Anchored Retaining Walls in Granite Residual Soils I . Parametric Study

This work aims to be a contribution for a better knowledge of anchored earth retaining structures, providing preliminary guidelines for their correct design, by establishing starting points. It also constitutes the introduction to a second paper in which an innovative solution for preliminary design is presented. Starting from an extensive parametric study using PLAXIS on a typical moderate to high strength soil, the study begins by evaluating the influence of parameters such as the excavation depth, the stiffness of the retaining wall and the anchors, the initial prestress, and the soil properties (stiffness, strength, coefficient of earth pressure at rest and bedrock depth). For each parameter influence laws are derived, which will allow the implementation of the simplified design method in a companion paper.


Introduction
The design of anchored walls to support deep excavations comprises difficulties and challenges since it depends on multiple variables, concerning the soil (strength, stiffness, at-rest state of stress), the retaining structure and the geometry of the cut.
The purpose of the parametric study presented in this paper, based on the work of Raposo (2007), is to evaluate the behavior of these structures.The study covers a wide range of geometries, as well as structural and soil parameters.
Subsequently, influence laws are derived, characterizing the effect of each individual variable under analysis.Using these influence laws, the results can be used to interpolate (or extrapolate) the same parameters for similar excavations.
The work is focused on excavations executed in soils with moderate to high strength, taking as reference the granite residual soils, similar to the ones found in the city of Porto, Portugal (Viana da Fonseca et al., 1997).In such ground, because of the frequent presence of batholites in the soil mass, diaphragm walls are avoided and the most common solution for the retaining wall is cast in place concrete piles, often with spacing larger than their diameter (Matos Fernandes, 2010;Viana da Fonseca & Quintela, 2011).
The tool used to accomplish the parametric study is the finite element method, through the commercial software Plaxis.This method was chosen because it allows evaluating, very accurately and promptly, the influence of the variation of a particular parameter, or of a set of parameters, on the overall behavior of complex soil-structure interaction problems.The possibility of using analytical models, similar to those of Saribas & Erbatur (1996) or Matos Fernandes et al. (2002), was considered, since they are more intuitive.However, due to the difficulty of applying them to highly hyperstatic structures such as the ones studied in this paper, this option was abandoned.
Given the nature of the soil and the type of retaining wall mentioned above, the water table was considered at the base of the excavation (Raposo & Topa Gomes, 2011).Thus, drained conditions were assumed and the analyses were performed in effective stresses.

General properties of the base excavation and the numerical model
The excavation used as the starting point for the parametric study (base excavation #A00) is 15.0 m deep and 30.0 m wide, performed in granite residual soils, as shown in Fig. 1.The length of the excavation was assumed to be much greater than its width, allowing the use of a plane strain model.
Two distinct geotechnical layers were considered: a surface layer of granite residual soil (W5) and a substratum, comprising highly weathered granite (W4).Although it may seem insufficient to consider only two layers for characterizing a given soil mass, it is shown in the Appendix how the adopted constitutive model allows the variation of mechanical properties in depth, especially in terms of stiffness, thereby improving the agreement between the numerical model and the reality.
The retaining structure consists of concrete piles with a diameter of 0.60 m and 1.20 m spacing between axes, presenting a flexural stiffness equivalent to that of a diaphragm wall 0.40 m thick.For the Young modulus, E, a value of substratum.Since the wall was considered permeable, the water table was assumed to coincide with the base of the excavation during all stages.The wall is supported by a grid of ground anchors, spaced 2.50 m in the vertical direction and 3.00 m in the horizontal direction.
In order to properly simulate the shear interaction between the structure and the soil mass, interface elements were used, whose strength was set to two thirds of the soil strength.In order to improve the stress distribution around the tip of the wall, the interface was extended 1.5 m below this extremity.In these extended interface elements no strength reduction was considered.This procedure increases the flexibility of the finite element mesh and prevents the generation of unrealistically high stresses (Van Langen & Vermeer, 1991).
In this study the modelling of the anchors was achieved through the introduction of linear elements, which simulate the grout body and are connected to the finite elements of the surrounding soil.To represent the tendon, another set of linear elements was included in the model, connecting the wall to the end of the grout body.In this case, there is no connection with the soil finite elements.The finite elements representing both the tendon and the grout body have only axial tensile stiffness (Guerra et al., 2007).
In the base excavation #A00, as well as in all other calculations of the parametric study, a tilt angle of 30 degrees was considered for the ground anchors.In all cases the length of the grout body was considered to be 6 m.The length of the tendon was consistently admitted equivalent to two thirds of the maximum excavation depth.
The anchor prestress was calculated according to the diagram shown in Fig. 1, resulting, for this base excavation, in a total force of 390 kN per anchor, due to an horizontal spacing between anchors of 3 m.As it was assumed a required tendon cross section of 1 cm 2 per 100 kN, 4.0 cm 2 were needed in this case.The steel Young modulus was admitted to be 200 GPa.For the sake of simplicity, the same prestress force was considered in all anchors.This last assumption produces a prestress diagram with trapezoidal shape, since the first and last anchor levels have a larger influence area than the remaining ones.
The calculation model involves a restricted area of the soil mass surrounding the wall.The model was truncated along the symmetry axis, 15 m to the left of the wall, allowing vertical displacements along this boundary.The right limit of the model it was located 75.0 m away from the wall.This distance corresponds to five times the maximum excavation depth, which is considered sufficient to obtain negligible horizontal displacements at this location (Wood, 2004).Below the excavation, the heavily weathered granite layer was considered to be 15.0 m thick.
The simulation of the construction process (stage 1) begins with the activation of the wall and the generation of the in situ stress state.Stage 2 corresponds to the first level of excavation, down to a depth of 2.5 m.Stage 3 is the activation of the first level of anchors, at 2.0 m depth, and the application of the prestress force.This sequence, with excavation followed by anchor placement and prestressing, is repeated until stage 12, when the depth in the excavated side reaches 15.0 m.
In the parametric study two constitutive models were used: an elastic perfectly plastic model with a Mohr- Coulomb failure envelope, for the heavily weathered granite; and the hardening soil model for the granite residual soil.Table 1 contains the required parameters for both models, as well as the values considered for the calculation named "base excavation #A00" (Topa Gomes, 2009;Viana da Fonseca et al., 1997).The first model is probably familiar to the majority of the readers.The latter is described in the Appendix.

Base excavation #A00 results
Figure 2 shows the displacement of the wall and of the ground surface for the final excavation phase, displaying a typical pattern for this type of geotechnical works (Matos Fernandes, 2010, 2015).In conjunction with the horizontal displacements, there is also a small heave of the wall, as a result of soil expansion, due to the considerable mean stress reduction occurred during the excavation.The maximum horizontal displacement, of about 30 mm, occurs near the excavation base, at 12 m depth.The top of the wall moves about 6 mm towards the excavation side.
As for surface displacements, the subsidence basin extends up to the external model boundary.This is a common limitation of the finite element models.Local instrumentation in several excavation works has revealed that the subsidence basin is much more concentrated near the wall than what Fig. 2 shows (Clough & O'Rourke, 1990;Kung, 2010).This difference results from two main contributions: first, soil stiffness for small strains is much higher and thus it would be necessary to use a model incorporating soil stiffness at very small deformations, such as the one proposed by Puzrin & Burland (1996) or the Hardening Soil model with small-strain stiffness implemented in Plaxis (Brinkgreve et al., 2011), to reliably reproduce behaviour in points considerably away from the wall; second, real excavations seldom present a length that may be assumed as infinite, and so 2D models tend to overestimate the in-plane deformation deformation, as they do not include the attenuation resulting from the settlement distribution over a length greater than the real excavation length.In real excavations this effect may be significant, reducing the settlements up to half of the value calculated for a plane strain condition.
Focussing the attention on the bending moments along the wall height, after the completion of the excavation, Fig. 3a shows an absolute maximum of 193 kNm/m.As for the horizontal displacements, such value also occurs near the bottom of the excavation, at 13.4 m depth.This maximum bending moment is compatible with the wall resistance, requiring an amount of reinforcement close to 0.6% of the piles cross section area.Comparing Fig. 3a with Fig. 3b, which shows the bending moments envelope, it can be concluded that the last excavation phase is dominant in the majority of the sections, particularly with regard to positive moments.Failure ratio (q f /q a ) R f 0.9 -*The dilatancy angle was considered as Y = f' -30.This situation is typical of cases where the prestress forces are correctly designed.It is also important to underline that these variations are modest, validating the hypothesis that the prestress forces are reasonably adequate.

Parameters studied
The object of the parametric study are excavations in geotechnical conditions similar to those described in 2.1, with a retaining structure analogous to that in Fig. 1.The effects of a few parameters with proved influence on the behaviour of the excavation are analysed.Table 2 presents the various parameters of this study, as well as the respective symbols.To facilitate the comparison between different excavations, some parameters were made dimensionless.
Two of the parameters may not be so familiar to the reader: the prestressing index and the support system stiffness index.
The prestressing index (x) measures, in a dimensionless form, the horizontal force applied to the wall by the   grid of anchors.Therefore, the prestress force to be applied to each anchor, F a , is defined by the equation: where x represents the prestressing index, g represents the soil unit weight, h represents the maximum excavation depth, h a and l a represent the average height and width of influence of each anchor, respectively, and a the tilt angle of the anchors.The influence height for the first level of anchors extends up to the surface and the influence height for the last level of anchors extends to the bottom of the excavation.
In structures supported by various levels of prestressed anchors or struts, the stiffness of the support system, r s , was defined by Mana (1978) as: where EI represents the wall bending stiffness and h M represents the maximum vertical spacing between consecutive supports.For this purpose, the soil below the base of the excavation acts as an additional support, located exactly at the base of the excavation.This definition of support system stiffness index is based on Goldberg et al. (1976), introducing additionally the soil unit weight, in order to make the parameter dimensionless.There are other alternatives to evaluate the stiffness of the support structure, such as the flexibility number in terms of displacements, defined by Addenbrooke et al. (2000), but since it is not dimensionless, it is discarded in favour of the definition of Mana (1978).

Designation and organization of the calculations
In the parametric study 158 calculations were performed.The designation of each of the calculations, as shown in Fig. 5, consists of three characters: the first corresponds to the series, the second to a certain parameter (subseries) and the third is an id of the calculation, corresponding to a predefined value of the parameter under study.
Each series corresponds to a particular set of calculations, created from the same base excavation.Comparing any calculation to the base excavation of the corresponding series, only one parameter differs.Each series consists of subgroups designated subseries.A subseries is a set of calculations (varying in number from four to six) where all parameters, except the parameter under study, remain constant.
The study begins by defining a base excavation, called #A00, which was presented in 2.1.This is the starting point of the series #A**.In parallel, three additional base excavations are defined, #B00, #C00 and D00, whose main characteristics are listed in Table 3.
Regarding the stiffness of the support system, the adopted values, between 100 and 350, correspond to a retaining structure constituted by 0.60 m and 0.80 m diameter piles, with spacing between, respectively, 1.20 m and 1.10 m.These values of the support system stiffness index can also correspond to diaphragm walls 0.40 m and 0.60 m thick.
The use of these four series has the intention of checking the validity of the influence curves, derived from each subseries, when taking different starting points in terms of geometry, prestress, stiffness of the support system and soil properties.As shown in Fig. 6  spond to two geotechnical scenarios and two different geometries and wall properties.
The subseries correspond to the variation of a particular parameter, of the soil or of the wall, according to Table 4.A maximum of 6 calculations was performed for each parameter, with a total of 158 different calculations.
For each subseries, several calculations were performed varying the parameter under study within reasonable limits.As an example, Table 5 presents the variation of the bedrock depth for the subseries # A1*.It involved five additional calculations, besides the base excavation #A00, in a total of six calculations with different values for the bedrock depth.

Normalization procedure
The variables of the parametric study on which the attention is focused have, above all, a practical interest: maximum bending moment in the wall, maximum force on the anchors and maximum horizontal wall and surface displacements.
The analysis of the calculations of a given subseries is not particularly problematic, since among the various calculations of that subseries only one parameter is changed.Therefore the differences in the results are a direct consequence of the changes in the parameter under study.However, when the calculations of two or more subseries are being compared, there are always differences in several parameters.These differences create difficulties when trying to determine the influence of a certain parameter.Hence, it is necessary to separate the effects of the parameters.
Taking as an example Fig. 7a, it can be noticed the difficulty in drawing conclusions about the influence of the maximum excavation depth on the maximum horizontal displacements of the wall.
To improve the comparability of results for the various subseries, a normalization procedure was introduced, defining a reference value for the variable under analysis.Thus, the maximum horizontal displacement of the wall, obtained in each calculation is divided by the maximum horizontal displacement obtained in the reference excavation of each subseries.This procedure consists, in its essence, in changing the vertical scale, so that the results of the several subseries intersect at a common point.
Figure 7b illustrates the normalization procedure using the data represented in Fig. 7a.The 15 m deep excavation has been taken as reference.To understand the effect of normalization attention should be given to the changes in the vertical scale.With these changes it is no longer possible to obtain from the figure an absolute value of the wall horizontal displacement.However, Fig. 7b allows determining the variation of the wall horizontal displacement as a consequence of the changes in the excavation depth.In this example, it can be verified that the increase of the maximum excavation depth from 15 m to 25 m causes an increase of the maximum horizontal displacement of the wall varying from 150% to 250%, depending on the subseries under study.
After normalization of the results, it is possible to use the method of least squares to define a function that best fits the results of several subseries, designated in this example b h .A few types of functions were considered: linear, quadratic, exponential, logarithmic and power.In each case, the function type selected was the one leading to the best correlation coefficient.
This normalization procedure was performed for all parameters of the study, both for the maximum wall bending moments and horizontal displacements.Figures 8 to 15 present the main results of the parametric study.Each figure has two graphs, corresponding to the maximum bending moment of the wall, on the left, and to the maximum horizontal displacement of the wall, on the right.To facilitate the understanding and future use of the results, the previously presented normalization procedure was applied to all the results.
All graphs comprise four curves, corresponding to the variation of each parameter from the four base excavations.An additional curve, a i or b i , was added, corresponding to the least squares approximation of all the calculations in the graph.The Greek letter a was used to denote the curve that best fits the normalized maximum bending moments, whereas the Greek letter b was used to denote the curve that best approximates the normalized maximum horizontal displacements of the wall.In each graph the mathematical equation and the correlation coefficient, R 2 , are displayed.
In general, for all the parameters it was possible to establish two curves, a and b, which approximate the results of the several subseries with reasonable accuracy, allowing the definition of the influence factor for each parameter on the maximum horizontal displacements and the maximum bending moments of the wall.In most cases the correlation coefficients, R 2 , are higher than 0.90, although presenting smaller values in a few particular situations.
The        moments, as illustrated by Fig. 9a, due to the fact that the considered factor is highly influenced by the adopted geotechnical scenario.In the calculations belonging to the subseries #A2 and #C2, increasing the prestressing index from 0.1 to 0.3 leads, in both cases, to reductions in the maximum bending moment close to 25%.In the calculations belonging to subseries #B2 and #D2, the same increase in the prestressing index has a very discrete influence on the maximum bending moment of the wall, leading to its slight increase.A detailed analysis of these results showed that this difference in behaviour is mainly due to the soil strength.The less resistant and stiff the soil is, the more favourable the prestressing.This effect is also found when analysing the maximum horizontal displacements of the wall, although with less intensity.Figure 9b shows that variations in the prestressing index have greater influence on excavations executed in less resistant and more deformable soils.
Table 6 summarizes the results of the parametric study, indicating the degree of importance of each parameter with regard to the maximum wall bending moment and horizontal displacement.Some of the parameters where classified as having moderate influence, by not having a particular influence over the analysed results.
The effect of the studied parameters on the maximum bending moment may be quite distinct from its effect on the maximum displacement.The best example of this fact is the support system stiffness index, which has a moderate influence on the displacement but considerably affects the maximum bending moment.Moreover, the support system stiffness index influences the displacement and the bending moments in opposite ways, as shown in Fig. 10.
During the parametric study of the different variables, in addition to the stresses and displacements of the wall, surface ground displacements were also calculated.A strong correlation between the displacements of the wall and the ground surface displacements was noticed.
In Fig. 16, where the maximum horizontal displacements of the ground surface are plotted against the maximum horizontal displacements of the wall, it becomes clear that the former are approximately half of the latter.Despite the large amount of calculations, based on quite diverse geotechnical conditions and different excavation geometries, the results show a significant consistency, as is proved by the high correlation coefficient obtained using the method of the least squares and assuming that the value at the origin is null.
The good correlation between the maximum horizontal surface displacements and the maximum horizontal wall displacements allows the use of the equation presented in Fig. 16 to estimate the former, at least for preliminary design situations.
Figure 17 shows a histogram indicating the variations of the force in the ground anchors, calculated as a percentage of the prestress force applied.Note that only one value -Grows with parameter increase; ¯-Reduces with parameter increase.per excavation is shown, corresponding to the most stressed anchor.In the majority of the excavations increments of 10% to 20% were obtained.
Regarding this point, calculation #C21 is in fact a singular case, by having a maximum increase of the anchor force of 57%.This abnormally high value is due to the small prestress used, corresponding to 0.1 g h, in conjunction with not so favourable geotechnical conditions.These facts lead to high stresses and large wall displacements, corresponding to a scenario in which the design could be considered inappropriate.

Conclusions
The parametric study aims to be a contribution towards understanding the effect of some of the variables that rule the behaviour of anchored retaining walls and their interaction with the supported ground.
The influence laws for each parameter and the results of all performed calculations allow a preliminary evaluation of the behaviour of anchored excavations.
On average, it appears that the maximum wall bending moment increases when the bedrock depth increases, the prestressing index reduces, the support system stiffness index increases, the maximum excavation depth increases, the soil stiffness decreases, the friction angle and soil cohesion decrease and the coefficient of earth pressure at rest increases.The parameter that most affects the maximum bending moment of the wall is the stiffness of the support system.
Concerning the maximum horizontal displacement of the wall, it was found that it increases when both the bedrock depth and the maximum excavation depth increase, the prestressing index and the support system stiffness index reduce, the friction angle and soil cohesion decrease and the coefficient of earth pressure at rest increases.The maximum excavation depth is particularly important in controlling the maximum horizontal displacement of the wall.
The comparative study of the maximum horizontal displacements of the wall vs. the maximum horizontal surface displacements allows concluding that the former can be estimated from the latter within a quite reasonable degree of confidence.
The overall attained results seem to be quite satisfactory, contributing to an alternative and economic method for the preliminary design of anchored retaining structures, to be presented in a companion paper.

Appendix: Hardening Soil Model
In this appendix a brief description of the hardening soil model is presented.Detailed information about this soil model can be found in Brinkgreve (2002).
In most geotechnical problems, there is usually reasonable information about the soil strength parameters, but reduced information concerning its stiffness.This situation results, fundamentally, from the complexity of the stressstrain relations of the soils, in particular the dependence of soil stiffness on the confining stress, the stress path and the strain level (Topa Gomes, 2009;Viana da Fonseca, 2003).
For the reasons listed above, it becomes difficult to establish a single stiffness that can be used in an elastic perfectly plastic constitutive model.In geotechnical problems such as the ones studied in this work, the hardening soil model has the ability to simulate the soil behaviour much closer to reality, especially when referring to the simulation of loading and unloading cycles due to successive excavation and anchor prestressing stages.Being an elastoplastic model, its yield surface is not fixed in the principal stress space.During the expansion of the yield surface, irreversible plastic deformation occurs.
Distinction can be made between two main types of hardening, namely shear hardening and compression hardening.Shear hardening is used to model plastic strains due to primary deviatoric loading.Compression hardening is used to model plastic strains due to primary compression in oedometer loading and isotropic loading.Both types of hardening are contained in the hardening soil model (Brinkgreve, 2002).
When subjected to primary deviatoric loading, soil shows decreasing stiffness and, simultaneously, irreversible plastic strains develop.In the special case of a drained triaxial test, the observed relationship between the axial strain (e 1 ) and the deviatoric stress (q) can be reasonably approximated by a hyperbola.Such a relationship, initially formulated by Kondner (1963) and Kondner & Zelasko (1963), was later used in the well-known hyperbolic model by Duncan & Chang (1970).The hardening soil model, however, supersedes the hyperbolic model in three relevant issues (Brinkgreve, 2002): i) it uses the theory of plasticity, rather than the theory of elasticity; ii) it includes soil dilatancy; iii) it introduces the yield cap, which corresponds to compression yielding, and creates a closed elastic region.
Among the main characteristics of this constitutive model, the following should be highlighted: i) the ability to change soil stiffness according to the confining stress (by means of the input parameter m); ii) the consideration of plastic deformations caused by shear stress (E 50 ); iii) the consideration of plastic deformations caused by isotropic stress (E oed ); iv) the use of different values for soil stiffness according to the stress path (for unloading and reloading E ur and v ur are used instead of the stiffness parameters listed above); v) the use of an yield criterion according to Mohr-Coulomb (c' and f'); vi) the control of the yield surface by means of the dilatancy angle (Y').
In a drained triaxial test, during primary loading, the relationship between axial strain (e 1 ) and deviatoric stress (q), illustrated by Fig. 18, can be described by the following equation: where q a represents the asymptote of the hyperbola and q f the maximum deviatoric stress (yield stress obtained in the test).Calculating the derivative of Eq. ( 3) with respect to q, results in an initial Young modulus of 2E 50 .
The value of q f can be derived from the Mohr-Coulomb failure criterion: When the deviatoric stress equals q f , the yield stress is reached and perfectly plastic flow occurs, as described by the Mohr-Coulomb criterion.The ratio between the ultimate deviatoric stress, q f , and the hyperbola asymptote, q a , determines the input parameter R f .In cases where there are not enough tests to estimate this parameter, Brinkgreve (2002) suggests the use of 0.9.
The secant Young modulus (E 50 ) for a deviatoric stress equal to one half of q f depends on the confining stress s' 3 .It can be calculated by the equation: where E ref 50 is the reference Young modulus of the soil in primary loading, determined for a confining pressure p' ref , which is usually 100 kPa.It should be noted that in Eqs. ( 4) and (5) the value s' 3 is positive for compressive stress, consistent with the usual Soil Mechanics sign convention.
The dependency of E 50 with respect to the stress level is given by the exponent m.This parameter can be considered equal to 1.0 for soft clayey soils.In numerous studies performed over sands and silts, this parameter ranges between 0.5 and 1.0 (Von Soos, 1990).In the case of Porto granite residual soils, values of m between 0.5 and 0.6 are common (Topa Gomes, 2009;Viana da Fonseca, 2003).
To reproduce the soil behaviour during loading and unloading cycles, the hardening soil model uses different stiffness parameters, depending whether it is a primary loading or a reloading stress path.This is a great improvement when compared to simpler soil models.The dependency of the Young modulus for unloading or reloading, E ur , upon the confining pressure p' ref , is expressed by the following equation: The hardening soil model allows an independent control of distortional and volumetric strain.This variable is controlled by the tangent oedometer modulus, given by:

Figure 2 -
Figure 2 -Displacements of the wall and ground surface at the end of the excavation.

Figure
Figure 4a shows the apparent earth pressure diagram, constructed from the horizontal projections of the anchor forces obtained at the end of the excavation works.This diagram is quite similar to the applied prestress diagram, although slightly higher.Figure 4b allows analyzing the evolution of the forces in the anchors during the various construction stages.The forces are represented as a percentage of the applied prestress.Without exception, these forces increase in excavation phases and decrease in stages where prestress forces are applied to the anchors below.

Figure 4 -
Figure 4 -Anchor forces: a) apparent earth pressures at the end of the excavation; b) anchor forces variation during construction.

Figure 7 -
Figure 7 -Influence of excavation depth on the wall horizontal movements: a) results before normalization; b) results after normalization.
most puzzling situation occurs regarding the influence factor of the prestressing index on the wall bending Soils and Rocks, São Paulo, 40(3): 229-242, September-December, 2017.Raposo et al.

Figure 8 -
Figure 8 -Influence of bedrock depth: a) maximum bending moments; b) maximum horizontal displacements of the wall.

Figure 9 -
Figure 9 -Influence of prestressing index: a) maximum bending moments; b) maximum horizontal displacements of the wall.

Figure 11 -
Figure 11 -Influence of maximum excavation depth: a) maximum bending moments; b) maximum horizontal displacements of the wall.

Figure 12 -
Figure 12 -Influence of soil stiffness: a) maximum bending moments; b) maximum horizontal displacements of the wall.

Figure 13 -
Figure 13 -Influence of soil effective friction angle: a) maximum bending moments; b) maximum horizontal displacements of the wall.

Figure 14 -
Figure 14 -Influence of soil effective cohesion: a) maximum bending moments; b) maximum horizontal displacements of the wall.

Figure 15 -
Figure 15 -Influence of soil coefficient of earth pressure at rest: a) maximum bending moments; b) maximum horizontal displacements of the wall.

Figure 16 -
Figure 16 -Maximum horizontal surface movements vs. maximum horizontal displacements of the wall.

Figure 17 -
Figure 17 -Histogram with the variation of anchor forces, as a percentage of prestressing force (sample: 158 excavations).
ref is the reference Young modulus of the soil in an unloading or reloading stress path, determined for a confining pressure p' ref .
ref is the reference oedometer Young modulus, determined for a confining pressure p' ref , as shown in Fig.19.In this case s' 1 is used instead of s' 3 , since this is the only principal stress controlled.

Figure 18 -
Figure18-Hyperbolic stress-strain relation in primary loading for a standard drained triaxial test, adapted fromBrinkgreve (2002).Figure19-Definition of E oed ref in oedometer test results.

Figure 19 -
Figure18-Hyperbolic stress-strain relation in primary loading for a standard drained triaxial test, adapted fromBrinkgreve (2002).Figure19-Definition of E oed ref in oedometer test results.

Table 1 -
Parameters considered in the base excavation #A00.

Table 6 -
Degree and type of influence of the several parameters over bending moments and horizontal wall displacements.
A -Very important; B -Important; C -Moderate.