Keywords

1 Introduction

Soft clay is widely distributed in China, especially in the coastal area, such as Shanghai, Tianjin, Hangzhou and Wenzhou, etc. It has been treated as one of the most problematic soils in China because of its high natural water content, low permeability, high compressibility and low bearing capacity. Lots of large storage facilities are usually constructed in this area, such as large coal bunkers and industrial plant warehouse. During the service life, these facilities will induce repeated loading-unloading on the ground soil, since these storages are filled and emptied periodically. One load-unload period may last from weeks to months. Therefore, this load is generally termed as long term low-frequency cyclical loading. This cyclic load results in the accumulated deformation of the ground soil, which in turn may collapse the structures for the excess post-construction deformation, such as the collapse of Shanghai Baosteel warehouse [1].

Many experimental studies have been carried out to investigate the response of soft clay to cyclic loading. Based on the cyclic triaxial tests on soft clay, the effective stress response and the development of pore water pressure for a saturated clay soil to repeat loading was studied [2,3,4]. Additionally, the effect of over-consolidation ratios on the cyclic stiffness degradation and pore water pressure variation of soft clay under cyclic loading was studied by Vucetic [5]. By comparison of the cyclic loading in the form of rectangular, Rahal stated that the cyclic loading in the form of sinusoidal wave produces a better simulation of the storage facilities induced load condition on ground soil [6]. The development of the pore water pressure in the critical state under cyclic loading was also studied [7, 8]. Based on the cyclic triaxial tests on Wenzhou soft clay the development of strain and pore water pressure with the cyclic load numbers in dynamic triaxial tests was studied [9,10,11].

However, current studies focused on the triaxial tests with a higher load frequency, typically, the loading period ranges from 1 s (seismic pulses) to 20 s (ocean waves) [4], which are larger than that experienced by the ground soil under storage facilities. It should be emphasized that this load condition experienced by the storage facilities is different from the dynamic load, whose frequency is high enough to induce the structural inertial force. Therefore, it is urgent to study the response of soft clay under low-frequency cyclic loading. This study presents series of triaxial tests on the Shanghai soft clay retrieved from a construction site at Pudong area. Monotonic and cyclic loading were applied on the 39.1 mm in diameter and 80 mm height saturated soil specimen. Under the condition of consolidated undrained (CU), the development of pore water pressure and stress-strain response was investigated extensively.

2 Experimental Program

The soil samples in this paper are soft clays of marine origin, retrieved from the Pudong area in Shanghai, China. At the depth of 3–20 m, Layer 3 silty clay and Layer 4 mucky clay layer are usually encountered. Soil samples may contain shell debris and other debris, the physical and mechanical properties of the soil are shown in Table 1. The average moisture content of the tested soil samples is 49.40%, 80 mm high and 39.1 mm in diameter. The average weight of soil samples is 164.53 g.

Table 1. Physical properties of Shanghai soft clay.
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Experimental study was performed with computer-controlled GDS stress path triaxial testing system. The specimens were installed on the base of the apparatus. At the beginning of tests, specimens were saturated with a back pressure of 100 kPa and an effective confining pressure of 5 kPa for a duration of 24 h. Specimens are assumed to be saturated when the value of B for each sample is no smaller than 0.98. Then, the test specimen was isotropically consolidated under a certain value of effective confining pressure. Finally, strain-controlled monotonic triaxial tests or one-way stress-controlled cyclic triaxial tests were performed under undrained conditions. Excess pore pressure is measured at the bottom of the specimen.

Series of monotonic triaxial tests were carried out under various values of effective confining pressures, which are summarized in Table 2. The selected confining pressure is less or greater than the average effective stress in the field, which is to study the mechanical properties of undisturbed soil under different consolidation pressures. The strain-controlled monotonic triaxial tests were conducted with a strain rate of 0.5% per hour.

Table 2. Summary of monotonic triaxial tests.
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One-way stress-controlled cyclic triaxial tests were performed with low-frequency, which are summarized in Table 3. After the isotropic consolidation stage, the deviator stress was applied directly to the datum value of qmean, = (qmax + qmin)/2, within a duration of 60 min, and then the one-way cyclic loading started. The sinusoidal loading form was adopted in the circular mode. Figure 1 illustrates the definitions of stresses and strains in the cyclic triaxial tests, in which the εa, εr and εp represent the axial strain, resilient strain and permanent strain, respectively, where εa = εr + εp.

Table 3. Test program of one-way cyclic loading tests.
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Fig. 1.
figure 1

Typical deformation behavior of clay under cyclic loading and definition of stress and strain.

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3 Test Results and Discussion

3.1 Monotonic Response of Shanghai Soft Clay

Response of stress-strain, pore pressure-strain and effective stress path under different confining pressures are measured in the monotonic triaxial tests and presented in Fig. 2. The stress-strain response in Fig. 2(a) shows a slight softening characteristic, which is more pronounced especially in the case with a higher confining pressure. The peak stress is reached at about 10% of the axial strain. Pore pressure generation shown in Fig. 2(b) during shearing is somewhat different, which continually increases as the increasing of axial strain, and a quick increasing is shown when the axial strain is smaller than about 5%, after which the pore pressure increases slightly. The failure envelope plotted in the p′ − q space for the undisturbed soft clay is in Fig. 2(c), in which the critical state line of this intact soft clay is added. According to Fig. 2(c), the critical state parameter M is estimated to be 1.18 for the intact Shanghai soft clay under consolidation undrained triaxial tests. This failure envelope can be described with the widely used Mohr-Coulomb failure criteria, see Fig. 2(d), from which the values of effective cohesion c′ and the effective internal friction angle ϕ′ are estimated and equal to 4.78 kPa and 26.91°, respectively.

Fig. 2.
figure 2

Monotonic response of intact Shanghai soft clay under various confining pressures: (a) stress-strain; (b) pore pressure-strain; (c) effective stress path; (d) effective stress Mohr circle and the failure envelope.

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3.2 Cyclic Response of Shanghai Soft Clay

Figure 3 shows the accumulated strain of the Shanghai intact soft clay during the cyclic triaxial tests. These two sets of curves were obtained from the cyclic loading of one-way and low-frequency tests, which carried out at two effective confining pressures of 75 kPa and 150 kPa. Figure 3(a) shows that the variation of axial strain εa is similar to that of permanent strain εp even under different cyclic stress ratios (CSR). With a smaller value of CSR, the accumulated strain and the increasing rate are both small and tends to reach a plateau. As the increasing of CSR, a larger accumulation rate of εa and εp is shown, e.g. almost a linear increasing is shown when the value of CSR is larger than 0.25 and the effective confining pressure is 150 kPa. A further study shows that when CSR = 0.3, the value of permanent strain εp reaches 12% after 60th cycles, which is larger than the failure stain (about 10%) in the monotonic triaxial tests. Therefore, there should be a threshold value of CSR between 0.25 and 0.3.

Fig. 3.
figure 3

The accumulated axial strain under various confining pressures.

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Comparison of Fig. 3(a) and (b) shows that the accumulated axial strain is not only related to the value of CSR, but also to the effective confining pressure and the deviator stress level. For example, when CSR = 0.3, the strain response is obviously different for the soft clay under various effective confining pressure. In the case of \( \sigma_{3}^{\prime } \) = 150 kPa, the sample was failed, but when \( \sigma_{3}^{\prime } \) = 75 kPa samples only showed a small accumulated strain. So the influence of CSR with various confining pressures and deviator stress levels need be considered in the low-frequency cyclic loading.

Figure 4 presents the variation of resilient modulus as the increasing of cyclic load numbers. The definition of resilient modulus Mr in this study is the ratio of qcyc to εr. It can be seen that resilient modulus increases rapidly during the first five cycles, which is different from that measured in the cyclic triaxial tests with high-frequency [9], especially in the first 5 cycles, after which, all decrease slowly and finally reach a steady state. It is shown that the Shanghai soft clay exhibits plastic deformation in the first few load cycles.

Fig. 4.
figure 4

The relationship of resilient modulus to the number of cycles under different confining pressure.

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Comparison of Figs. 4(a) and (b) shows that the resilient modulus decreases with the increase of CSR, A further study on Fig. 4(b) shows that the difference between the resilient modulus almost is twice when CSR = 0.3. For example, when CSR = 0.3, cycle datum values are 100 kPa and 110 kPa, the resilient modulus are 7.56 MPa and 15.84 MPa, respectively, under the effective confining pressure 75 kPa.

At the beginning of the cyclic triaxial tests, the pore water pressure u = u0. As the number of cycles increases, the pore water pressure is expressed as u = u0 + Δu, where u0 is the initial pore pressure and Δu is the excess pore pressure. The corresponding ΔuN is the residual excess pore pressure at the end of each cycle and the ∆uN/\( \sigma_{3}^{\prime } \) is the normalized residual excess pore pressure.

Figure 5(a) and (b) present the normalized residual excess pore pressure versus the number of cycles with various CSR in effective confining pressures of 150 kPa and 75 kPa. It can be seen that pore pressure increases rapidly during the first few cycles. After that, the increase becomes slower, finally reaches a steady state. The reason for this maybe there is no time for the pore pressure to equilibrate at the beginning of the tests. A similar response was observed for soft clay under high-frequency cyclic loading [4, 9]. So the development of pore water pressure is a time dependent phenomenon, independent of frequency. Comparison of Figs. 5(a) and (b) shows that the normalized residual excess pore pressure is equilibrated fast with the decrease of effective confining pressure. A similar trend is shown with the variation of CSR. Figure 4(b) also shows that the normalized residual excess pore pressure is almost approaching a constant value even under different deviator stress levels.

Fig. 5.
figure 5

Development of pore pressures under various values of CSR: (a) \( \sigma_{3}^{\prime } \) = 150 kPa; (b) \( \sigma_{3}^{\prime } \) = 75 kPa; (c) ΔuNmax versus number of cycles in 150 kPa.

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Figure 5(c) shows that the maximum excess pore pressure under low-frequency cyclic loading is larger than that of monotonic loading, even in the same deviator stress 75 kPa, 87 kPa and 95 kPa with effective confining pressure 150 kPa. However, the difference is getting smaller, with the increase of CSR, especially when CSR = 0.3. For example when the soil sample is loaded till failure, the difference is only 3.65 kPa and CSR = 0.3, but differences are 14.52 kPa and 13.54 kPa, when CSR are 0.17 and 0.25, respectively. So it is necessary to study the variation of excess pore pressure for saturated soft clay under low-frequency cyclic loading.

4 Conclusions

In this study, a series of monotonic triaxial tests and cyclic triaxial tests with low-frequency were conducted to investigate the undrained behavior and excess pore pressure of intact soft clay retrived from Shanghai, China. The resilient modulus, axial strain and permanent strain of the tested samples are evaluated and discussed under various cyclic stress ratios and confining pressures. The following conclusions are made:

  1. (1)

    The results of monotonic loading triaxial tests under various confining pressures show that the stress-strain curves present softening behavior, and the behavior is more pronounced in the case of a higher confining pressure.

  2. (2)

    The variation of axial strain εa is similar to that of permanent strain εp even under different cyclic stress ratios. A liner increase of εa and εp is almost shown when the value of CSR is larger than 0.25 with the effective confining pressure of 150 kPa. The accumulated axial strain is not only related to the CSR, but also to the effective confining pressure and the deviator stress levels.

  3. (3)

    The resilient modulus decreases with the increase of CSR. But the difference of the resilient modulus almost is twice when CSR = 0.3, and this difference between the cycle datum value is only 10 kPa. Compared with high-frequency cyclic loading, the soft clay exhibits plastic deformation in advanced during low-frequency cycle loading.

  4. (4)

    The normalized residual excess pore pressure is equilibrated fast with the decrease of effective confining pressure, which is the same case as the variation of CSR. The normalized residual excess pore pressure is almost equal at the various deviator stress levels. The development of pore water pressure is a time dependent phenomenon, and independent of cyclic load frequency.

  5. (5)

    The maximum excess pore pressure under low-frequency cyclic loading is larger than that under monotonic loading, in the case of the same deviator stress 75 kPa, 87 kPa and 95 kPa with the effective confining pressure 150 kPa. This difference is getting smaller as the increasing of CSR, especially when CSR = 0.3.