Measurement in a Sand Using Back Volume Change

An experimental technique, using a computer controlled triaxial test to evaluate the coefficient of earth pressure at rest, K0, is presented. The method does not require the use of any radial measurement transducers and is free from any side friction effects, typical of oedometer testing. It uses commercial software (GDSlab) which applies ramps of radial stress with back volume measurement, ensuring that the diameter change remains zero. The method is applicable only to saturated specimens in drained conditions. The equipment used is briefly described, as well as the testing procedure. Results of a laboratory test, on a granular material, applying a loading-unloading-reloading condition, are presented, and the relation of K0 with OCR (overconsolidation ratio) is investigated. The experimental results are compared with empirical equations given by other publications, suggesting the adequacy of this test method to determine K0 either in normally consolidated or overconsolidated stress paths.


Introduction
The deposition of soils has a history of one-dimensional deformation in the vertical direction with zero lateral strains.When the soil gets unloaded, due to erosion of overlying strata, it follows also a one dimensional path.The coefficient of earth pressure at rest, K 0 , where there has been no lateral strain within the ground, refers to effective stresses, as: where: s' 3 is the effective radial stress; s' 1 is the effective axial stress.
In fact, each state of deformation of a soil, during one dimensional normal compression, is essentially similar to all the preceding states and, if the soil is normally consolidated, the effective stress states have the same similarity.The value of K 0 is then found to be a constant (Wood, 1990).Therefore, in normally consolidated soils at any stress state not smaller than in situ one, the undisturbed initial stress state can be known measuring K 0 (Lirer et al., 2011).
The importance of estimating K 0 for predicting the initial conditions for soil/water coupled finite element analysis of geotechnical structures has been emphasized by a number of researchers that used either analytical correlations or experimental evidence to measure K 0 .They recognized that the K 0 -values of normally consolidated soils ( ) K NC 0 could be well estimated from the Jaky's equation: where f' is the effective angle of internal friction.
Some of them also studied the coefficient of earth pressure at rest in overconsolidated soils and, based on experimental evidence, they found that K 0 is typically represented as a function of OCR (overconsolidation ratio), by an empirical relationship in the form: where a is an exponent (a £ 1) proposed in previous publications, as follows.Mayne and Kulhawy (1982) suggested, for granular materials, that usually a = sin f'.Meyerhoff (1976), cited by Hanna et al. (2008), suggested that a should be equal to 0.5.Hanna et al. (2008) suggested a = sinf' -0.18.Lirer et al. (2011) tested two coarse grained materials and, in an over consolidated stress path, they found a = 0.6.K 0 can be determined by either laboratory or in-situ tests.The in-situ methods gave some variations due to many uncertainties related to the sensitivity of K 0 value to the small disturbance caused by inserting the probe into the ground.Laboratory test methods that have been published fall into two distinct classes (Teerachaikulpanich et al., 2007): rigid lateral boundary and flexible lateral boundary.The first one allows the required zero lateral strain but also allows undefined friction between the wall and the soil.The second has no side friction but requires a feedback system to control the soil specimen to achieve zero lateral strain.
This paper focuses on a laboratory test for determination of K 0 by means of a triaxial cell (flexible lateral boundary) with back volume change control ensuring that the cross section area remains constant.K 0 consolidation tests were performed in a consecutive loading-unloading-reloading cycle and it was clarified the influence of OCR on the K 0 -values.

Testing equipment
The most conventional and simple laboratory test to measure K 0 is the method where a specimen is confined in an oedometer ring, with a rigid boundary, instrumented in order to measure the lateral stresses.In these methods, the wall friction of the ring may induce some effects on measured K 0 -values (Okochi and Tatsuoka, 1984).In order to avoid such effects, many previous publications refer the use of a triaxial cell with its flexible lateral boundary around the specimen.This method uses a feedback system to maintain the boundary in position in a condition of null radial strain (Teerachaikulpanich et al., 2007).The most popular method of measuring K 0 by this technique is loading axially a sample in a triaxial cell and continuously adjusting the cell pressure with an automated system, in order to maintain the zero lateral strain condition.This requires accurate strain measurements, with local radial strain measurement devices, provided that the sample is saturated and is deforming uniformly (Lo and Chu, 1991;Piriyakul and Haegeman, 2005).
But there are alternative methods of determining K 0 in a triaxial test, without the need of radial measurement transducers.These require controlling the incremental ratio between volumetric and axial strain, in order to obtain e v /e 1 = 1 (where e v and e 1 are, respectively, the volumetric and axial strains).This can be accomplished by strain path (Menzies, 1988;Lo and Chu, 1991;Eliadorani et al., 2005), provided that the volume change in the pore water duct be always equal to the volume of axial deformation times the original average cross-sectional area.This paper presents a method of determining K 0 in a common triaxial system, with back volume measurement, without the requirement of any special local instrumentation to give feedback on lateral strain, based on a stress path test.
The equipment used to perform K 0 triaxial tests is a computer controlled system, which controls two GDS digital pressure/volume controllers, a submersible internal load cell and a 50 kN servo-hydraulic load frame, as shown in Fig. 1.Each pressure/volume controller regulates accurately both pressure and volume change of de-aired water supplied either to the triaxial cell or to the interior of the specimen.The submersible load cell measures the axial load acting on the specimen and has a capacity of 16 kN.Pore water pressure is measured with a pressure transducer and the axial displacement is also monitored externally with an LVDT.
It is used a commercial software, GDSLAB, to control the K 0 stress path tests, using a ramp of radial stress with back volume change measurement.On a saturated specimen, the test begins with an imposed radial stress ramp, with a certain loading rate chosen to ensure drained conditions.The volume change of the sample is extracted out of the back-pressure controller and, in order to guarantee zero radial strain increment (e 1 = e v ), each axial displacement (DH) is calculated, as follows: where H 0 is the initial height of the sample and e v is the volumetric strain.
To ensure the new required specimen height, the system applies the necessary velocity to the load frame inducing a new axial stress on the load cell.As shown in Fig. 2, during the test, radial stress is a perfect ramp, while axial stress and axial strain have to adjust automatically during the test.
Several continuous plots given by the software, during the test, enable the detection of any slight out of control.The loading rate of the radial stress ramp had to be deter-  mined by trial, so that only negligible excess pore water pressures develop in the specimen.This was accomplished subjecting a specimen to successively faster rates of loading, until an excess of pore water pressure began to develop in the specimen.This was taken as the satisfactory loading rate for the ramp of radial stress.
An over-consolidated condition can be simulated by loading the sample to a pre-consolidation axial stress and then unload (and reload if it is the case) along a stress-path to the target radial stress.

Material and testing procedures
The material used in this study is the Toyoura sand, which is an uniform, clean and fine sand having an uniformity coefficient, C u = 1.46, a specific gravity, G = 2.65 and a maximum and minimum void ratios, e max = 0.977 and e min = 0.597, respectively.
Triaxial specimens of Toyoura sand, having 70 mm of nominal diameter and 134 mm of height, were reconstituted by tamping.The sand was compacted in four layers in a mold, by tamping manually with a rod which has a foot with a 66 mm of diameter.The tamping was adjusted to the desired target density.The void ratio achieved was e 0 = 0.7.
Following the reconstitution, a vacuum of 10 kPa was applied to the specimen when removing the mold.Saturation was accomplished, firstly by flushing the specimen with carbon dioxide for approximately 15 min, after which de-aired water was added to the bottom of the specimen to circulate through the drainage line.Afterwards, a linear increase of the cell and back pressures was applied till it was reached a B-value of 96%.The sample was considered fully saturated and reached an equilibrium state when, after consolidation, there was no excess of pore water pressures.The effective stress state, prior to initiating K 0 test, was hydrostatic, that is, p' 0 = 20 kPa.
After setting up the triaxial cell in the loading frame, a K 0 test was conducted as explained above.The radial stress ramps tested are shown in Table 1, all of them performed at a stress rate of 6 kPa/h.The sample was loaded, then unloaded and reloaded again, along stress-paths targeting the radial stresses.Because of this system requirement, it is only possible to obtain the exact value of OCR, after the test is complete.The value of OCR is given by s' 1 / s' p , being s' p the effective axial stress at which unloading initiates (Table 1).

Validation
The applied radial stresses and the correspondent vertical effective stresses are shown in Fig. 3 for the entire test.It can be seen that radial stress-paths performed perfect ramps, while axial stress-paths have adjusted their values, not only during loading, but during unloading and reloading.
Figure 4 shows the evolution of the ratio e 3 /e 1 during the K 0 test, where e 3 is the radial strain.It may be noted that, as soon as this strain ratio falls below about 2%, the approach to the K 0 state appears virtually complete.
Other verifications of the K 0 condition with this technique are shown in Figs. 5 and 6.In Fig. 5, the area change is not greater than 0.2% during whole test.Figure 6 shows the pore water pressure developed during the test, which indicates that the test was clearly drained.
The plot of the void ratio against the effective vertical stress is shown in Fig. 7.It presents typical stress paths for both normally consolidated and over consolidated conditions.It clearly shows that after an unload-reload cycle (after s' 1 = 520 kPa), the reload stress path merges back on to the normal consolidated path.

K 0 values
With the technique used validated, it can be seen from the results presented in Fig. 8 that the stress path followed a more or less linear pattern during normally consolidated conditions and followed a curve during overconsolidated Soils and Rocks, São Paulo, 38(1): 3-8, January-April, 2015.5 K 0 Measurement in a Sand Using Back Volume Change  conditions.The ratio s' 3 / s' 1 is the value of K 0 , which is independent of s' 1 , during the first load.This is more clearly shown in Fig. 9, where the variation of K 0 vs. s' 1 is presented.Initially, K 0 is significantly affected by isotropic consolidation but it reduces rapidly from its initial value of 1.0, to a constant value of 0.38.During unload and reload the soil is in an over-consolidated condition where K 0 depends on the effective vertical stress.However, during reloading, K 0 seems to be again independent of s' 1 for values of s' 1 greater than 520 kPa, the pre-consolidation pressure (s' p ), following a straight line.
In Fig. 9 it can be also seen that the maximum value of K 0 reached in the test is about 0.9.
In Fig. 10 it is possible to observe the trend of K 0 in relation to different values of OCR for unloading and reloading test data.
It appears that exists a unique K 0 -OCR relationship for unloading and reloading, at least for the values of OCR tested.
The relationship obtained is of the type: As it can be seen in the same Fig. 10, the value obtained for the exponent a is about 0.4.

Comparison of the test results with previous publications
During first loading the coefficient of earth pressure at rest of 0.38 is in agreement with the theoretical values given by the Jaky's equation.In fact, a drained triaxial com-   pression test, carried out after the anisotropic consolidation, gave a f' value near 38°.
During unloading and reloading, as already seen in Fig. 10, the equation is similar to the one obtained by other publications.
Figure 11 has a comparison with previous proposals referred in item 1, for different values of a, for overconsolidated soils.These correlations, for K NC 0 038 = ., gave K 0 values higher than the experimental study where the trend resembles the most with the empirical correlation presented by Hanna et al. (2008).

Conclusions
The K 0 laboratory test carried out in this study, using a triaxial stress path test, with back volume measurement to constantly adjusting the axial stress, showed that this method can be used to determine K 0 value in normally consolidated and overconsolidated conditions.K 0 value is estimated with an anisotropic consolidation, keeping a constant ramp of radial stress and constantly adjusting the axial stress on the load frame by means of a computer control.
Before starting K 0 test, the specimen must be in equilibrium, i.e., fully saturated and consolidated with no excess of pore water pressures.
During the K 0 test, the maximum radial strain of the sample was kept into acceptable values, with e 3 /e 1 < 2%.Also the negligible excess of pore water pressures developed indicated that the test was clearly drained.
The relation between radial effective stresses and axial effective stresses gave a straight line during the first load.The estimated K 0 value was 0.38, clearly similar to the one obtained from Jacky's formula for this soil.
The K 0 values during unload and reload increased with the increase of OCR.For the stress state tested, it was found an empirical correlation similar to the one found in previous publications, Eq. ( 3) with a = 0.447.From the test results it can be concluded that the method used in this work to determine K 0 is practical enough for both normally and overconsolidated soils.

Figure 2 -
Figure 2 -Ramps of radial and axial stresses and axial strain.

Figure 3 -
Figure 3 -Effective stress paths during the test.

Figure 6 -
Figure6-Excess of pore water pressure developed during the K 0 test.

Figure 5 -
Figure 5 -Variation the area of the specimen during the K 0 test.

Figure 4 -
Figure 4 -Evolution of the ratio e 3 /e 1 with s' 1 during the K 0 test.

Figure 7 -
Figure 7 -Relation between axial strain and axial effective stress during all stages of K 0 test.

Figure 10 -
Figure 10 -K 0 vs. OCR for the stress paths: unload-reload.Figure 11 -Comparison of K 0 values with other publications.