Density-Dependent Pore Water Pressure Evolution in a Simplified Cyclic Shear Test

When specimens of different sands are produced using the same preparation method and sheared under the same conditions (consolidation stress, loading, etc.), while simultaneously keeping the drainage closed, the resulting tendencies of these sands regarding the PWP build-up will be different. This research paper presents a simplified cyclic shear test, which is used to evaluate the accumulation of PWP in sands under defined specimen preparation procedure and testing conditions. In the proposed experiment, a comparison of different sands with this respect is easily achieved. The principle of this experimental method is based on the evolution of the PWP during cyclic shearing of a water-saturated sand sample. Undrained conditions during the experiment allow for the evolution of the PWP, which is quantified by the rate of the PWP build-up. The duration of a single cyclic shear test, including specimen preparation, is approximately 30 min. The evaluation of the rate of the PWP build-up for different densities resulted in an exponential dependence of the PWP build-up on the variation of the relative density. The results confirmed a higher generation of PWP in a fine sand compared to a coarse sand. A comparison with the results of undrained cyclic triaxial tests in the case of eight different sands demonstrated a good agreement between both experimental methods. The basis for the comparison was the density-dependent evolution of PWP in these methods. The presented method delivers a value (index) that quantifies the PWP build-up in sands under the defined testing conditions.


Introduction
The mechanical behaviour of coarse-grained soils depends particularly on effective stress and relative density. Loose soils tend to be densified when sheared, while dense soils decrease their density. Densification of loose, saturated soils occurs through the expulsion of pore water. Depending on the soil permeability and loading rate, the tendency for densification can lead to the generation of pore water pressure (PWP). The generation of PWP in loose coarse-grained soils during shearing is most commonly associated with the phenomenon of soil liquefaction.
The laboratory investigations of the PWP build-up usually include testing of specimens with different initial densities, stress levels and load amplitudes in undrained cyclic triaxial tests [1][2][3][4][5][6][7] and undrained cyclic simple shear tests [7][8][9][10]. Different criteria are used for performing the experiments and for the evaluation and interpretation of the test results [1,3,11]. These experiments are complicated, time-consuming and require a high level of professional experience and expertise. Furthermore, there is no unique testing procedure that would enable a comparison of the test results for the same initial conditions. Both previously mentioned experimental approaches are far from being easy and effective in a short time. The present research is devoted to a fast and simple method for testing density-dependent PWP build-up. A simplified method, such as the one here described, would increase efficiency and flexibility during soil testing and PWP build-up evaluation. This can be useful, especially in regions with high variability in soil properties, such as flooded man-made open pit dumps, e.g. in Lusatia, Germany.
It is generally known that sands have the highest tendency to soil liquefaction. The granulometric properties (grain size distribution, grain shape and roughness) are the most important but not the only influencing factors. The role of stress-dependent relative density and soil structure in soil liquefaction is undisputed [3,6,[12][13][14][15][16][17][18][19][20][21][22][23][24]. In order not to mix the influence of different factors, it would be useful to eliminate the variation of the soil structure by using a strictly defined specimen preparation procedure. On this basis, a very similar soil structure is obtained for different sands, which enables the testing of the effect of the density variation on the PWP generation.
After the specimen preparation via a defined procedure, the soil state is the same for different sands. Although a similar soil structure is produced in soil specimens, due to their different granulometric properties, different relative densities after the specimen installation are obtained. Regardless of these differences, using the installation method decribed in the sequel, the initial state of each sand corresponds to the loosest possible packing under the installation conditions. Under the same testing conditions (soil structure, loading amplitude, stress level), the PWP build-up of different sands due to the varying relative densities will be different, which can be attributed to different soil granulometries. A clear analogy to the classical index tests (e. g. determination of the liquid or plastic limit for fine-grained soils) can be seen here. If only one factor is changed while keeping all others the same, it is possible to determine the soil's tendency towards the relevant factor and quantify it with an index value. When assessing the tendency for PWP build-up (often related to soil liquefaction), it is reasonable to vary the relative density.
Obviously, such a method works with disturbed soil specimens and cannot provide a direct assessment of the in-situ state. It delivers a dependence of the PWP build-up with regard to relative density and thus enables an easy comparison of different sands in this respect.
The presented method using a so-called PWP Tester aims to establish a simple (index) test that enables a comparison of density dependent PWP build-up in different coarse-grained soils while being prepared and tested under the same conditions. A comprehensive experimental study, including the determination of the grain shape and surface roughness for different sands, is planned as a part of future research. As the PWP build-up strongly depends on the grain shape and surface roughness, it should also be possible to use the results of this method in order to draw conclusions about different particle morphologies with the same particle size distributions. Such a routine determination of the grain shape and surface roughness could become an alternative application of the test.

Tested Materials
Nine different sands were used in this research study. The grain size distribution curves of these sands can be taken from Fig. 1, while the classification properties are summarised in Table 1. All sands have narrow grain size distribution curves with C U < 5. Sand HS is known as Hostun sand, a reference sand widely used, which has been extensively tested by other researchers [25][26][27][28]. Sand W6 is known as Karlsruhe fine sand in the literature. An experimental database with both monotonic and cyclic tests on this sand can be taken from [4,5]. Sand W3 can be found in the literature as Karlsruhe sand [6,24]. The remaining six sands, W1, Two different experimental studies were performed with the above described sands. During the first study, Hostun sand (HS) and Karlsruhe fine sand (W6), as well as sands W1 and W9 were used for a detailed testing and analysis of the dependence of the PWP build-up and the relative density. The results of the first study are discussed in Section "Comparison of different sands". The second comparative study had the aim of validating the newly developed procedure using the results of undrained cyclic triaxial tests (see Section "Comparison with cyclic triaxial tests"). For this purpose, eight W-sands were tested. Testing programme is summarised in Table 4 (see Appendix A).

PWP Tester
The principle of the presented cyclic shear test is based on the evolution of the PWP in a saturated sand specimen during a constant volume cyclic shearing. The testing device is called a "PWP Tester". The testing procedure involves a fast and reproducible installation of fully saturated cylindrical specimens without an additional saturation phase and the application of back pressure. The specimen is loaded cyclically at its top boundary. The top cap is displaced horizontally with a controlled constant frequency and amplitude. Because of undrained conditions during the test, the PWP rises with the number of loading cycles. The tendency of a coarse-grained soil to soil liquefaction under clearly defined initial and loading conditions is expressed through the rate of the PWP build-up.

Specimen Preparation
Prior to the specimen installation in the PWP Tester, dry sand is mixed with water and de-aired in a vacuum chamber.
During the entire specimen preparation phase, sand is completely submerged in water. Subsequently, the de-aired sand-water mixture is installed using a funnel into the rubber membrane that is supported by a cylindrical split mould. A vacuum is used to align the rubber membrane to the wall of the split mould (analogously to the preparation of the triaxial specimens). During installation, the funnel is slowly pulled upward while the fully saturated sand-water mixture continuously fills the specimen volume limited by the rubber membrane. The specimen preparation method described here ensures that the tested specimens are saturated without a saturation phase and saturation pressure. The degree of saturation, S r can be evaluated by determining the water content w of a sand specimen after the test (see Eq. 1) and ranges normally between 95 and 100 %.
Here, d is the dry density of the installed specimen, while s and w are the grain density and the density of water, respectively.
The dry density of soil after the specimen installation under water varies in the case of different sands as it depends on their granulometric properties. When compared to the conventional density limits d,min and d,max , the relative density after the described specimen installation and consolidation is mostly in the medium dense range. 1 However, regarding the installation procedure under water, this is the loosest possible state.
In a separate experimental study, 14 differently graded sands 2 were installed under water in a cylinder using a funnel and their densities and void ratios e max,w were determined. As it is shown in Fig. 2, the obtained void ratios were lower than the void ratios e max determined by pouring dry sand into a cylinder using a funnel according to the German standard [30]. Clearly, the void ratio obtained by installation under water is lower for each tested sand. This means that the presented preparation method yields the loosest state under water, even though the obtained density after the specimen installation lies in a medium dense range when related to the conventionally defined limiting soil densities (after [30]). It can be assumed that the same specimen installation procedure results in a similar soil structure for each sand, which, due to their differences in granulometric properties, is reflected in the different minimum densities under water. In order to obtain sand specimens with higher densities, tapping strokes on the sides of the split mould are applied. The dimensions of an installed and with the top cap sealed sand specimen are D∕H = 50/100 mm.

Consolidation and Cyclic Shearing
The PWP Tester is shown in Fig. 3. The effective stress after the specimen installation comes solely from the self-weight of the specimen and the top cap and can be neglected. The total stress results from the relative air pressure acting on the rubber membrane and stays unchanged and equal to p = 0 kPa during the entire test.
An isotropic consolidation of the sand specimen is achieved by applying suction (negative PWP u 0 ) at its bottom. This is realised via a volume-pressure controller. As the total stress equals to 0 kPa, the effective stress is increased by the value of the negative PWP, see Eq. 2.
Herein, compression stresses are considered as positive.
Finally, the consolidated sand specimen is cyclically moved at the top cap in a horizontal direction under undrained conditions (the valve to the volume-pressure controller remains closed). This form of specimen oscillation results in a deformation mode similar to a cyclic simple shear. The sinusoidal loading is applied at a defined amplitude A and frequency f. The horizontal displacement is applied by an electric step motor, where the rotational motion is converted into the translational (reciprocating) motion.
A steel cylinder with an eccentricity A to the rotational axis of the step motor is mounted on it and connected via a steel rod and a switch-releasable electromagnet to the soil specimen. In this way, by varying the steel cylinder's eccentricity, arbitrary amplitudes can be achieved within this setup. A constant loading amplitude is mechanically guaranteed and cannot be varied during the test. The loading frequency is kept constant by a PC control and is dependent on the performance of the step motor installed in the PWP Tester. The lowest possible frequency of the step motor currently installed in the PWP Tester is 0.01 Hz and the largest tested is 5 Hz.
The evolution of the PWP u in the specimen and the relative air pressure p around the specimen are measured and evaluated during the test. Furthermore, the horizontal displacement s h and the settlement of the top cap are measured contactless via two triangulation laser distance sensors. The duration of a single test, including the specimen installation, is ca. 30 min.
The experimental procedure can be divided into three phases (see Fig. 4). The first phase (1) corresponds to the installation of a saturated sand specimen. This phase is crucial for repeatable and plausible test results. After the specimen installation, both the effective and total stresses and the PWP are equal to 0 kPa ( p � = p = u ≈ 0 kPa). The second phase (2) includes the isotropic consolidation of the sand specimen, which is achieved by applying suction u 0 to the installed specimen. The total stress p remains equal to 0 kPa during this phase ( p � 0 = −u 0 ;p = 0 kPa). Finally, during the third phase (3), the sand specimen is loaded cyclically in undrained conditions. The total stress remains zero. As a result of the imposed cyclic loading, the PWP in the Fig. 2 Comparison of maximum void ratios determined after the installation under water and maximum void ratios in dry state (the notations in the X-axis denote the IDs of the tested sands, as in [29]) specimen rises which leads to a reduction of the effective stress ( Δu > 0kPa → Δp � < 0 kPa).
The test is terminated when the PWP reaches the value of the total stress. At this state, the specimen doesn't possess any stiffness due to zero effective stress. In Fig. 5, an exemplary PWP build-up (decrease in effective stress) in a cyclic shear test is plotted against the number of loading cycles N.
The results of the repeatability tests in the PWP Tester can be taken from Fig. 6. Obviously, there is a good correspondence between the initial relative density after the specimen installation and isotropic consolidation D r0 as well as the test outcome expressed through the number of cycles N. More details on the testing conditions and the material used in these tests can be found in [31].

Interpretation of the Cyclic Shear Test
A method that was previously described is suitable for a comparison of different sands because it has a strictly defined installation procedure and thus an identical initial state. When shearing different sands under the same conditions and varying only the density of the specimens, it is possible to assign a characteristic value to each sand based

Evaluation of a Single Cyclic Shear Test
An index test delivers an index (value) that characterises a certain property of the material. This cyclic shear test yields a dimensionless value that quantifies the average rate of the PWP build-up at a particular relative density. The measured PWP u is normalised with an initial value of the PWP, u 0 , to determine this dimensionless parameter. In the sum − u∕u 0 diagram, the rate of the PWP build-up, C l , is defined as a secant line to the normalised data curve (see Fig. 7). Here, sum is the summed shear strain imposed to the top cap of the soil specimen and can be calculated as the ratio between the summed horizontal displacement s sum h = ∑ �s h � and the initial height of the specimen H 0 , sum = s sum h ∕H 0 . This secant line is defined between 40 % and 80 % of the PWP build-up with respect to the initial value of the PWP. The determination of C l follows from Eq. 3.
The C l -value is a state variable, as it is dependent on the relative density, consolidation pressure, loading displacement, grain and contact orientations in the soil structure, etc. Sand with a higher C l -value at a certain relative density is more susceptible to the PWP build-up than sand with a lower C l -value at the same relative density when prepared and tested under the same conditions.
The choice of the range for the determination of C l has a very low impact on the outcome of the test evaluation. Still, the initial part and the final stage of the test should not be

Density-Dependent Rate of Pore Water Pressure Build-Up
An exemplary evolution of the PWP in test with different initial relative densities in shown in Fig. 8. Here, the initial relative densities are increasing from the lowest D r0,1 to the highest D r0,5 . Each test was evaluated according to the procedure described in Section "Evaluation of a single cyclic shear test". As a result, the relationship between the rate of the PWP build-up and relative density was obtained (see Fig. 9). These two state variables obviously have an exponential dependence.
The C l -values were logarithmically scaled to denote the dependence between D r0 and C l (Fig. 10). A regression coefficient k l can be calculated under the assumption of a linear regression between ln(C l ) and D r0 , and represents a unique parameter for each sand which quantifies the dependence between the rate of the PWP build-up and the relative density. The determination of k l follows from Eq. 4.
The k l -parameter represents a soil specific parameter, as it is strongly dependent on the soil's granulometric properties, e.g. grain size and shape. The resistance to the PWP build-up in a sand with a higher k l -parameter can be more effectively increased by densification than in a sand with a lower k l -parameter. A reference value of the rate of the PWP build-up C l,ref can be related to the reference value of the relative density D r0,ref . Taking into account k l and C l,ref , the rate of the PWP build-up can be determined for any arbitrary initial relative density (see Eq. 5).
This kind of test interpretation enables a comparison of the rate of the PWP build-up for different sands at various relative densities.

Exemplary Test Evalution on Hostun Sand
Several tests on Hostun sand specimens with different relative densities were performed in order to investigate the influence of the relative density on the evolution of PWP in the PWP Tester. All specimens were prepared according to the installation procedure described in Section "Specimen preparation". Further testing conditions are summarised in Table 2.
The evolution of the PWP in tests with different relative densities is shown in Fig. 11. The logarithmic scaling of the horizontal axis is used to better illustrate the PWP build-up in tests on specimens with low relative densities. As expected, the PWP evolves more slowly in soil of a higher relative density, and a larger number of loading cycles is needed to completely erase the effective stress.
The dependence of the rate of the PWP build-up on the initial relative density for Hostun Sand is given in Fig. 12. The relative density ranges between a loose packing with D r0 = 0.322 3 and a dense packing with D r0 = 0.734. Accordingly, C l has its maximum at 2.1 (for the loosest tested state) and its minimum at 0.02 (for the densest tested state).
A linearized dependence of the rate of the PWP buildup on the initial relative density for Hostun Sand can be taken from Fig. 13. The reference value of the initial relative

Comparison of Different Sands
Four different sands (HS, W1, W6 and W9) introduced in Section "Tested materials" were tested at different relative densities (specimen preparation method from Section "Specimen preparation") and evaluated according to the procedures in Sections "Evaluation of a single cyclic shear test" and "Density-dependent rate of pore water pressurebuildup". The testing conditions are summarised in Table 2.
Karlsruhe fine sand and Hostun sand are both clean sands, but Karlsruhe fine sand is much finer than Hostun sand. Therefore, it is reasonable to expect that the latter one has a higher resistance to the generation of the PWP [12,24,[32][33][34]. Sands W1 and W9 have almost identical grain size distribution curves and contain both a small amount of fines and a few fine gravel grains. Therefore, a similar PWP build-up is expected in the case of these two sands. The dependence between C l and D r0 for these sands is shown in Fig. 14.
To compare the sands, C l -values were calculated at a relative density of D r0 = 0.6 (see Fig. 15a). Obviously, the sand W9 has the highest rate of the PWP build-up at this relative density, while this rate is the lowest for Hostun sand. The remaining two sands lie between these two limiting cases and have very similar C l -values. A comparison of the rates of the PWP build-up at a relative density D r0 = 0.8 reveals a very slow accumulation of the PWP for all sands since all C l -values are quite low (Fig. 15b). As expected, the densification of the sand leads to a reduced PWP build-up. The reduction of the rate of the PWP build-up through soil densification is governed by the k l -parameter. The higher the k l -parameter is, the greater is the impact of the soil's densification on the reduction of the PWP build-up. Figure 16 shows a comparison of the k l -parameter for the four sands considered. The highest k l is obtained in the case of Hostun sand, indicating that the liquefaction resistance of this sand can be strongly increased through densification. On the other hand, the lowest k l -value was obtained for sand W1. Figure 17 represents the dependence between the mean grain size d 50 and the rate of the PWP build-up at relative density D r0 = 0.6 whereas the images of grains of these four sands taken with a digital microscope can be found in Fig. 18. The fine-grained Karlsruhe sand is more susceptible to the evolution of excess PWP than the medium-coarse Hostun sand. These sands also have similar k l -parameters, which can probably be attributed to the similar C U of these sands (Table 1). While the grain size distribution curves of the sands W1 and W9 are almost identical (Fig. 1), the PWP build-up in these sands is very different (yelow and brown triangular markers in Fig. 17). The sand W9 is much more prone to the generation of the PWP (higher C l -value) than Fig. 12 Exponential dependence between the rate of the PWP buildup and the relative density for Hostun sand Fig. 13 Linearization of the dependence between the rate of the PWP build-up and the initial relative density for Hostun sand Fig. 14 Dependence between the rate of the PWP build-up and the initial relative density for five tested sands the sand W1. The reason for this lies probably in the differences of their grain shape and surface roughness [35]. Therefore, the mean grain size d 50 solely (low and similar C U values) is not a sufficient indicator of a soil's tendency to PWP build-up. Despite the different C l -values, the k l -parameters of these sands are very similar, which presumably can be linked again to the same C U -values (see Table 1).

Comparison with Cyclic Triaxial Tests
An additional validation of the presented cyclic shear tests in the PWP Tester was carried out using the results of the undrained cyclic triaxial tests. Sands W1, W3, W4, W5, W6, W7, W8 and W9 were part of an extensive field and laboratory testing campaign published in [6]. These sands were anonymously labelled and sent to the authors in order to be used in a comparative study. A slightly different testing conditions (see Table 3) and the interpretation of the cyclic shear test results were used for this purpose. Here, the number of cycles N 50 necessary for the increase of PWP to 50 % of its initial value ( Δu = 0.5u 0 ) was evaluated as a charasteristic value from a single cyclic shear test. This parameter is analogous to the previously introduced C l .
The results of the cyclic triaxial tests on these sands are shown in Fig. 19. The notation of sands in brackets corresponds to the one used in [6]. The cyclic resistance ratio CRR , that is read as the cyclic stress ratio CSR causing failure of the soil specimen in N f = 10 cycles, is used to characterise the triaxial test results. CSR represents the ratio between the cyclic shear stress q ampl and the mean effective stress 2p ′ 0 . Assuming a linear dependence between CRR and D r0 , a regression coefficient k triax can be determined as a characteristic parameter for each sand. Figure 20 depicts the results obtained in the PWP Tester for these sands as a dependence between the number of cycles N 50 needed for Δu = 0.5u 0 and the initial relative densities D r0 . To compare the results of these two testing methods quantitatively, the N 50 -values were divided by a scaling factor N c . Using N c = 4000, values of N 50 ∕N c are (b) (a) Fig. 15 Comparison of the C l -values for all sands at a D r0 = 0.6 and b D r0 = 0.8. Note the different scales for C l in these graphs  transformed to a range similar to CRR -values from the triaxial tests. For a chosen density range, a linear regression between N 50 ∕N c and D r0 is obtained. Here, a regression coefficient k pwpt can be determined.   Fig. 19 Cyclic resistance ratio CRR from the cyclic triaxial tests (data from [6]) Fig. 20 Dependence between the number of cycles N 50 and the initial relative density D r0 for all tested sands (PWP Tester) A large difference in relative densities in the cyclic shear and triaxial tests can be recognised. Using a conventional density description, the densities of the triaxial specimens lie between loose and medium dense states, while the shear test specimens are in a medium dense and dense state. This difference emphasises a significant impact of the specimen installation methods used in these tests. The sands in the PWP Tester were installed under water using the installation method described in Section "Specimen preparation", whereas a free fall method of the moist sand was applied in triaxial tests.
The outcomes of these two different testing approaches can be compared using the slopes of the regression lines in Figs. 19 and 20. As it can be seen in Fig. 21, a good correspondence between the k-parameters from both tests exists (a certain discrepancy in case of sands W1 and W7 will be analysed in a further study). Thus, a good qualitative and quantitative correlation between the liquefaction resistances, as expressed by N 50 in the cyclic shear tests and CRR in the triaxial tests, respectively, in dependence of relative densities can be concluded for these two approaches.

Conclusions
In this study, a simplified cyclic shear test in the PWP Tester was presented. The test results have shown that this method can successfully be used for fast and systematic testing of the PWP build-up in coarse-grained soils. The test can be used to analyse both clean sands and sands with a certain amount of fines and gravel grains. The main finding drawn from this study are summarized as following: • A significant dependence between the PWP build-up and the relative density has been confirmed. An exponential relationship between these two variables has been observed.
• The test evaluation yields a C l -parameter that represents an average rate of the PWP build-up related to a certain relative density. This parameter is defined as the gradient of a secant line to the normalised PWP build-up and can be used for the assessment of the soil's PWP generation at a certain relative density. A soil with a high C l -value has a higher rate of the PWP generation than a soil with a low C l -value at the same relative density. • Another parameter derived from the test interpretation is the regression coefficient k l , which quantifies the dependence between C l and D r0 , i.e. between the PWP build-up and the relative density. Densification of a soil with a high k l results in a significant increase of the liquefaction resistance. • A comparison between the results of the presented cyclic shear tests and cyclic triaxial tests, expressed through the k pwpt and k triax , respectively, revealed a good agreement. This confirms the suitability of the proposed test for a fast investigation of the PWP build-up in coarse-grained soils.

Appendix A
Testing programme (see Table 4).