Figure 43). Thereafter, knowing the function ( ) t C η ε (not discussed in this article), one can predict the curve t t ε ′× and the ESP for a CIUCL test starting out from the same ' e p but carried out with any t ε .

General normalization and basic curves
Consider the ESPs of the four CIUCL tests shown in Figure 46. The  According to the complementary principle 1, all points on ESPs starting out from the same ' e p , irrespective of the strain rate t ε imposed, will show the same shear strain t ε , the same excess pore pressure u ∆ and the same ' emob φ provided they are all on the same 45º sloped straight line. This is the case of points X and C and G and J in Figure 46. Take, for instance, points G and J that are on the same 45º sloped straight line and on the ESPs starting from 2 The right hand side of Equation 83 is the expression for ( ) ' . emob tan φ C This leads to the conclusion that On the other hand, considering points C and G in Figure 46, both belonging to ESPs corresponding to the same strain rate 1 t ε , the following expression can be written: Since for the same strain rate 1 t ε the curve / ' e t u p ε ∆ × is assumed to be unique, points C and G are assumed to have the same t ε . On the other hand, it should be noted in Figure 46 that the ratio ( ) 2 2 / ' e u p ∆ also holds for point J, which belongs to an ESP whose strain rate is 2 t ε . It is worth recalling that points G and J belong to different ESPs departing from the same 2 ' e p but corresponding to the strain rates 1 t ε and 2 t ε , respectively. However, for a fixed ' e p the pore pressure u ∆ does not depend on the strain rate t ε (see hypothesis based on experimental evidences shown in section 7.2 - Figure 40). This leads to the conclusion that points X, C, G and J have the same values of t ε , ( ) / ' e u p ∆ and ' emob tanφ . This conclusion, which comes from the complementary principle 1 and the above reasoning, allows to redraw Figure 46 using the normalized parameters / ' ' e s p and / ' ' e t p for coordinate axes, as shown in Figure 47. Figure 47 shows that, although points X, C, G and J belong to distinct normalized ESPs associated with different strain rates t ε , they lie on the same 45º sloped straight line.
The discussion presented above leads to the generalization of the complementary principle 1, which can be stated as follows: The generalized complementary principle 1 leads to three corollaries, namely: The 8th Victor de Mello lecture: role played by viscosity on the undrained behaviour of normally consolidated clays

Corollary 1: CIUCL tests carried out on a normally consolidated clay showing homothetic ESPs for any fixed  t ε and a unique curve
Corollary 1 can be demonstrated as follows: According to the generalized complementary principle 1 (see Figure 47) Equation 83 can be rewritten as Taking into account Figure 46, Equation 72 can be applied to points X and C, which are on the same 45º sloped straight line, obtaining Equation 86: Besides the fact that , Equation 89 is obtained as follows: As points G and J lie on the same 45º sloped straight line (see Figure 46) and on ESPs starting out from the same s p t p × plane, it can be observed from Figure 47 that

Martins
Finally, it is worth reminding that points X, C, G and J have the same shear strain t ε , which implies a one-toone correspondence between / ' ' b e t p and t ε , leading to the conclusion that the basic curve / ' ' b e t t p ε × is unique, as it was to be demonstrated.

s p t p , whatever  t ε is.
Corollary 2 results from the following reasoning: Starting from Equation 74, which gives the expression for ' b s , and following a similar line of reasoning adopted in the proof of corollary 1, it can be shown that a unique curve s p × t ε curve, it will also be obtained a unique curve formed by the ordered pairs e b e s p t p ), which is, by definition, the normalized basic effective stress path (bESPn).

Corollary 3: CIUCL tests carried out on a normally consolidated clay showing homothetic ESPs for any fixed  t ε and a unique curve
Corollary 3 can be demonstrated following the reasoning presented below: Considering corollaries 1 and 2, both curves / will also be a sole function of t ε , which proves corollary 3, as illustrated in Figure 48.
Thus, it can be concluded that curves /

Introduction
A model of behaviour for saturated normally consolidated clays subjected to CIUCL tests taking into account strain rate ( ) t ε was developed in section 7. Based on the developed model, the main results expected for an ideal plastic soil subjected to CIUCL tests were also presented.
At first, this work was intended to present a testing program consisting of CIUCL , undrained creep and stress relaxation tests carried out on samples from a very soft clay deposit close to the city of Rio de Janeiro, called Sarapuí II [see Danziger et al. (2019)]. The main aim would be to check whether the results from such testing program could be predicted by the model presented in section 7. However, the arrival of the pandemic in the beginning of 2020 made such testing program unfeasible. For this reason, the tests herein analyzed are those carried out by Lacerda (1976) on San Francisco Bay Mud samples.
Although the Lacerda's (1976) testing program was not planned to study the behavioural aspects presented in section 7, it is suitable since it is consisted of CIUCL , undrained creep and stress relaxation tests, which can be analyzed under the light of the proposed model. Furthermore, San Francisco Bay Mud is a worldwide known and comprehensively studied soil. The main disadvantage of using Lacerda's (1976) tests is that they were carried out when computer-aided data acquisition systems were not available for soil testing. This disadvantage makes it harder to experimentally identify special aspects already discussed such as the "viscosity jump". Nevertheless, the Lacerda's (1976) testing program is useful to check whether its experimental results are in agreement with the main propositions made by the presented model.

Summary of the model hypotheses and steps to be followed to check their validity
To check the validity of the model, it is necessary to verify if its 11 hypotheses are fulfilled. Among these hypotheses, listed below, the first four come from experimental evidences. The next six are working hypotheses of theoretical nature and the last one is hybrid since it comes from experimental evidences as well as from theoretical considerations.  s t is a straight line passing through the origin. 4. When CIUCL tests are carried out with the same isotropic effective stress ' e p and different shear strain rates t ε , the deviator stresses are higher the higher the shear strain rate. However, pore pressure values are not affected by shear strain rate. This means that for each t ε there is just one curve / the state of mobilized friction, which is represented by the friction ellipse. The sum of these two elipses corresponds to the Mohr's circle of effective stress Thus, the two ellipses cannot exist separately since only the stresses given by the Mohr's circle satisfy equilibrium. 10. As a consequence of hypotheses (6) and (7), during the undrained shear phase of a CIUCL test carried out with constant t ε =  , ηα τ is instantaneously mobilized and remains constant up to the end of shear. During the undrained shear phase of a CIUCL test there is no volume change but only shear strains. Thus, the deviator stress increase during the undrained shear is due to friction mobilization, which occurs as shear strains increase. Therefore, failure process is ruled by friction mobilization. For a given distortion γ , friction is fully mobilized and failure occurs. This means that, in a normally consolidated clay, failure will occur when the friction ellipse touches the strength envelope, which is the straight line passing through the origin with slope ' e tanφ , as illustrated in Figure 28. In other words, failure will occur when Equation 62 is met. 11. Finally, the last hypothesis assumes the viscous resistance . This means that, even though ( ) C η γ is a non-linear function of distortion rate and of soil structure, for any constant This hypothesis is a hybrid one because, although it comes from hypotheses (6) and (7), which are of theoretical nature, it also appears as experimental evidence via the "viscosity jumps", as shown in Figures 34 and 35. As  is proportional to ' e p , this hypothesis is also in agreement with hypothesis (1), which assumes a normalized behaviour in relation to ' e p .
Instead of using distortion γ and distortion rate γ as they appear in hypotheses (7), (10) and (11), the shear strain t ε and the shear strain rate t ε will respectively be used from now on.
The validity of hypotheses (1) to (4) can be directly checked by observing whether or not the plots mentioned in each of them are fulfilled. Hypotheses (6) to (10), of theoretical nature, are concerned with the effects of the viscous adsorbed water on the behaviour of plastic soils. Hypothesis (11), a hybrid one, concerns the "viscosity jump". The "viscosity jump" is a theoretical aspect of the instantaneous mobilization of the viscous resistance. On the other hand, experimental evidences show that the "viscosity jump" is proportional to the effective isotropic stress ' e p , as shown in Figures 34 and 35. The hybrid nature of hypothesis (11) resides in these two aspects.
The eleven hypotheses together with the discussions presented in section 7 lead to the generalized complementary principle 1, from which corollaries 1, 2 and 3 are consequences. Thus, in order to check whether or not the model holds valid for a given soil, it is enough to check if hypotheses (1) to (4) and (11) as well as the generalized complementary principle 1 are fulfilled. If so, the other hypotheses will automatically be fulfilled since they are embedded in the generalized complementary principle 1. The same will happen to corollaries 1, 2 and 3 because they are consequences of the generalized complementary principle 1. This will be the task to be accomplished in the next sections so as to check if Lacerda's (1976) CIUCL test results follow the predictions of the presented model.

Mud by Lacerda (1976)
The soil samples tested by Lacerda (1976) were taken with thin-walled 125 mm-diameter and 300 to 450 mm-long fixed piston samplers. The samples were taken at Hamilton Air Force Base, Marin County, between the 5.20 m and 7.60 m depth.
According to Lacerda's (1976) description, San Francisco Bay Mud "is a normally consolidated, saturated clay, composed of illite, and chlorite with some montmorillonite, vermiculite and kaolinite. Very thin silty lenses are found along horizontal planes and small broken shells are occasionally present, but the soil as a whole is fairly intact and easily trimmable" (Lacerda, 1976, p. 262). Characterization tests results are summarized in Table 1.
From the tests carried out by Lacerda (1976) only those which allow the comparison and interpretation of their results under the light of the concepts presented in section 7 were selected. Such tests are identified in the first two columns of Table 2. In the other columns of Table 2, the specific volume ( v ) after isotropic consolidation, the isotropic effective stress to which the specimen was consolidated ( ) is applied in steps, each step lasting for a given time period. At the beginning of a new step, the deviator stress is raised by increasing a σ , whereas r σ is kept constant throughout the whole test. During each step, shear strains t ε and pore pressures u ∆ are measured over time and strain rates t ε are computed. Thus, the undrained step creep test can be compared to the conventional CIUCL tests, made with constant t ε =  , provided the points to be compared from both test types have the same t ε values. An undrained creep test where a single deviator stress value is applied during the whole undrained creep stage can also be compared to a CIUCL test. However, in this case, the comparison is restricted to only the two points having the  (Lacerda, 1976).
Natural water content w (%) Liquid limit w L (%) Plastic limit w P (%)

Plasticity index I P (%)
Specific gravity G σ σ − and pore pressure u ∆ are measured over time. After observing stress relaxation over a certain time period, the load frame motor is switched on again with the same or a different strain rate t ε used during the t ε interval which preceded the current stress relaxation phase. This is the case shown in Figure 40, where different shear strain rates t ε were used between consecutive stress relaxations phases.
From now on, the Lacerda's (1976) tests results are compared to the predictions of the model presented in section 7.
The data concerning the isotropic compression of San Francisco Bay Mud normally consolidated specimens (presented in Table 2) are plotted in Figure 49. The virgin isotropic compression line (VICL) is presented in Figure 49, showing the relationship between specific volume v and isotropic effective stress ' e p obtained by Lacerda (1976) for San Francisco Bay Mud. Although presented in Figure 49, test CR-I-2 will not be taken into account in the analysis that follows since it presents a specific volume which is considerably distant from the ' e v p × line. This suggests that such specimen is slightly overconsolidated, with an overconsolidation ratio of 1.3. The undrained shear phases of SR-I-5 test will not also be analysed herein since the shear strain rate 1.15 % / min.
, is considered too high. Such strain rate has probably not allowed an adequate equalization degree of pore pressure measured at the base of the specimen.

Checking the model using San Francisco Bay Mud tests results
The eleven hypotheses listed in section 8.2 and the discussions of section 7 have led to the generalized complementary principle 1, from which corollaries 1, 2 and 3 emerge. Thus, to check whether or not the model holds valid for a given plastic soil, it is enough to verify if the hypotheses (1) to (4) and (11) and the generalized complementary principle 1 are fulfilled. If so, the remaining hypotheses will automatically be fulfilled since they are embedded in the generalized complementary principle 1. Besides, once the validity of the generalized complementary principle 1 is shown, corollaries 1, 2 and 3 will also be automatically fulfilled.
In a few words, to check whether or not San Francisco Bay Mud normally consolidated specimens fulfill the model presented in section 7, the tasks listed and explained at the end of section 8.2 must be carried out. These tasks are: (i) Validity check of hypotheses (1) to (4), which come from experimental evidences.
(iii) Validity check of the generalized complementary principle 1.
Following the sequential tasks listed above, the first thing to do is to check the validity of hypothesis (1)     Hypothesis (2) Figure 51.
Although there is a lack of data to obtain M and φ′ corresponding to t ε values different from 0.10 % / min. ≅ , the available data corresponding to 4 5.5 1 0 % / min. t ε − = ×  and 0.7 % / min. ≅ , suggest that for each shear strain rate there is only one CSL (see also Figure 31 and the discussion associated with it).
Hypothesis (4) must be checked next. This hypothesis assumes that, in CIUCL tests, the higher the shear strain rate applied, the higher the values /  ' e t t p ε × curves but hardly noted on / ' e t u p ε ∆ × , where, regardless the strain rate, experimental results fall within a narrow zone. In Figure 54 it should be noted that t ε assumes four different orders of magnitude. One can argue that, with 3.4 % / min. t ε =  , the strain rate criterion which should have been used aiming pore pressure equalization along the specimen was not probably fulfilled during the first undrained shear phase of test SR-I-9. Thus, u ∆ values measured during the first undrained shear phase of test SR-I-9 are probably underestimated. After this observation, it can be concluded from Figure 54   [data from Lacerda (1976)].
After checking the validity of hypotheses (1) to (4), one can now check hypothesis (11), which, being from a hybrid nature, is made up of two parts: one that comes from experimental evidences and the other that comes from theoretical considerations.
According to hypothesis (11), . This means that for a given shear strain rate t ε the "viscosity jump" is proportional to ' e p , as shown in Figures 34 and 35. Thus, the normalized corresponding to the same t ε should be represented by a unique ESP beginning with a "viscosity jump" along a 45º sloped straight line, which suddenly changes its direction moving up and to the left, showing an elbow shaped curve like those presented in Figure 47.
Although the normalized ESPs for 0.10 % / min. Figure 51 can be considered as a unique curve, the absence of the "viscosity jump" is noteworthy. Such absence can be possibly assigned to the fact that an automatic data acquisition system was not used, which greatly harms the measurement of s', t' and Δu corresponding to the beginning of the tests. Another possible explanation for the absence of the "viscosity jump" is the occurrence of bedding errors, which will be not discussed here. One of the signs that some "disturbance" has affected the beginning of CIUCL test data is the fact that points belonging to ESPs associated with 0.09% / min. In order to obtain ( ) t C  and ' e φ , it will be necessary to make use of the undrained creep tests data. As previously explained, undrained creep tests are carried out by keeping the deviator stress constant, measuring t ε and u ∆ over time and evaluating t ε . This way of evaluating t ε makes its values more reliable, particularly in the early phase of the test when bedding errors are of greater magnitude. Accordingly, the normalized ESPs for the undrained creep tests are shown in Figure 56.   Figure 56, are presented in Table 3.
Based on values from Table 3 and on ESPs shown in Figures 51 and 56, ESPs for some selected shear strain rates t ε can be sketched. ESPs sketches corresponding to 1 10 % / min.  Figure 57.
In Figure 57, each ESP corresponding to a fixed t ε intersects the normalized total stress path at a point whose ordinate gives the C η value for that fixed t ε . Thus, from Figure 57 Figure 58 is obtained. Figure 58 shows that, making the appropriate "corrections" of the initial parts of the ESPs in Figure 51 and taking into account the undrained creep tests, hypothesis (11) is also fulfilled.
The results of all tests ( CIUCL , stress relaxation and undrained creep) are presented in Figure 59 to show that normally consolidated San Francisco Bay Mud follows hypotheses (1) to (4) and (11), regardless of the test type.
Going ahead with the task of checking whether or not the model is appropriate to predict the behaviour of normally consolidated San Francisco Bay Mud, now it is necessary to check the validity of the generalized complementary principle 1, whose statement is repeated below.

Generalized complementary principle 1: During undrained shear of CIUCL tests carried out on normally consolidated clay specimens, points on the plane
, thus Equation 97 can be rewritten as:  Figure 60, which clearly shows the validity of corollary 1.
It will be shown next that normally consolidated specimens of San Francisco Bay Mud also fulfill corollary 2, whose statement is repeated below: In order to plot the normalized basic effective stress path for normally consolidated San Francisco Bay Mud, the ordered pairs ( / , / )   By plotting the ordered pairs ( )

Corollary 2: CIUCL tests carried out on a normally consolidated clay showing homothetic ESPs for any fixed
e b e s p t p , one can then obtain the normalized basic effective stress path (bESPn), which is presented in Figure 61. Except for the points corresponding to the beginning of tests FP-13, FP-23, FP-32 and FP-42, which are not plotted in Figure 61 for being suspected of having been affected by bedding errors, as already discussed, all points of the remaining tests can be assumed as lying on a single line. This line is the bESPn (normalized basic effective stress path) for normally consolidated San Francisco Bay Mud. For being associated with the strain rate 0 t ε =  , the bESPn shown in Figure 61 only represents the mobilization of the frictional part of shear resistance.    Figure 62 to be drawn.
It can be observed from Figure 62 that, to fully mobilize the true angle of friction ( )

Undrained creep tests
Undrained creep is meant in this article as the phenomenon by which a soil specimen is deformed over time when subjected to a constant state of total stress under undrained conditions.
The undrained creep studied in this article will be restricted to those cases where the specimens are of cylindrical shape, subjected to an axysimmetric state of stress, with the axial (vertical) total stress, denoted by a σ , being the major principal stress and the radial (horizontal) total stress, denoted by r σ , being the minor principal stress. The study will be also restricted to normally consolidated, saturated plastic clays with no cementation between grains.
To understand the undrained creep under the light of the concepts presented in this article and how it can be related to During the undrained shear phase of a CIUCL test starting from point A in Figure 63 with a strain rate of  Figure 63). When point P is reached, the undrained creep comes to its end because all the viscous resistance will have been transferred to frictional resistance.
This process holds valid for each and every plane given , is kept constant throughout the whole process.
The previous paragraph also leads to the following discussion: during undrained creep shown in Figure 63  , 0 u ∆ = and the mobilized frictional resistance is equal to zero, whatever the plane may be. Thus, the viscosity ellipse and the Mohr's circle of effective stress coincide and . Thus, at point N, In brief, as undrained creep goes on, the minor axis of the viscosity ellipse decreases, making the minor axis of the friction ellipse increases. This is what is shown in Figure 64b.
At point D in Figure 63, the shear strain The shear strain rate At point D the minor axis of the viscosity ellipse becomes smaller than it was at point N, whereas the minor axis of the friction ellipse at point D becomes larger than it was at point N, as shown in Figure 64c.
Finally, at point P in Figure 63,  Figure 64d and pore pressure magnitude is given by PH in Figure 63.
If another undrained creep test was carried out with a ' t value corresponding to point V in Figure 63, the same mechanism of transference from viscous resistance to frictional resistance would take place. In this case, however, the ESP to be followed in Figure 63 would be VIEY and undrained creep would come to an end at point Y on the basic bESP. As ' uc t in this test would be higher than ' uc t corresponding to the test whose ESP is HNDP, the shear strain t ε at the end of undrained creep would be The final excess pore pressure would be higher than that observed in the previous test, being represented by YV in Figure 63. It is worth observing that, except for a particular but important feature to be discussed further, undrained creep phenomenon is analogous to isotropic consolidation. During isotropic consolidation, the state of total stress is kept constant and there is an increase in effective stress equal to the dissipation of the excess pore pressure along time. During undrained creep, the state of total stress is also kept constant and there is an increase in the mobilized frictional resistance equal to the decrease in the mobilized viscous resistance along time. The 8th Victor de Mello lecture: role played by viscosity on the undrained behaviour of normally consolidated clays ε ε = and the strain rate at failure can be predicted. Before going on with the study of undrained creep, it is adequate to recall the excerpt from Taylor (1948, pp. 379-380), reproduced at the end of section 4, which reveals his ideas about the action of adsorbed water. Most of these ideas have inspired the author to develop the model presented in this article.
The undrained creep mechanism was also clearly depicted by Bjerrum (1973) in an excerpt of his classic state-of-the-art report, which is reproduced below to avoid loss of fidelity to the original: "In general, in a natural clay an applied shear stress will be carried partly as cohesion in the semi-rigid water-film type contact points and partly as friction in contact points with mineral contact. However, as demonstrated by Schmertmann and Hall (1961), with time the effect of the interparticle creep will be a tendency to transfer loads from the cohesive to the more rigid and stable frictional contact points with the result that the mobilized cohesion decreases and a correspondingly greater part of the available friction becomes mobilized. As this process will lead to a reduction in shear stress in the cohesive contact points, the result is a reduction in the rate of failure of contact points, and thus in the rate of creep deformation. If the shear stress acting on the clay element is smaller than the available friction, the cohesive contact points will ultimately be relieved and the creep deformations will come to a halt. If the shear stresses exceed the available frictional resistance, the difference will have to be carried by the cohesive-type contact points. The rate of creep will therefore decrease until this condition is reached, and from then on it will remain constant." (Bjerrum, 1973, p. 125).
With the reproduction of the above excerpts, there is no doubt that both Taylor (1948) and Bjerrum (1973) captured the mechanism the author tried to quantify in this article using the concept of viscous resistance, improperly called cohesion, as already discussed.
After discussing undrained creep and its consequences under the light of the model presented in section 7, one can now check its validity when applied to normally consolidated samples of San Francisco Bay Mud.

Undrained creep tests on normally consolidated San Francisco Bay Mud specimens
In order to check whether or not the proposed model applies to the undrained creep tests carried out on normally consolidated specimens of San Francisco Bay Mud, the following Lacerda's (1976) undrained creep tests listed in Table 2 are available: CR-I-1, CR-I-2, CR-71-1 and CR-I-ST-2.
According to section 9.1, in order to distinguish among the undrained creep tests listed above those that would fail from those in which creep would cease, one must know the / ' ' bf e t p value for normally consolidated San Francisco Bay Mud as well as the / ' ' uc e t p value corresponding to each of the undrained creep tests to be analyzed.
Test CR-71-1 was interrupted after about 100 minutes. Therefore, the available data are so scarce that they are not useful. As test CR-I-2 specimen seemed to be slightly overconsolidated (with an 1.3 OCR ≅ ), it has been decided not to include its data in the analyses presented in section 8. However, as test CR-I-2 lasted more than 10000 minutes and the specimen failed, it was decided to take it into account in this section due to the data scarcity concerning Lacerda's (1976) undrained creep tests. Due to such scarcity, to better analyze the model's ability in predicting soil behaviour during undrained creep, two additional tests carried out by Lacerda (1976) have been selected. Although these additional tests data are not entirely available in Lacerda's (1976) PhD thesis dissertation, the available data can provide valuable information to be considered in this section. Such additional tests, denoted by S-I-3 and CR-I-5, are both undrained creep tests.
It would also be interesting to analyze the step creep test CR-I-ST-2 carried out in seven steps. However, among these seven steps, only the last one is of interest for this section. So, it was decided to only make a brief comment about the last step of test CR-I-ST-2. The undrained creep tests to be analyzed will then be those whose data are summarized in Table 5.
In order to identify among the tests listed in Table 5 those that would fail and those in which creep would cease, one must compare their /  . The ESP to be followed in Figure 67 is AHIJKLM. Initially, there will be a "viscosity jump" AH and from then on shear strains will become to occur. Failure will take place when the ESP reaches point M.
Suppose now that the CIUCL test previously described will be repeated, except for a detail: at point I, the load frame motor is turned off, starting a stress relaxation stage. From then on, what does the model predict?
Since the soil is saturated and the test is undrained, 0 v ε = . In addition, from the moment the load frame motor is switched off, 0 t ε =  . Thus, during an undrained stress relaxation stage shear strain does not change with time.
According to the model, since 0 t ε =  , the viscous resistance will vanish. Besides, since t ε = constant, according to the generalized complementary principle 1, u ∆ and ' emob φ are expected to have constant values during undrained stress relaxation. As a consequence, the ESP to be followed during undrained stress relaxation is IQCW, a 45º sloped straight line, as shown in Figure 67. Point W is expected to be the end of the stress relaxation effective stress path IQCW, since at point W the specimen would already have got rid off all viscous resistance and would become to resist to the remaining shear stress only by friction.
If the load frame motor is turned on during a stress relaxation stage, the viscous resistance will instantaneously be reactivated and the CIUCL test will continue following the ESP associated with the shear strain rate t ε applied. For instance: suppose that during the stress relaxation IQCW in Figure 67 the load frame motor is turned on again at point C, with a shear strain rate 2 t t ε ε =   . Thus, there will be an instantaneous jump, represented by CQ, corresponding to the viscous resistance reactivation and the test will continue following the effective stress path QRSTV.
However, if at point T the load frame motor is turned off again, another stress relaxation stage will start following the effective stress path TFY.

Stress relaxation tests on normally consolidated San Francisco Bay Mud samples
To illustrate what was discussed in the previous section, three stress relaxation tests carried out by Lacerda (1976) on normally consolidated specimens of San Francisco Bay Mud will be presented. The main features of these tests, denoted by SR-I-5, SR-I-8 and SR-I-9, are summarized in Table 6.
What was presented in section 9.3 for the ESPs can be extended, without loss of generality, to the normalized plane by 45º sloped straight lines with descending direction.
Four stress relaxation stages have been carried out in each of the three tests listed in Table 6. The normalized ESPs for these stages are shown in Figure 68. These ESPs show that stress relaxation is also in agreement with the proposed model.
The discussions and experimental results presented in this article concerning undrained creep and undrained stress relaxation suggest that Taylor's and Bjerrum's ideas can be gathered in another general principle, which should be tested for other soils and which will be called generalized  Figure 67. Effective stress paths for CIUCL tests with stress relaxation stages.

Martins
complementary principle 2 or Taylor's and Bjerrum's law, whose statement is written below:

Generalized complementary principle 2 or Taylor's -Bjerrum's law
A normally consolidated plastic soil subjected to a given state of stress, in which the shear stresses are resisted partially by frictional resistance and partially by viscous resistance, will tend to get rid off the viscous resistance over time and will try to resist the remaining shear stresses only by friction.
In a clearer and more direct way, the generalized complementary principle 2 states that a normally consolidated plastic soil under a normalized state of effective stresses given by (

Summary and conclusions
What has been presented and discussed throughout the article can be summarized as listed below: 1. Phenomena that do not obey Terzaghi's principle of effective stress (PES) are related to strain rate and time effects (such as creep and stress relaxation). 2. The usual approach to deal with phenomena which do not obey the PES is to preserve the PES essence and develop tools to tackle each of these particular phenomena as being outside the PES validity domain.
The approach followed in this article is different: the original PES is extended to encompass strain rate and time effects in such a way that these effects become natural consequences of the extended PES version. Concepts that allow such PES extension are presented in some classical texts from the beginning of soil mechanics. 3. The word "cohesion" has been used in soil mechanics with different meanings, bringing misunderstanding and conceptual confusion. Concerning earth natural materials, the term "cohesion" should be understood as a resistance coming from cementation between soil grains. This "cohesion" provides a tensile strength under tensile effective stress which makes the difference between rocks and soils. 4. The word "cohesion" is also often used to describe a sticky earthy material that is soft to the touch when moistened. Earth materials that show such a feature are also called "cohesive soils". To avoid misunderstanding, these materials would more properly be called plastic soils. For the sake of conceptual clearness and objectivity, the expression "plastic soil" should be used for all soils that present liquid and plastic limits. 5. When plastic soils are sheared, there is a component of shear resistance that comes from the action (distortion) of the highly viscous adsorbed water layers surrounding particles in contact. The closer the adsorbed water is to the particles surface, the higher its viscosity. Thus, it is expected that the lower the void ratio, the higher the shear resistance Figure 68. Normalized effective stress paths during stress relaxation stages for normally consolidated specimens of San Francisco Bay Mud [data from Lacerda (1976)].
The 8th Victor de Mello lecture: role played by viscosity on the undrained behaviour of normally consolidated clays component due to the action of the adsorbed water, which is of viscous nature. 6. Hvorslev (1960) showed it is possible to express the shear strength of a clay as: φ a constant, called the true angle of internal friction. Since the soil tested by Hvorslev was a remoulded clay, it could have no cementation. Thus, the Hvorslev's "true cohesion" could not have the same nature of Coulomb's "cohesion". Hvorslev (1960) assumed that the "true cohesion" e c of a saturated clay depends not only on void ratio but also on strain rate and clay structure. 7. Since normally consolidated, saturated clays have straight line strength envelopes passing through the origin in a × ' σ τ plot, they do not have "cohesion" in the sense used by Coulomb but they do have plasticity. In other words: normally consolidated clays do not have "cohesion" in the sense used by Coulomb but do have "true cohesion" in the sense used by Hvorslev. Furthermore, when normally consolidated specimens of a given clay, with the same void ratio, are subjected to undrained shear, the higher the strain rates, the higher their strengths. These features suggest that Hvorslev's "true cohesion" should more properly be called viscous resistance and expressed by the product of the coefficient of viscosity and a function of the shear strain rate. 8. The model presented herein assumes that, in plastic soils, the shear stress α τ acting on a plane whose normal makes an angle α with the direction of 1 σ