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Cyclic behavior of saturated soft clay under stress path with bidirectional shear stresses
Soil Dynamics and Earthquake Engineering 104 (2018) 319–328
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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Cyclic behavior of saturated soft clay under stress path with bidirectional shear stresses
MARK
⁎
Xiuqing Hu, Yan Zhang, Lin Guo, Jun Wang , Yuanqiang Cai, Hongtao Fu, Ying Cai College of Architecture and Civil Engineering, Wenzhou University, Wenzhou 325035, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Cyclic stress ratio Bidirectional shear frequency Soft clay Stress–strain loop Figure-eight-shaped stress path
Under seismic loading, soil layers experience multidirectional cyclic shear stresses with different amplitudes and frequencies. Therefore, the deformation behavior of soft clay under complex stress paths is practically relevant. In this study, cyclic tests are performed on normally consolidated soft clay. To simulate the situation induced by seismic load, the complex figure-eight-shaped stress path is realized by applying shear stresses in two directions simultaneously. Under the figure-eight-shaped shear stress path, the cyclic strain, cyclic modulus, and cyclic strength of soft clay are found to be significantly dependent on the CSR (cyclic shear stress ratio) and the bidirectional shear frequencies. With an increase in the CSR and a decrease in the shear frequency, the dynamic shear modulus decreases and cyclic strain accumulation increases with an increasing number of cycles. Based on the test results, an empirical formula was presented to predict the cyclic strength under different shear frequencies.
1. Introduction Soft clay is widely distributed in the coastal area of China, which is located in the circum-Pacific seismic belt. The dynamic behavior of soft clay under seismic loading has become a topic of interest for engineers. For sedimentary soil, most of the deformation is caused by seismic waves transmitted from the underlying layer and these waves are always assumed to be horizontal shear waves (Fig. 1). At large stratum depths, shear waves with different amplitudes, shear directions, frequencies, and durations are continuously propagated, and the coupling effect of multiple shear waves causes the soil layer to experience shear waves with different amplitudes and frequencies. In the horizontal direction, multidirectional shear stresses with different amplitudes and frequencies are formed, leading to large cyclic deformations, which may affect the structures located on the associated soil layers and may cause damage. Therefore, geotechnical engineers have shown increasing interest in the evaluation and analysis of the dynamic properties of soils under multidirectional shear stresses to decrease the vulnerability of structures. Under cyclic loading, cohesive soils are more stable than sandy soils [1–3], and consequently, cohesive soils are less used than cohesionless soils in laboratory investigations [4]. However, the earthquakes in Mexico City in 1985 [5] showed that instantaneous settlement occurs and leads to the instability of structures on a soft clay layer. However, studies on the dynamic characteristics of clay under multiple stresses
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with different amplitudes and frequencies appear to be limited. In the last few decades, the behavior of soft clays subjected to cyclic loading has been studied by many researchers. Chen and Pan [6] investigated the effects of the initial principal stress direction, initial ratio of deviatoric stress, and initial average effective principal stress on the threshold shear strain using dynamic hollow-cylinder torsional apparatus. Guo et al. [7] performed a series of monotonic and cyclic triaxial tests to investigate the undrained deformation behavior of undisturbed soft clay. The stress–strain hysteretic loop, resilient modulus, and permanent strain of the tested samples were found to be significantly dependent on the cyclic shear stress ratio (CSR) and the confining pressure. Based on the test results, two equations were established for the prediction of the long-term resilient modulus and the permanent strain and a new critical value was suggested for the CSR. Gu et al. [8] studied the undrained dynamic behavior of saturated clays by performing cyclic triaxial tests at variable confining pressures and found that in cases where strong P-waves propagate in soil layers, variable confining pressure tests are more appropriate for the simulation of in situ stress fields than conventional cyclic triaxial tests performed at a constant confining pressure. Some local studies on the typical clay response to repeated or cyclic loading have been reported [9–21]. In these studies, the stress–strain relationship and strength properties of clay were evaluated based on cyclic triaxial shear tests. Another group of studies has been reported in the literature [22–33] where the stress–strain–pore pressure behavior of clays was investigated using triaxial tests
Corresponding author. E-mail addresses: [email protected] (X. Hu), [email protected] (Y. Zhang), [email protected] (L. Guo), [email protected] (J. Wang), [email protected] (Y. Cai).
https://doi.org/10.1016/j.soildyn.2017.10.016 Received 27 May 2017; Received in revised form 30 September 2017; Accepted 25 October 2017 0267-7261/ © 2017 Elsevier Ltd. All rights reserved.
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Table 1 Physical properties of test samples. ρ (g/cm3)
W0 (%)
e0
Gs
wl
Ip
1.59–1.62
59–62
1.66–1.70
2.66–2.69
69
38
Fig. 1. Shear wave propagation from bedrock to soil cover.
Fig. 4. Schematic of multidirectional cyclic simple shear test apparatus.
modes for physically modeling the behavior of soil subjected to untrained multidirectional cyclic loading. Matsuda et al. [40] showed that the shear strain amplitude has a significant effect on the changes in the effective stress of granular materials. Matsuda et al. [41] investigated the effects of the shear strain amplitude and the number of cycles on the accumulation of excess pore water pressure and the recompression of saturated soft clay by using multidirectional cyclic shear. However, they focused on only the cyclic behavior of sand or granular materials. In this study, a series of cyclic tests are performed on normally consolidated soft clay using multidirectional cyclic shear test apparatus. By applying shear stresses in two directions simultaneously, the complex figure-eight-shaped stress path is realized to simulate the situation induced by seismic load. The effects of the bidirectional shear frequency and the CSR on the cyclic strain, cyclic modulus, and cyclic strength during cyclic shear are investigated. The relationship between failure cycles and the shear frequency is established as an empirical formula to evaluate the deformation of the soft clay.
Fig. 2. Schematic of loading modes of samples.
Fig. 3. Typical deformation mode of specimen.
2. Materials and methods performed at variable confining pressures. The cyclic behavior of clays was also studied by other researchers, e.g., the torsional simple shear test by Cai et al. [34] and the resonant-column test by Kallioglou and Pitilakis [35]. Studies on soil characteristics have been conducted previously using cyclic triaxial shear tests or hollow torsional shear tests. Nevertheless, the cyclic simple shear tests provide a more reasonable approximate representation of the seismic loading conditions than the former tests. Recently, some researchers have studied the deformation behavior of soil under seismic loading using cyclic simple shear test apparatus. Fangcheng et al. and Qian Jianguo et al. [36,37] performed a series of cyclic simple shear tests on undisturbed silty clay. They found that volumetric strains increase with the development of cyclic load cycles and the improvement in the cyclic shear strain amplitude. Furthermore, with the accumulation of volumetric strain, the characteristics of the clay are strengthened. Fakharian and Evgin [38] investigated the cyclic behavior of a sand–steel interface under constant normal stress and normal stiffness conditions. However, they focused on only the case of unidirectional cyclic shear. In fact, it is widely known that the shear strain induced during earthquakes shows multidirectional hysteresis paths. Several experiments have also been performed to investigate the soil dynamic behavior induced by multidirectional shaking. Lin et al. [39] clarified that a simple shear system capable of inducing radial shear strain on the vertical plane is a better approach than other shearing
2.1. Sampling method and soil properties Remolded Wenzhou soft clay was used in this study. The clay specimens were prepared as follows. Considering that the uniform undisturbed soft clay samples very difficult to obtain, remolded samples are used this paper by a large consolidation apparatus. The procedures include 4 steps:(1) Drying: the clay blocks are cut into small blocks whose volume does not exceed 200 cm3 with the maximum side length, not more than 5 cm. Then the bricks will be placed in an oven with a temperature of 105 °C. The drying time is generally not less than 48 h, to make the free water in the clay bricks lost completely. (2) Powdering and sieving: the dried clay blocks are smashed to clay blocks smaller than 1 mm3 by a large grinder and then ground into powder by a fineness of 50–200 ultrafine powder grinding machine. Then the soil powder is sieved by a 0.03 mm vibration sieve to ensure its uniform. (3) Stirring: the powder is mixed with distilled water to get a clay mud with a water content of 80%. Then the mud is stirring to ensure that it is uniform. (4) Consolidation: the clay mud is put into the large consolidation apparatus with a diameter of 300 mm and a height of 400 mm slowly. Then vertical pressures are applied step by step in the order of 12.5 kPa, 25 kPa, 50 kPa and so on. The duration time of every step is 24 h. The final vertical pressures are 50 kPa, 75 kPa, and 100 kPa respectively. After 3 days, the settlement of the clay mud reaches a steady value and then the samples are consolidated completely. The 320
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Fig. 5. Details of soil cutting instrument.
Table 2 Summary of test conditions. Set no.
Test no.
τd = τx= τy (kPa)
fx (Hz)
fy (Hz)
CSR (τd/σ0)
A
A1 A2 A3 A4 A5 B1 B2 B3 B4 B5 C1 C2 C3 C4 C5
14.14 14.14 14.14 14.14 14.14 17.67 17.67 17.67 17.67 17.67 21.21 21.21 21.21 21.21 21.21
0.5 0.3 0.25 0.2 0.16 0.5 0.3 0.25 0.2 0.16 0.5 0.3 0.25 0.2 0.16
0.25 0.15 0.125 0.1 0.08 0.25 0.15 0.125 0.1 0.08 0.25 0.15 0.125 0.1 0.08
0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3
B
C
prepared specimen was 50 mm in diameter and 25 mm in height. The cutting procedure are as follows: (1) Pushing the soil samples out of the tube slowly and take the center part of each sample. (2) Fixing the remolded soft clay blocks on the setting of the cyclic simple shear cutting instrument, as shown in Fig. 5(a), and then using a steel wire cut off the outer edge of the soil sample, a cylindrical specimen with a diameter of 50 mm was made. (3) Putting it into a opening mold, due to the opening mold was made according to the standard size of sample manufacturing, so only cut off the excess soil of two port of the mold (Fig. 5(b)), the height of the sample can be raised to a standard height (25 mm).
Fig. 6. Configuration of shear box: (a) soil specimen in shear box and (b) final setting of shear box.
Fig. 7. Cyclic waves obtained in present study.
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Fig. 8. Curves of dynamic shear strains in x- and y-directions under different shear frequencies and CSRs.
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Fig. 8. (continued)
Fig. 9. Strain paths under different shear frequencies for CSR = 0.3.
A schematic of the loading modes and a typical deformation mode of a specimen are presented in Figs. 2 and 3, respectively. The physical properties of the test samples are listed in Table 1.
2.2. Test apparatus and procedures The schematic of the multidirectional cyclic simple shear test apparatus used in this study is shown in Fig. 4. The specimen was covered
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with a rubber membrane and placed in contact with the inner side of 25 Teflon-coated rings, which were stacked one above the other (thickness of each Teflon-coated ring: 1.0 mm). Lateral swelling of the specimen was not permitted, whereas shear deformation was allowed. This apparatus can provide any type of cyclic displacement to the bottom of a specimen from two perpendicular directions using an electrohydraulic servo system. A predetermined vertical stress can be applied to the specimen using an electrically controlled aero-servo system. This apparatus is the same as that used previously by Nie et al. [42] to investigate the undrained response of soils under multidirectional cyclic simple shear conditions. Fig. 6(a) shows a soil specimen in the shear box, whereas Fig. 6(b) shows the final setting of the shear box. During cyclic loading, the Teflon-coated rings slide smoothly on each other, and thus, constant volume conditions can be achieved. By using the same type of shear box, Wang et al. [43] performed two-way stresscontrolled cyclic shear tests under undrained conditions to evaluate the relationship between the pore water pressure and the number of cycles for a saturated clay layer. They found that the test results were not influenced by any friction between the rings. After consolidation, the specimen was subjected to cyclic shear for a predetermined number of cycles, cyclic stress ratio, and frequency under the undrained condition. In this study, the specimens were subjected to stress-controlled multidirectional cyclic simple shear. The test conditions are listed in Table 2. The main focus of this test program was to investigate the effect of the bidirectional shear frequency on the undrained response of Wenzhou soft clay under multidirectional cyclic simple shear conditions. The x-direction frequency was varied in the range f = 0.2–0.5, whereas the y-direction frequency was varied in the range f = 0.1–0.25. The cycle stress ratio was fixed as 0.20, 0.25, and 0.30. The waveform of the cyclic shear stress was sinusoidal (two-way cyclic stress). During the cyclic shear test, the vertical stress and the horizontal displacement were recorded every 10 s, and thereby, 50 data points were obtained in each cycle. These data points were used to determine the experimental results. The y-axis intersects the x-axis perpendicularly at the center of the bottom part of the specimen (Fig. 2). Fig. 7(a) shows the shear waveform obtained during the bidirectional cyclic shear tests, in which shear stress was applied simultaneously in both the x- and y-directions. In each test, a predetermined frequency difference between the waves in the x- and y-directions was applied. When the x-direction frequency was half the y-direction frequency, the orbits represented the figureeight cyclic shear condition (Fig. 7(b)). In this paper, for the bidirectional case, the shear stress amplitude represents the amplitude in the xand y-directions (i.e., τd = τx = τy). The tests were continued until the total strain amplitude reached 10% or until the number of cycles reached 100. Fig. 10. Changes in total shear strain, γd, with respect to number of load cycles, N, for various shear frequencies.
3. Test results and discussion 3.1. Cyclic strain
in the CSR, the differences in the shear strains under variable frequencies became larger. When the CSR was 0.25, the shear strain in the x-direction was 0.9% after 100 cycles for fx = 0.5. For the other three lower frequencies (fx = 0.3, 0.25, and 0.2), all the specimens reached failure before 100 cycles. Fig. 9 shows the relationship between the x- and y-direction strains for different shear frequencies. It was clear that at a high shear frequency (fx = 0.5), the x-direction strain was almost the same as the ydirection strain; thus, the shape of the strain path was similar to that of a regular figure eight. However, when the frequency reduced further (fx = 0.2), the development of the x-direction strain was not consistent with that of the y-direction strain and the strain path became irregular. It is also noteworthy that the fluctuating range in the x-direction for the positive strain increased as the shear frequency decreased. The strain in the y-direction kept swinging between the positive and
Fig. 8 shows the relationship between the cyclic shear strain γ and the number of cycles N for different CSR values and frequencies. As shown in Fig. 8, when the CSR was low (CSR = 0.2), the strains in the x- and y-directions grew slowly and remained stable after a certain number of cycles. However, when the CSR was 0.25 or 0.3, the strains in the x- and y-directions developed rapidly and the specimens even reached failure before 100 cycles. These results demonstrated that the cyclic shear stress ratio had a significant effect on the deformation behavior of the soft clay. In addition, the frequency had a significant influence on the deformation behavior of specimens with the same CSR. When the CSR was 0.2, the shear strains in both the x- and y-directions increased with a decrease of frequency. For example, the shear strain in the x-direction was 0.45% for fx = 0.5. For fx = 0.2, the value was 0.59%, which is an increase of 0.14% compared to the strain for fx = 0.5. With an increase 324
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Fig. 11. Stress–strain hysteretic loops under different shear frequencies.
the stress–strain relationship for different number of cycles, the stress–strain hysteretic loops for cycle nos. 1, 5, 10, and 20 are plotted in Fig. 12. With an increase in the number of cycles, the stress–strain loop inclined toward the horizontal axis. This trend can be attributed to the cyclic degradation of soft clay caused by the generation of pore water pressure. When the number of cycles became large, the cyclic degradation decreased more rapidly and the shape of the stress–strain hysteretic loop in the x-direction changed more clearly. Again, the shear modulus was normalized by its value before being compared under different shear frequencies. The relationship between the shear modulus and the number of cycles for various shear frequencies in both the shearing directions with CSRs of 0.25 and 0.3 were shown in Fig. 13. The dynamic shear modulus decreased rapidly during the first few cycles. Then, the decreasing trend became slower. In addition, the dynamic shear modulus had a positive correlation with the shear frequency and an inverse correlation with the CSR. A nearly linear relationship was found between the dynamic shear modulus and the number of cycles for all the four shear frequencies before the specimen was failed.
negative strains. This phenomenon may be related to the applied stress paths, as shown in Fig. 7(a). When the x-direction stress was considered for an odd number of laps, the shear stresses in both the directions produced positive strain. However, when the x-direction stress was considered for an even number of laps, the negative strain produced in the y-direction had a certain effect on the x-direction strain. To consider the shear strains in the x- and y-directions simultaneously, the total shear strain (γd) was proposed as follows: γd = γx2 + γy2 . The relationship between γd and the number of load cycles, N, was plotted in Fig. 10 for various shear frequencies. All the γd–N curves were nonlinear, and the development speeds of the cyclic strain were significantly different for different CSRs and shear frequencies. Fig. 10 indicates that for the same cyclic stress ratio, a larger shear frequency resulted in the sample requiring a higher number of load cycles to reach failure for 0.2 ≤ fx ≤ 0.3. The strain development speed on soil samples increased more slowly at fx = 0.5 than at lower shear frequencies. Thus, the number of load cycles to reach failure, Nf, was greater. This is because when the shear frequency increased, the pore water pressure did not have sufficient time to develop, causing the total shear strain to be considerably less than those at lower shear frequencies. This conclusion is in agreement with that of a previous study [44].
3.3. Cyclic strength The relationships between the shear frequency and the number of load cycles required to reach an amplitude strain of 10% (cyclic failure, Nf) [45] are shown in Fig. 14, which gives a comparison of the cyclic strength between CSR = 0.25 and CSR = 0.30. For CSR = 0.2, the specimens did not fail, so the corresponding plot is not shown. When fx increased from 0.2 to 0.5, the cyclic strength increased. For the same value of frequency, an increase in the CSR resulted in a decrease in the cyclic strength. Based on the test results, the relationship between the shear frequency and Nf was derived as follows:
3.2. Cyclic resilient behavior Fig. 11 shows the stress–strain hysteretic loops for specimens with fx = 0.2, 0.25, 0.3, and 0.5 Hz. When the shear frequency was high, the shear strains in both the directions gradually increased; thus, the shear strains in the two directions remained consistent with each other. However, when the shear frequency was low, the shear strain in the xdirection was barely consistent with that in the y-direction. To compare
Nf = m*f n 325
(1)
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Fig. 12. Stress–strain hysteretic loops in (a) y-direction and (b) x-direction under different shear frequencies.
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Fig. 13. Relationships between G and f versus number of cycles, N, for CSR = 0.25 and 0.3.
2. The γd–N relationship curves were dependent on both the cyclic stress ratio and the shear frequency. With an increase in the cyclic stress ratio, the effect of the shear frequency on the strain was more apparent.
The parameters m and n in Eq. (1) can be determined empirically by the curve-fitting. Considering the effect of the shear frequency, it was concluded that when CSRs were relatively high, the shear strain was significantly influenced by the shear frequency. The higher the CSRs, the larger was the effect of the shear frequency on the strain development. 4. Conclusions In this study, a figure-eight-shaped stress path was formed by controlling the shear frequency in the x-direction to be twice that in the ydirection. To clarify the effect of both the cyclic shear frequency and the cyclic shear stress ratio on the properties of cohesive soft clay from Wenzhou, China, several series of cyclic simple shear tests were performed under the figure-eight-shaped shearing stress path. The main conclusions of the study are summarized as follows: 1. When the shear frequency was high, the cyclic strain in the x-direction was almost consistent with that in the y-direction under the same CSR and the shape of the strain path was still similar to that of a regular figure eight. However, when the shear frequency was low, the x-direction cyclic strain was not consistent with the y-direction cyclic strain and the strain path had a shape of an irregular figure eight.
Fig. 14. Relationship between shear frequency, f, and number of cycles, N.
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3. With an increasing number of cycles, the shape of the stress–strain hysteretic loop changed and the dynamic shear modulus decreased because of the degradation of the soft soil. 4. The lower the shear frequency, the fewer were the load cycles needed to reach failure. A new equation relating the shear frequency to the number of cycles needed to reach failure was suggested for soft clay.
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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Cyclic behavior of saturated soft clay under stress path with bidirectional shear stresses
MARK
⁎
Xiuqing Hu, Yan Zhang, Lin Guo, Jun Wang , Yuanqiang Cai, Hongtao Fu, Ying Cai College of Architecture and Civil Engineering, Wenzhou University, Wenzhou 325035, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Cyclic stress ratio Bidirectional shear frequency Soft clay Stress–strain loop Figure-eight-shaped stress path
Under seismic loading, soil layers experience multidirectional cyclic shear stresses with different amplitudes and frequencies. Therefore, the deformation behavior of soft clay under complex stress paths is practically relevant. In this study, cyclic tests are performed on normally consolidated soft clay. To simulate the situation induced by seismic load, the complex figure-eight-shaped stress path is realized by applying shear stresses in two directions simultaneously. Under the figure-eight-shaped shear stress path, the cyclic strain, cyclic modulus, and cyclic strength of soft clay are found to be significantly dependent on the CSR (cyclic shear stress ratio) and the bidirectional shear frequencies. With an increase in the CSR and a decrease in the shear frequency, the dynamic shear modulus decreases and cyclic strain accumulation increases with an increasing number of cycles. Based on the test results, an empirical formula was presented to predict the cyclic strength under different shear frequencies.
1. Introduction Soft clay is widely distributed in the coastal area of China, which is located in the circum-Pacific seismic belt. The dynamic behavior of soft clay under seismic loading has become a topic of interest for engineers. For sedimentary soil, most of the deformation is caused by seismic waves transmitted from the underlying layer and these waves are always assumed to be horizontal shear waves (Fig. 1). At large stratum depths, shear waves with different amplitudes, shear directions, frequencies, and durations are continuously propagated, and the coupling effect of multiple shear waves causes the soil layer to experience shear waves with different amplitudes and frequencies. In the horizontal direction, multidirectional shear stresses with different amplitudes and frequencies are formed, leading to large cyclic deformations, which may affect the structures located on the associated soil layers and may cause damage. Therefore, geotechnical engineers have shown increasing interest in the evaluation and analysis of the dynamic properties of soils under multidirectional shear stresses to decrease the vulnerability of structures. Under cyclic loading, cohesive soils are more stable than sandy soils [1–3], and consequently, cohesive soils are less used than cohesionless soils in laboratory investigations [4]. However, the earthquakes in Mexico City in 1985 [5] showed that instantaneous settlement occurs and leads to the instability of structures on a soft clay layer. However, studies on the dynamic characteristics of clay under multiple stresses
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with different amplitudes and frequencies appear to be limited. In the last few decades, the behavior of soft clays subjected to cyclic loading has been studied by many researchers. Chen and Pan [6] investigated the effects of the initial principal stress direction, initial ratio of deviatoric stress, and initial average effective principal stress on the threshold shear strain using dynamic hollow-cylinder torsional apparatus. Guo et al. [7] performed a series of monotonic and cyclic triaxial tests to investigate the undrained deformation behavior of undisturbed soft clay. The stress–strain hysteretic loop, resilient modulus, and permanent strain of the tested samples were found to be significantly dependent on the cyclic shear stress ratio (CSR) and the confining pressure. Based on the test results, two equations were established for the prediction of the long-term resilient modulus and the permanent strain and a new critical value was suggested for the CSR. Gu et al. [8] studied the undrained dynamic behavior of saturated clays by performing cyclic triaxial tests at variable confining pressures and found that in cases where strong P-waves propagate in soil layers, variable confining pressure tests are more appropriate for the simulation of in situ stress fields than conventional cyclic triaxial tests performed at a constant confining pressure. Some local studies on the typical clay response to repeated or cyclic loading have been reported [9–21]. In these studies, the stress–strain relationship and strength properties of clay were evaluated based on cyclic triaxial shear tests. Another group of studies has been reported in the literature [22–33] where the stress–strain–pore pressure behavior of clays was investigated using triaxial tests
Corresponding author. E-mail addresses: [email protected] (X. Hu), [email protected] (Y. Zhang), [email protected] (L. Guo), [email protected] (J. Wang), [email protected] (Y. Cai).
https://doi.org/10.1016/j.soildyn.2017.10.016 Received 27 May 2017; Received in revised form 30 September 2017; Accepted 25 October 2017 0267-7261/ © 2017 Elsevier Ltd. All rights reserved.
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Table 1 Physical properties of test samples. ρ (g/cm3)
W0 (%)
e0
Gs
wl
Ip
1.59–1.62
59–62
1.66–1.70
2.66–2.69
69
38
Fig. 1. Shear wave propagation from bedrock to soil cover.
Fig. 4. Schematic of multidirectional cyclic simple shear test apparatus.
modes for physically modeling the behavior of soil subjected to untrained multidirectional cyclic loading. Matsuda et al. [40] showed that the shear strain amplitude has a significant effect on the changes in the effective stress of granular materials. Matsuda et al. [41] investigated the effects of the shear strain amplitude and the number of cycles on the accumulation of excess pore water pressure and the recompression of saturated soft clay by using multidirectional cyclic shear. However, they focused on only the cyclic behavior of sand or granular materials. In this study, a series of cyclic tests are performed on normally consolidated soft clay using multidirectional cyclic shear test apparatus. By applying shear stresses in two directions simultaneously, the complex figure-eight-shaped stress path is realized to simulate the situation induced by seismic load. The effects of the bidirectional shear frequency and the CSR on the cyclic strain, cyclic modulus, and cyclic strength during cyclic shear are investigated. The relationship between failure cycles and the shear frequency is established as an empirical formula to evaluate the deformation of the soft clay.
Fig. 2. Schematic of loading modes of samples.
Fig. 3. Typical deformation mode of specimen.
2. Materials and methods performed at variable confining pressures. The cyclic behavior of clays was also studied by other researchers, e.g., the torsional simple shear test by Cai et al. [34] and the resonant-column test by Kallioglou and Pitilakis [35]. Studies on soil characteristics have been conducted previously using cyclic triaxial shear tests or hollow torsional shear tests. Nevertheless, the cyclic simple shear tests provide a more reasonable approximate representation of the seismic loading conditions than the former tests. Recently, some researchers have studied the deformation behavior of soil under seismic loading using cyclic simple shear test apparatus. Fangcheng et al. and Qian Jianguo et al. [36,37] performed a series of cyclic simple shear tests on undisturbed silty clay. They found that volumetric strains increase with the development of cyclic load cycles and the improvement in the cyclic shear strain amplitude. Furthermore, with the accumulation of volumetric strain, the characteristics of the clay are strengthened. Fakharian and Evgin [38] investigated the cyclic behavior of a sand–steel interface under constant normal stress and normal stiffness conditions. However, they focused on only the case of unidirectional cyclic shear. In fact, it is widely known that the shear strain induced during earthquakes shows multidirectional hysteresis paths. Several experiments have also been performed to investigate the soil dynamic behavior induced by multidirectional shaking. Lin et al. [39] clarified that a simple shear system capable of inducing radial shear strain on the vertical plane is a better approach than other shearing
2.1. Sampling method and soil properties Remolded Wenzhou soft clay was used in this study. The clay specimens were prepared as follows. Considering that the uniform undisturbed soft clay samples very difficult to obtain, remolded samples are used this paper by a large consolidation apparatus. The procedures include 4 steps:(1) Drying: the clay blocks are cut into small blocks whose volume does not exceed 200 cm3 with the maximum side length, not more than 5 cm. Then the bricks will be placed in an oven with a temperature of 105 °C. The drying time is generally not less than 48 h, to make the free water in the clay bricks lost completely. (2) Powdering and sieving: the dried clay blocks are smashed to clay blocks smaller than 1 mm3 by a large grinder and then ground into powder by a fineness of 50–200 ultrafine powder grinding machine. Then the soil powder is sieved by a 0.03 mm vibration sieve to ensure its uniform. (3) Stirring: the powder is mixed with distilled water to get a clay mud with a water content of 80%. Then the mud is stirring to ensure that it is uniform. (4) Consolidation: the clay mud is put into the large consolidation apparatus with a diameter of 300 mm and a height of 400 mm slowly. Then vertical pressures are applied step by step in the order of 12.5 kPa, 25 kPa, 50 kPa and so on. The duration time of every step is 24 h. The final vertical pressures are 50 kPa, 75 kPa, and 100 kPa respectively. After 3 days, the settlement of the clay mud reaches a steady value and then the samples are consolidated completely. The 320
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Fig. 5. Details of soil cutting instrument.
Table 2 Summary of test conditions. Set no.
Test no.
τd = τx= τy (kPa)
fx (Hz)
fy (Hz)
CSR (τd/σ0)
A
A1 A2 A3 A4 A5 B1 B2 B3 B4 B5 C1 C2 C3 C4 C5
14.14 14.14 14.14 14.14 14.14 17.67 17.67 17.67 17.67 17.67 21.21 21.21 21.21 21.21 21.21
0.5 0.3 0.25 0.2 0.16 0.5 0.3 0.25 0.2 0.16 0.5 0.3 0.25 0.2 0.16
0.25 0.15 0.125 0.1 0.08 0.25 0.15 0.125 0.1 0.08 0.25 0.15 0.125 0.1 0.08
0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3
B
C
prepared specimen was 50 mm in diameter and 25 mm in height. The cutting procedure are as follows: (1) Pushing the soil samples out of the tube slowly and take the center part of each sample. (2) Fixing the remolded soft clay blocks on the setting of the cyclic simple shear cutting instrument, as shown in Fig. 5(a), and then using a steel wire cut off the outer edge of the soil sample, a cylindrical specimen with a diameter of 50 mm was made. (3) Putting it into a opening mold, due to the opening mold was made according to the standard size of sample manufacturing, so only cut off the excess soil of two port of the mold (Fig. 5(b)), the height of the sample can be raised to a standard height (25 mm).
Fig. 6. Configuration of shear box: (a) soil specimen in shear box and (b) final setting of shear box.
Fig. 7. Cyclic waves obtained in present study.
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Fig. 8. Curves of dynamic shear strains in x- and y-directions under different shear frequencies and CSRs.
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Fig. 8. (continued)
Fig. 9. Strain paths under different shear frequencies for CSR = 0.3.
A schematic of the loading modes and a typical deformation mode of a specimen are presented in Figs. 2 and 3, respectively. The physical properties of the test samples are listed in Table 1.
2.2. Test apparatus and procedures The schematic of the multidirectional cyclic simple shear test apparatus used in this study is shown in Fig. 4. The specimen was covered
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with a rubber membrane and placed in contact with the inner side of 25 Teflon-coated rings, which were stacked one above the other (thickness of each Teflon-coated ring: 1.0 mm). Lateral swelling of the specimen was not permitted, whereas shear deformation was allowed. This apparatus can provide any type of cyclic displacement to the bottom of a specimen from two perpendicular directions using an electrohydraulic servo system. A predetermined vertical stress can be applied to the specimen using an electrically controlled aero-servo system. This apparatus is the same as that used previously by Nie et al. [42] to investigate the undrained response of soils under multidirectional cyclic simple shear conditions. Fig. 6(a) shows a soil specimen in the shear box, whereas Fig. 6(b) shows the final setting of the shear box. During cyclic loading, the Teflon-coated rings slide smoothly on each other, and thus, constant volume conditions can be achieved. By using the same type of shear box, Wang et al. [43] performed two-way stresscontrolled cyclic shear tests under undrained conditions to evaluate the relationship between the pore water pressure and the number of cycles for a saturated clay layer. They found that the test results were not influenced by any friction between the rings. After consolidation, the specimen was subjected to cyclic shear for a predetermined number of cycles, cyclic stress ratio, and frequency under the undrained condition. In this study, the specimens were subjected to stress-controlled multidirectional cyclic simple shear. The test conditions are listed in Table 2. The main focus of this test program was to investigate the effect of the bidirectional shear frequency on the undrained response of Wenzhou soft clay under multidirectional cyclic simple shear conditions. The x-direction frequency was varied in the range f = 0.2–0.5, whereas the y-direction frequency was varied in the range f = 0.1–0.25. The cycle stress ratio was fixed as 0.20, 0.25, and 0.30. The waveform of the cyclic shear stress was sinusoidal (two-way cyclic stress). During the cyclic shear test, the vertical stress and the horizontal displacement were recorded every 10 s, and thereby, 50 data points were obtained in each cycle. These data points were used to determine the experimental results. The y-axis intersects the x-axis perpendicularly at the center of the bottom part of the specimen (Fig. 2). Fig. 7(a) shows the shear waveform obtained during the bidirectional cyclic shear tests, in which shear stress was applied simultaneously in both the x- and y-directions. In each test, a predetermined frequency difference between the waves in the x- and y-directions was applied. When the x-direction frequency was half the y-direction frequency, the orbits represented the figureeight cyclic shear condition (Fig. 7(b)). In this paper, for the bidirectional case, the shear stress amplitude represents the amplitude in the xand y-directions (i.e., τd = τx = τy). The tests were continued until the total strain amplitude reached 10% or until the number of cycles reached 100. Fig. 10. Changes in total shear strain, γd, with respect to number of load cycles, N, for various shear frequencies.
3. Test results and discussion 3.1. Cyclic strain
in the CSR, the differences in the shear strains under variable frequencies became larger. When the CSR was 0.25, the shear strain in the x-direction was 0.9% after 100 cycles for fx = 0.5. For the other three lower frequencies (fx = 0.3, 0.25, and 0.2), all the specimens reached failure before 100 cycles. Fig. 9 shows the relationship between the x- and y-direction strains for different shear frequencies. It was clear that at a high shear frequency (fx = 0.5), the x-direction strain was almost the same as the ydirection strain; thus, the shape of the strain path was similar to that of a regular figure eight. However, when the frequency reduced further (fx = 0.2), the development of the x-direction strain was not consistent with that of the y-direction strain and the strain path became irregular. It is also noteworthy that the fluctuating range in the x-direction for the positive strain increased as the shear frequency decreased. The strain in the y-direction kept swinging between the positive and
Fig. 8 shows the relationship between the cyclic shear strain γ and the number of cycles N for different CSR values and frequencies. As shown in Fig. 8, when the CSR was low (CSR = 0.2), the strains in the x- and y-directions grew slowly and remained stable after a certain number of cycles. However, when the CSR was 0.25 or 0.3, the strains in the x- and y-directions developed rapidly and the specimens even reached failure before 100 cycles. These results demonstrated that the cyclic shear stress ratio had a significant effect on the deformation behavior of the soft clay. In addition, the frequency had a significant influence on the deformation behavior of specimens with the same CSR. When the CSR was 0.2, the shear strains in both the x- and y-directions increased with a decrease of frequency. For example, the shear strain in the x-direction was 0.45% for fx = 0.5. For fx = 0.2, the value was 0.59%, which is an increase of 0.14% compared to the strain for fx = 0.5. With an increase 324
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Fig. 11. Stress–strain hysteretic loops under different shear frequencies.
the stress–strain relationship for different number of cycles, the stress–strain hysteretic loops for cycle nos. 1, 5, 10, and 20 are plotted in Fig. 12. With an increase in the number of cycles, the stress–strain loop inclined toward the horizontal axis. This trend can be attributed to the cyclic degradation of soft clay caused by the generation of pore water pressure. When the number of cycles became large, the cyclic degradation decreased more rapidly and the shape of the stress–strain hysteretic loop in the x-direction changed more clearly. Again, the shear modulus was normalized by its value before being compared under different shear frequencies. The relationship between the shear modulus and the number of cycles for various shear frequencies in both the shearing directions with CSRs of 0.25 and 0.3 were shown in Fig. 13. The dynamic shear modulus decreased rapidly during the first few cycles. Then, the decreasing trend became slower. In addition, the dynamic shear modulus had a positive correlation with the shear frequency and an inverse correlation with the CSR. A nearly linear relationship was found between the dynamic shear modulus and the number of cycles for all the four shear frequencies before the specimen was failed.
negative strains. This phenomenon may be related to the applied stress paths, as shown in Fig. 7(a). When the x-direction stress was considered for an odd number of laps, the shear stresses in both the directions produced positive strain. However, when the x-direction stress was considered for an even number of laps, the negative strain produced in the y-direction had a certain effect on the x-direction strain. To consider the shear strains in the x- and y-directions simultaneously, the total shear strain (γd) was proposed as follows: γd = γx2 + γy2 . The relationship between γd and the number of load cycles, N, was plotted in Fig. 10 for various shear frequencies. All the γd–N curves were nonlinear, and the development speeds of the cyclic strain were significantly different for different CSRs and shear frequencies. Fig. 10 indicates that for the same cyclic stress ratio, a larger shear frequency resulted in the sample requiring a higher number of load cycles to reach failure for 0.2 ≤ fx ≤ 0.3. The strain development speed on soil samples increased more slowly at fx = 0.5 than at lower shear frequencies. Thus, the number of load cycles to reach failure, Nf, was greater. This is because when the shear frequency increased, the pore water pressure did not have sufficient time to develop, causing the total shear strain to be considerably less than those at lower shear frequencies. This conclusion is in agreement with that of a previous study [44].
3.3. Cyclic strength The relationships between the shear frequency and the number of load cycles required to reach an amplitude strain of 10% (cyclic failure, Nf) [45] are shown in Fig. 14, which gives a comparison of the cyclic strength between CSR = 0.25 and CSR = 0.30. For CSR = 0.2, the specimens did not fail, so the corresponding plot is not shown. When fx increased from 0.2 to 0.5, the cyclic strength increased. For the same value of frequency, an increase in the CSR resulted in a decrease in the cyclic strength. Based on the test results, the relationship between the shear frequency and Nf was derived as follows:
3.2. Cyclic resilient behavior Fig. 11 shows the stress–strain hysteretic loops for specimens with fx = 0.2, 0.25, 0.3, and 0.5 Hz. When the shear frequency was high, the shear strains in both the directions gradually increased; thus, the shear strains in the two directions remained consistent with each other. However, when the shear frequency was low, the shear strain in the xdirection was barely consistent with that in the y-direction. To compare
Nf = m*f n 325
(1)
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Fig. 12. Stress–strain hysteretic loops in (a) y-direction and (b) x-direction under different shear frequencies.
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Fig. 13. Relationships between G and f versus number of cycles, N, for CSR = 0.25 and 0.3.
2. The γd–N relationship curves were dependent on both the cyclic stress ratio and the shear frequency. With an increase in the cyclic stress ratio, the effect of the shear frequency on the strain was more apparent.
The parameters m and n in Eq. (1) can be determined empirically by the curve-fitting. Considering the effect of the shear frequency, it was concluded that when CSRs were relatively high, the shear strain was significantly influenced by the shear frequency. The higher the CSRs, the larger was the effect of the shear frequency on the strain development. 4. Conclusions In this study, a figure-eight-shaped stress path was formed by controlling the shear frequency in the x-direction to be twice that in the ydirection. To clarify the effect of both the cyclic shear frequency and the cyclic shear stress ratio on the properties of cohesive soft clay from Wenzhou, China, several series of cyclic simple shear tests were performed under the figure-eight-shaped shearing stress path. The main conclusions of the study are summarized as follows: 1. When the shear frequency was high, the cyclic strain in the x-direction was almost consistent with that in the y-direction under the same CSR and the shape of the strain path was still similar to that of a regular figure eight. However, when the shear frequency was low, the x-direction cyclic strain was not consistent with the y-direction cyclic strain and the strain path had a shape of an irregular figure eight.
Fig. 14. Relationship between shear frequency, f, and number of cycles, N.
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3. With an increasing number of cycles, the shape of the stress–strain hysteretic loop changed and the dynamic shear modulus decreased because of the degradation of the soft soil. 4. The lower the shear frequency, the fewer were the load cycles needed to reach failure. A new equation relating the shear frequency to the number of cycles needed to reach failure was suggested for soft clay.
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