The effect of variable confining pressure on the strain accumulation in soft marine clay was investigated to gain a better understanding of the deformation characteristic in the subgrade of pavements due to traffic loading. A series of variable confining pressure (VCP) experiments and corresponding constant confining pressure (CCP) experiments were conducted on Wenzhou soft clay using an advanced cyclic triaxial apparatus. A wide range of deviatoric stress amplitudes (^{ampl}), combined with different isotropic stress amplitudes (^{ampl}), and partially drained conditions are simulated in the experiments. The test results indicate that the variable confining pressure significantly influences the permanent axial strain and might exacerbate the potential of subgrade invalidation in soft marine clay area. The normalized permanent axial strain (_{CCP}), and one-unit increment in the amplitude of cyclic confining pressure will induce an increment of 0.0213% in the permanent axial strain regardless of the CSR values. Based on the data from the CCP tests, a cyclic deviatoric stress ratio threshold is determined to be about 0.7, which may suggest that the upper bound of criterion will limit the cyclic traffic loadings on soft marine clayey deposit. Finally, the effect of variable confining pressure on the permanent axial strain is quantified and incorporated in a logarithmic model for the subsoil deformation prediction under traffic loading.

The rapid development of modern transport infrastructures, such as motorways, railways, and airports, around the southeast-coastal major cities of China has led to the construction of low embankments on thick soft clay ground with poor geotechnical characteristics, namely, with low bearing capacity, low permeability, and high compressibility. When the stress increments induced by long-term repeated traffic loading in these soils are high, the subgrade and underlying soft clay layers have become increasingly overloaded due to a lack of maintenance, and notable subgrade settlements have often been observed, which may exceed the acceptable limits and even compromise the functionality of the infrastructure [

The permanent deformation measurement of soils under traffic loading is generally performed using undrained one-way cyclic triaxial tests with constant confining pressure (CCP). In these one-way cyclic triaxial tests, traffic loading was simulated by a single cyclic deviatoric stress only, which is purely compressive without reversal. A number of empirical models have been proposed to predict the permanent strain of soft soil due to repeated traffic loading [

The effect of drainage and variable confining pressure on permanent deformation behavior and cyclic stress threshold of soft clay has not been sufficiently studied. Cai et al. [

Therefore, this paper intends to analyze the deformation behavior of Wenzhou soft marine clay in partially drained condition as indicated by CCP and VCP tests. The study focuses on the analysis of the effect of the stress level and stress paths on the permanent axial strain, and a new prediction model was established. Additionally, a cyclic deviator stress ratio threshold determined by the CCP tests in partially drained condition is suggested as an upper boundary in pavement subgrade design on Wenzhou soft marine clay. The findings from the current research advanced the understanding of deformation characteristics of soft marine clay under traffic load.

The soft clay samples used in this study were obtained from a deep excavation site in Wenzhou at a depth of 10–12 m, where problematic soils with high water content, high compressibility, low permeability, and low bearing capacity are often encountered [_{p} was 98 kPa.

Physical properties of Wenzhou soft clay.

Index properties | Values |
---|---|

Specific gravity, _{s} (g/cm^{3}) | 2.71 |

Natural water content, | 59.7 |

Initial density, _{0} (g/cm^{3}) | 1.65 |

Initial void ratio, _{0} | 1.62 |

Liquid limit, | 60 |

Plasticity index, _{p} | 37 |

Clay fraction (%) | 41 |

Silt fraction (%) | 55 |

Compression curve of samples from odometer test.

Testing was performed using a dynamic triaxial apparatus (DTA), manufactured by GDS Instruments Ltd. The DTA, which tests specimens with 50 mm diameter and 100 mm height, is described in many literatures [

(a) General view of the apparatus. (b) Schematic diagram of advanced cyclic triaxial device.

Prior to each cyclic experiment, cylindrical specimens of 50 mm diameter and 100 mm height were firstly hand-trimmed from the core of every sample by a wire saw in a rotary manner in a sample preparation platform and then mounted in the triaxial cell. Following this, a backpressure of 300 kPa with an effective stress of 10 kPa was applied until B values of the B-check process are greater than 0.98. Subsequently, all specimens were isotropically consolidated under a mean effective confining pressure of 100 kPa, which is slightly larger than the preconsolidation pressure _{p} to make sure that the tested soft clay is normally consolidated. Then, the designed stress paths were conducted through independently controlled half-sine form deviator and isotropic stress to simulate the coupling of cyclic vertical normal stresses and cyclic horizontal normal stresses induced by moving wheel load. As suggested by Cai et al. [

Figure ^{ampl} was introduced following RondóN et al. [^{ampl}^{ampl}, in which ^{ampl} is the amplitude of cyclic deviator stress and ^{ampl} is the amplitude of cyclic mean principal stress. ^{ampl} is calculated by _{3}^{ampl} is the amplitude of cyclic compressive confining pressure. In accordance with the nature of the CCP tests, the slopes of the stress paths in

Stress paths of the tests in p-q space.

The detailed test program is illustrated in Table ^{ampl} values. The cyclic stress ratio (CSR) is defined as CSR = ^{ampl}/_{f}, where _{f} is the static deviator stress at failure. The preliminary compression tests showed that _{f} is approximately 72 kPa for the testing sample. All the tests were performed at room temperature (approximately 20°C) according to the annual average temperature of Wenzhou. The loading frequency was set to 0.1 Hz, and 50 test data points (one per 0.02 s) were recorded per cycle according to the previous studies, and the number of cycles in the tests was set as 3,000. The reason for this particular choice in the number of cycles was driven by an analysis period compatible with laboratory work constraints and a practical method to characterize the mechanical behaviors of the soft clay.

Scheme of CCP and VCP tests.

Number of tests | _{0} (kPa) | ^{ampl} (kPa) | CSR | ^{ampl} | Number of load cycles |
---|---|---|---|---|---|

D01 | 100 | 15 | 0.208 | 3 | 3000 |

D02 | 100 | 15 | 0.208 | 1.0 | 3000 |

D03 | 100 | 15 | 0.208 | 0.5 | 3000 |

D04 | 100 | 20 | 0.278 | 3 | 3000 |

D05 | 100 | 20 | 0.278 | 1.0 | 3000 |

D06 | 100 | 20 | 0.278 | 0.5 | 3000 |

D07 | 100 | 20 | 0.278 | 0.4 | 3000 |

D08 | 100 | 20 | 0.278 | 0.3 | 3000 |

D09 | 100 | 25 | 0.347 | 3 | 3000 |

D10 | 100 | 25 | 0.347 | 1.0 | 3000 |

D11 | 100 | 25 | 0.347 | 0.5 | 3000 |

D12 | 100 | 35 | 0. 486 | 3 | 3000 |

D13 | 100 | 35 | 0.486 | 1.0 | 3000 |

D14 | 100 | 35 | 0.486 | 0.5 | 3000 |

D15 | 100 | 35 | 0.486 | 0.4 | 3000 |

D16 | 100 | 45 | 0.625 | 3 | 3000 |

D17 | 100 | 45 | 0.625 | 1.0 | 3000 |

D18 | 100 | 45 | 0.625 | 0.5 | 3000 |

D19 | 100 | 55 | 0.764 | 3 | 3000 |

D20 | 100 | 60 | 0.833 | 3 | 3000 |

D21 | 100 | 65 | 0.903 | 3 | 3000 |

Test results on the axial strain of the specimens in CCP and VCP tests are presented in this section. The permanent axial strain of subsoil can be used to evaluate the cumulative settlement of the subgrade under vehicle moving loads.

The typical deviatoric stress changes with the axial strain _{a} of the specimens at CSR = 0.347 and 0.625 obtained from CCP (^{ampl} = 3) and VCP (^{ampl} = 1, 0.5) tests are selected and plotted in Figure ^{ampl} value and the level of the cyclic deviatoric stress. For example, for the specimen subjected to a CSR = 0.278, the permanent axial strain under the conditions of ^{ampl} = 0.5 (1.309%) is about 1.74 times greater than that of the specimen under the conditions of ^{ampl} = 3 (2.277%), which suggests that higher cyclic confining pressure can effectively promote the development of permanent axial strain in a specimen.

Typical stress–strain hysteretic loops: (a) CSR = 0.347, ^{ampl} = 3; (b) CSR = 0.347, ^{ampl} = 0.5; (c) CSR = 0.625, ^{ampl} = 1; (d) CSR = 0.625, ^{ampl} = 0.5.

To achieve a better view of the influence of deviatoric stress and variable confining pressure on the development of axial strain, the typical comparison of _{a} among tests with the same CSR but different ^{ampl} values is plotted in Figure _{a} among tests with the same ^{ampl} but different CSR values is presented in Figure _{a} are similar to each other except for the magnitudes, and _{a} tends to reach a steady value at the end of the tests regardless of ^{ampl} and CSR. Otherwise, under identical conditions, the increase of both deviatoric and isotropic stress amplitudes will promote the accumulation of _{a} greatly. As shown in Figure _{a} can be divided into permanent axial strain ^{p}_{a} and resilient strain ^{r}_{a}. While, in Figure ^{r}_{a} with cycle numbers is relatively small, and it cannot be said how cyclic confining pressure affects it, the difference in the ^{p}_{a} with cycle numbers is significant. Higher ^{ampl} values resulted in a larger ^{p}_{a} with the same CSR values and cycle numbers. Figure ^{ampl} and ^{r}_{a} and ^{p}_{a} are consistently larger if the CSR is higher. Furthermore, Figure ^{r}_{a} and ^{p}_{a} with ^{ampl} is not extremely different at two different CSR values, which means that the stress paths effect does not depend significantly on CSR.

Typical time-history curves of axial strains: (a) CSR = 0.278; (b) CSR = 0.486.

Typical time-history curves of axial strains: (a) ^{ampl} = 1; (b) ^{ampl} = 0.5.

The development of permanent axial strain, _{a}^{p}, with the number of load applications in CCP and VCP tests, is shown in Figure _{a}^{p} with cyclic numbers occurs slowly. In the later phases, the _{a}^{p} grew rapidly with cyclic numbers and reached stability after 1,000 cycles. This phenomenon may be attributed to the partially drained effect. During cyclic loading, the specimens were compacted continuously through water removal, and the compaction effect began to decrease until a particular number of cycles (i.e.,

Relationships between permanent axial strains and cycle numbers: (a) ^{ampl} = 3; (b) CSR = 0.278.

A better view of the permanent axial strain _{a}^{p} influenced by the magnitude of deviatoric stress, for tests with ^{ampl} = 1 and 0.5, _{a}^{p} at selected cycle numbers (e.g., _{a}^{p} is linearly varied with CSR in a log-log plot. For a given number of cycles, the relationship between _{a}^{p} and CSRs can be written as follows:^{ampl} values.

Relationships between permanent axial strains at selected cycle numbers and CSR: (a) ^{ampl} = 1; (b) ^{ampl} = 0.5.

According to the previous CCP and VCP tests on granular materials [_{a}^{p} and stress path length, _{a}^{p}. Therefore, the effect of _{a}^{p} of soft clay in this study is presented in Figures _{a}^{p} with _{a}^{p} increases with _{a}^{p} depends on both the CSR values and _{a}^{p} is found to increase with the increase of both

Permanent axial strain after 1000 cycles versus the length of stress path. (a) CSR = 0.278.

Figure _{CCP}), regardless of the CSR values.

Normalized permanent axial strain after 1000 cycles versus the normalized length of stress path.

Figure

Relationships between the permanent axial strain at

Figure

Relationships between the increment of permanent axial strain at

To achieve a better view of the importance of cyclic confining pressure, the influence of ^{ampl} values on the permanent axial strain _{a}^{p} is quantified. As can be seen from the comparisons of _{a}^{p} between VCP and corresponding CCP tests in Figure ^{p}_{a,VCP} (^{ampl} = 1, 0.5, 0.4 and 0.29), was plotted against the counterparts ^{p}_{a,CCP} in CCP tests (^{ampl} = 3). Furthermore, the fitting parameters _{a}^{p} to ^{p}_{a,CCP} plotted versus the ^{ampl} values and are shown in Figure ^{ampl} values, the ^{ampl} relationship can be closely approximated using the following form:

Relationships between permanent axial strains in VCP and CCP tests.

Relationships between k and ^{ampl} values.

Shakedown analyses provide a theoretical basis for pavement designs and safety assessments [

Through the above mentioned analysis, it can be found that VCP tests resulted in a larger permanent axial strain than the corresponding CCP tests. The threshold of cyclic deviatoric stress ratio determined by the CCP test results can be used as an upper bound of criterion to discerning whether the growth of plastic strains will eventually level off or exhibit an incremental failure. Because the permanent axial strain has reached a stable state after 1,000 cycles, herein, the permanent axial strain of specimens at 1,000 cycles, ^{p}_{a,1000}, was plotted against the CSR values in Figure ^{p}_{a,1000}–CSR curve, while it should be noted that some subjectivity was unavoidable in locating the marked bend point as the curves were nonlinear from the beginning. In this study, the threshold of cyclic deviatoric stress ratio corresponding to the marked bend point of the ^{p}_{a,1000}–CSR curve in Figure

Relationships between

Power modes and logarithmic models are the two most wide-spread approaches to describe the increase of permanent axial strain ^{p}_{a} with increasing number of cycles _{1} and _{2} are fitting parameters depending on the CSR values and are listed in Table _{1}-CSR and _{2} –CSR relationship can be expressed by a constitutive expression and a linear function of the following form, respectively:

Development of permanent axial strain with increasing cycle numbers in CCP tests. ^{ampl} = 3.

Regression parameters _{1} and _{2} in equation (

Test number | CSR | _{1} | _{2} |
---|---|---|---|

D01 | 0.208 | 6.7094 | 0.0026 |

D04 | 0.278 | 4.8348 | 0.0058 |

D09 | 0.347 | 3.7465 | 0.0100 |

D12 | 0.486 | 2.0861 | 0.0216 |

D16 | 0.625 | 1.6655 | 0.0489 |

Setting equations (

Furthermore, setting Eq. (

Figure

Comparison of the measured and calculated permanent axial strains. (a) CSR = 0.208. (b) CSR = 0.278. (c) CSR = 0.347. (d) CSR = 0.486. (e) CSR = 0.625.

A series of one-way CCP and VCP tests on an intact saturated soft marine clay were performed in this study. The combined effects of the vertical and horizontal stress changes to which subgrade soils are subjected are simulated by the combination of cyclic deviator stress and cyclic confining pressure. Based on the experimental results, the major conclusions are summarized as follows:

The generation of axial strain is significantly affected by cyclic loading levels and stress paths. However, for all loading patterns considered, the normalized permanent axial strain at a given number of cycles can be uniquely related to the normalized stress path length,

The increment of the permanent axial strain at a given number of cycles is generally proportional to the increment of the amplitude of cyclic confining pressure. One-unit increment in the amplitude of cyclic confining pressure will induce an increment of 0.0213% in the permanent axial strain at

Based on CCP test results and shakedown theory, a CSR threshold of 0.7 was determined for Wenzhou soft marine clay, which can be suggested as a basis for controlling subgrade settlement in soft marine area.

A logarithmic model of permanent axial strain provided an extremely good simulation of the measured permanent axial strain data of CCP and VCP test by not only accounting for the combined effects of cyclic deviatoric and confining stresses, but also accounting for the effects of cycle numbers.

Future work in this area should address the effects of wave form, frequency, cyclic intermediate principal stress, rotation of principal stress, and a larger number of loading cycles on permanent strain potentials of soft marine clays.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare no conflicts of interest.

This study was supported by the Nature Science Research Project of Anhui province (no. 1908085QE215) and professor/doctoral scientific research project of Suzhou College (no. 2016jb05).