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Liquefaction of sand under monotonic and cyclic shear conditions: Impact of drained preloading history
Soil Dynamics and Earthquake Engineering 126 (2019) 105775
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Liquefaction of sand under monotonic and cyclic shear conditions: Impact of drained preloading history
T
K. Pana, Y.Q. Caia,b, Z.X. Yangb,*, X.D. Pana a b
College of Civil Engineering and Architecture, Zhejiang University of Technology, Hangzhou, Zhejiang, 310014, China Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou, Zhejiang, 310058, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Preloading history Monotonic loading Cyclic loading Liquefaction Shear strength Cyclic resistance Correspondence
In-situ sand deposits inevitably undergo a preloading history caused by factors such as overlying structures, adjacent construction work, or repeated sedimentation and erosion; this will in turn affect their mechanical behavior and liquefaction susceptibility during subsequent loading. An experimental program was developed to explore the potential influence of the drained preloading history on the undrained response of sand subjected to both monotonic and cyclic loadings. The results indicate that the shear strength, dilatancy, and stiffness characteristics in monotonic tests depend on the relative directions of the drained preloading and subsequent undrained shearing. Two typical types of behavior are observed and identified in the cyclic tests, i.e., cyclic mobility and residual deformation accumulation failure, depending on the stress state prior to the undrained cycling. The cyclic resistance is quantified based on a failure criterion defined in terms of the triggering of flow behavior, and it is compared to that determined using a criterion of specified strain threshold. In particular, the direction–wise (compressional or extensional) influence of the preloading history on the liquefaction resistance and pore pressure generated in sand during cyclic loading agrees well with that observed during monotonic loading. Furthermore, a correspondence between the cyclic and monotonic tests can be derived, and a unified approach is proposed to evaluate both the monotonic and cyclic responses, irrespective of the drained preloading history.
1. Introduction The terms liquefaction or liquefaction failure describe a phenomenon whereby a saturated cohesionless soil undergoes a substantial loss of strength and stiffness in response to an applied stress, typically accompanied by the development of excessive deformation and high pore pressures. A comprehensive laboratory study of the undrained responses of sandy deposits is of vital importance for assessing their susceptibility to liquefaction and the potential for related catastrophic damage, such as the sinking of structures on the surface, spreading of embankments, and lateral displacement of the ground [1–5]. Numerous experimental results have demonstrated that liquefaction phenomena can be classified into flow liquefaction and cyclic mobility based on the different triggering mechanisms [6–8]. Flow liquefaction, which is characterized by tremendous instabilities (known as a strain–softening response) in loose or contractive sand, can be induced under either monotonic or cyclic shear conditions [9–11]. However, for dense or dilative sand, cyclic mobility accounts for the excessive strain development and progressive stiffness degradation when the sand
*
experiences transient states of zero effective stress during cyclic loading [12–14]. In addition to the initial state of the sand, the liquefaction behavior is also influenced by the preloading history prior to the application of undrained monotonic or cyclic shear stress. In practical engineering, in–situ soils may experience a preloading history, such as the driving static shear stress that is imposed on subsoils beneath sloping ground or underneath structures. The existence of a static shear stress and its influence on the undrained responses of sands have been extensively studied [15–18]. These experimental results suggested that the static shear may enhance the liquefaction resistance and would be beneficial to dilative sand, but it tends to be detrimental when the static shear stress increases for contractive sand. Triaxial experimental tests conducted by Sivathayalan and Ha [10] and Pan et al. [19] indicated that the presence of static shear may increase the possibility of strain–softening of soil under subsequent monotonic shearing. Under cyclic loading conditions, Hyodo et al. [16], Yang and Sze [20], and Pan and Yang [14] found that the failure of sand with a large initial shear stress can be attributed to gradually accumulated residual deformation, rather
Corresponding author. E-mail addresses: [email protected] (K. Pan), [email protected] (Y.Q. Cai), [email protected] (Z.X. Yang), [email protected] (X.D. Pan).
https://doi.org/10.1016/j.soildyn.2019.105775 Received 9 April 2019; Received in revised form 24 June 2019; Accepted 25 July 2019 0267-7261/ © 2019 Elsevier Ltd. All rights reserved.
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Abbreviations CSR Dr Eu e0 Nf,5% Nf,flow p0’ q0
qcyc qIS, qPT
cyclic stress ratio relative density of sand undrained secant Young's modulus initial void ratio prior to undrained shearing number of cycles required to attain axial strain of 5% number of cycles required to trigger cyclic flow initial mean normal effective stress initial deviatoric stress prior to undrained shearing
SIS, SPT uC, uE
εa
than the flow liquefaction or cyclic mobility that is usually observed in sands without an initial shear stress. Moreover, soils in the field may have experienced excavation, refilling, and repeated sedimentation and erosion, and thus involve an unloading stress path in addition to the initial sustained shear stress; therefore, a loading–unloading cycle of shear stress is usually applied prior to the subsequent shear tests [21–23]. Since the pioneering work of Finn et al. [24], many studies have been conducted to assess the effect of an undrained preloading cycle followed by reconsolidation on the liquefaction susceptibility of soils. Previous studies performed by Ishihara and Okada [25], Suzuki and Toki [26], and Bouferra et al. [27] indicated that the undrained preloading at small stress or strain amplitude can delay the occurrence of liquefaction failure, while a preloading cycle with large amplitude usually weakens the liquefaction resistance. However, the effect induced by the drained preloading history, which can also be encountered in field conditions [28–30], on the liquefaction behavior of sand has not been adequately elucidated and should be investigated further. In particular, to quantify the drained preloading effect, it is necessary to analyze the respective influences of the loading and unloading processes of the initial shear stress and their interaction on the subsequent undrained response of sand in a systematic manner. It has long been recognized that the soil fabric or inherent anisotropy is an important factor governing its mechanical behavior; for example, sand under triaxial compression exhibits enhanced dilation and much stiffer response than sand under triaxial extension [31,32]. It should be noted that the inherent anisotropy formed during the deposition process of natural sands may undergo further alteration due to the preloading history, which is known as the stress–induced fabric anisotropy. The existing experimental data from monotonic and cyclic shear tests have focused primarily on the induced fabric or stress anisotropy caused by a compressional preloading path. For example, Gajo and Piffer [28] and Finge et al. [33] examined the effect of a compressional preloading cycle on the undrained responses of sand, and concluded that the induced anisotropy may significantly affect the elastic deformation characteristics and shear resistance during subsequent loadings. However, few studies have considered the anisotropy induced by preloading in extension, which also often occurs in soil deposits under field conditions, as described by Yoshimine and Hosono [34], Andersen [35], and Yang and Pan [11]. Furthermore, there is still no consensus regarding the impact of inherent and induced anisotropy that can be determined based on the correspondence between the undrained responses of sand under monotonic and cyclic loading conditions. Mao and Fahey [36], Baki et al. [37], and Li et al. [38] confirmed that the stress path of a monotonic test defines a boundary surface for the corresponding cyclic behavior, which implies that flow failure with abrupt deformation could be triggered when the cyclic stress path is
cyclic deviatoric stress deviatoric stresses at instability state and phase–transformation state, respectively normalized shear strengths at instability state and phase–transformation state, respectively residual pore pressure components developed in compression and extension segments of the first cycle, respectively axial strain
close to or beyond the stress path of the monotonic test under the same initial conditions. On the other hand, it has also been argued that cyclic flow occurs when the stress state in the cyclic tests meets the instability line determined in the corresponding monotonic test [16,39,40]. Hence, it seems reasonable to explore the liquefaction behavior of sand under both compressional and extensional preloading paths through a sophisticated experimental program, and to further establish the correlation between the undrained responses during monotonic and cyclic loadings. In summary, the primary aim of this study is to assess the influence of induced anisotropy created by varying the drained preloading history on the undrained strength, deformation, and pore pressure responses of sand through monotonic and cyclic triaxial tests. Dramatic differences in the influence of the imposed compression and extension preloading paths on the monotonic and cyclic responses can be observed, depending on the relative direction between the drained preloading and subsequent undrained shearing. Based on failure criteria defined as a specified strain magnitude or the triggering of flow behavior, the effect of the preloading history on the cyclic resistance of sand can be determined. Remarkably, this effect is much more significant when the samples are sheared from the anisotropic stress state than the isotropic stress state. Moreover, by normalizing the cyclic strength to the corresponding monotonic strength, a unified approach can be developed to quantify the correspondence between the undrained responses under monotonic and cyclic shear conditions. The experimental observations and quantitative findings for the preloading effect obtained in this study can offer insight into the correlation between the undrained monotonic and cyclic responses of sand, and thus provide useful guidance for the practical design of engineering projects.
2. Test procedures The experiments in this study were conducted using an automated triaxial system capable of performing both monotonic and cyclic loading tests, as described by Pan and Yang [41]. Toyoura sand was employed as the test material, as it has been extensively characterized in the literature; Table 1 lists the physical properties of Toyoura sand [32]. Ample experimental evidence has indicated that the fabric anisotropy of a sample prepared for laboratory testing is strongly dependent on the preparation technique [1,32,39]. In this study, the dry deposition method was used to prepare the reconstituted samples, mimicking the gravitational deposition process of sand in the field. The samples have a diameter of approximately 70 mm and a height of 140 mm. Fully saturated samples with Skempton's B-values > 0.96 are obtained through backpressure saturation facilitated by preceding circulation of carbon dioxide.
Table 1 Index properties of the test material. Mean particle diameter, D50: mm
Uniformity coefficient, Uc
maximum void ratio, emax
minimum void ratio, emin
specific gravity, Gs
0.17
1.7
0.977
0.597
2.65
2
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The saturated samples were first isotropically consolidated to a mean effective stress of p0’ = 100 kPa. They were then preloaded to the desired initial stress state along a constant p’ stress path prior to the undrained shearing tests. As illustrated in Fig. 1, four preloading paths were considered in this study: drained compressional loading with a magnitude of 80 kPa (‘O-A-C’), drained extensional loading with a magnitude of −60 kPa (‘O-A-E’), and drained compressional and extensional loading–unloading paths (‘O-A-C-A’ and ‘O-A-E-A’, respectively). In contrast to the first two paths, the latter two paths aim to examine the effect of induced fabric anisotropy caused by loading–unloading cycles and to isolate the influence of the initial stress anisotropy. Moreover, a sample subjected to isotropic consolidation (path ‘O-A’) without any preloading history was also tested as a benchmark for comparison. At the end of the drained preloading, the void ratios, e0, of all specimens ranged from 0.732 to 0.748 (relative density Dr = 59%–63%), and can thus be classified as medium–dense sand [19,42]. The small variation in the density of specimens is not expected to produce significant discrepancies in the results of the subsequent undrained shear tests, which include triaxial compression (TC), triaxial extension (TE), and cyclic loading (Cyc). In the monotonic tests, a strain rate of 0.1%/min was employed, while in cyclic tests, a sinusoidal waveform was applied at a frequency of 1 Hz. Table 2 summarizes the test details, such as the drained preloading types and undrained shearing modes.
significantly reduce the strength in TE, and vice versa. Second, the effective stress paths shown in Fig. 4(a) vary dramatically between these two preloading paths, especially in the incipient shearing stage of TC or TE. When the undrained shearing commences from the same direction as the drained preloading, i.e., the UTCC and UTEE tests, the mean effective stress changes only slightly during the incipient stage. When the undrained shearing is imposed in the opposite direction of the drained preloading, a dramatic decrease in the effective stress can be observed in the UTCE and UTEC tests. This scenario is in agreement with the shear test results reported by Yimsiri and Soga [44] and Gu et al. [45] from discrete element simulations, and provides evidence supporting the anisotropic elasticity interpretation described by De Gennaro et al. [39], Ye et al. [30], and Pan et al. [19]. The nonlinear stress–strain response shown in Fig. 4(b) indicates that the stiffness degradation of sand is also affected by the preloading history. Fig. 5(a) and (b) show the variations in the undrained Young's modulus (Eu), which is defined as the secant slope of the deviatoric stress–strain curve [19,46], with the development of axial strain under TC and TE loadings, respectively. In each plot, the stiffness characteristics of the sand subjected to the drained loading–unloading history are compared to those of isotropically consolidated sand. Broadly, a significant reduction in the secant Young's modulus with the strain is observed. Under the undrained TC condition, as shown in Fig. 5(a), the stiffness of the specimen subjected to the extensional loading–unloading path (UTCE) is lower than that of the specimen subjected to the compressional loading–unloading path (UTCC). The stiffness reduction curve for the sample without preloading (ITC) falls in between those for the UTCE and UTCC. However, when the samples were subjected to TE, the above trends were reversed, as shown in Fig. 5(b), in which the curve obtained in the UTEE test is above that obtained in the UTEC test, with the ITE curve in between. The results presented in Fig. 5 reveal that the drained loading–unloading history on one side can enhance the stiffness if the sample is subsequently subjected to undrained shear on the same side.
3. Undrained responses during monotonic loading Fig. 2(a) and (b) show the effective stress paths and stress–strain curves obtained from undrained TC and TE tests on isotropically consolidated sand (ITC and ITE). It is clear that the monotonic response of sand differs dramatically between TC and TE under otherwise identical testing conditions. The shear resistance increases monotonically and the strain–hardening response dominates in the ITC test, accompanied by significant dilation in the post phase–transformation state (PTS) stage [43]. In contrast, in the ITE test, the shear resistance initially increases to a negative maximum, known as the instability state (IS) [9], after which a strain–softening response prevails, with a reduction in shear resistance until the PTS stage. It is worth noting that to avoid the occurrence of cavitation due to the high negative pore pressure in TC or necking (severe non–uniform deformation) in TE, the axial strains imposed on the specimens during monotonic loading are not sufficient for the specimens to reach the critical state. The influence of the preloading history on the effective stress paths and stress–strain curves of sand is presented in Figs. 3 and 4 for the cases with drained loading and loading–unloading paths, respectively. It can be seen from Fig. 3(a) and (b) that the overall behavior of the sand exposed to drained compressional and extensional loading appears similar to that of the isotropically consolidated sand shown in Fig. 2(a) and (b), i.e., it exhibits predominately dilative behavior with stable strain–hardening in TC and an unstable response with slight strain–softening in TE. In particular, as shown in Fig. 3(b), under either TC or TE conditions, the stress–strain curve is shifted in the direction of the drained preloading (upward or downward). As a result, the shear stress at the PTS under TC is slightly higher for the LTCC test, while the peak resistance at the IS obtained under TE is lower for the LTEC test. The test results for samples with a drained loading–unloading path are shown in Fig. 4. It can be seen that unlike the strain–softening response observed in the TE condition, the undrained TC results exhibit strain–hardening and a more dilative response. For instance, as shown in Fig. 4(a), no discernible contraction is observed in the UTCC test. Although the initial stress state of the samples in Fig. 4 is the same as that subjected to isotropic consolidation alone (Fig. 2), some key differences in the responses due to the drained preloading can be identified. First, as shown in Fig. 4(b), the loading–unloading history on the compression side may enhance the undrained shear strength in TC but
4. Undrained responses during cyclic loading 4.1. Typical types of cyclic behavior Figs. 4 and 5 show that the drained loading–unloading path has a significant influence on the dilative response and stiffness degradation of sand. To examine the influence of the loading–unloading history on the cyclic behavior of sand, the results of three typical tests, illustrated by the effective stress paths, the stress–strain curves, and development of the axial strain and excess PWP with the number of cycles, are presented in Figs. 6–8. These tests were conducted with an equal magnitude of the cyclic deviatoric stress, qcyc = 40 kPa, but with different preloading histories. Fig. 6 shows the cyclic behavior of isotropically consolidated sand without any preloading history, which is the typical cyclic mobility
Fig. 1. Schematic diagram for drained preloading path. 3
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Table 2 Summary of monotonic and cyclic triaxial tests. Series
Preloading type
Shearing mode
e0
q0 (kPa)
qcyc (kPa)
CSR
Test IDa
I
I(O-A) I(O-A) I(O-A) I(O-A) I(O-A) I(O-A) I(O-A) L(O-A-C) L(O-A-C) L(O-A-C) L(O-A-C) L(O-A-C) L(O-A-E) L(O-A-E) L(O-A-E) L(O-A-E) L(O-A-E) U(O-A-C-A) U(O-A-C-A) U(O-A-C-A) U(O-A-C-A) U(O-A-C-A) U(O-A-E-A) U(O-A-E-A) U(O-A-E-A) U(O-A-E-A) U(O-A-E-A)
TC TE Cyc Cyc Cyc Cyc Cyc TC TE Cyc Cyc Cyc TC TE Cyc Cyc Cyc TC TE Cyc Cyc Cyc TC TE Cyc Cyc Cyc
0.739 0.735 0.742 0.741 0.737 0.744 0.740 0.748 0.746 0.740 0.742 0.739 0.737 0.739 0.732 0.741 0.741 0.738 0.747 0.744 0.737 0.741 0.739 0.733 0.740 0.742 0.736
0 0 0 0 0 0 0 80 80 80 80 80 −60 −60 −60 −60 −60 0 0 0 0 0 0 0 0 0 0
/ / 30 35 38 40 45 / / 70 80 90 / / 15 25 30 / / 30 35 40 / / 35 40 50
/ / 0.15 0.175 0.19 0.2 0.225 / / 0.35 0.4 0.45 / / 0.075 0.125 0.15 / / 0.15 0.175 0.2 / / 0.175 0.2 0.25
ITC ITE ICyc_30 ICyc_35 ICyc_38 ICyc_40 ICyc_45 LTC(C) LTE(C) LCyc(C)_70 LCyc(C)_80 LCyc(C)_90 LTC(E) LTE(E) LCyc(E)_15 LCyc(E)_25 LCyc(E)_30 UTC(C) UTE(C) UCyc(C)_30 UCyc(C)_35 UCyc(C)_40 UTC(E) UTE(E) UCyc(E)_35 UCyc(E)_40 UCyc(E)_50
II
III
IV
V
Note: e0, initial void ratio prior to undrained shearing, q0, qcyc, initial and cyclic deviatoric stresses, respectively; CSR, cyclic stress ratio (the ratio of the cyclic shear stress amplitude to that of the initial mean effective stress, CSR=qcyc/(2p0’)). a The designation identifies: 1) the drained preloading type–I for isotropic consolidation, L for loading, U for loading-unloading, (C) and (E) for preloading in compression and extension, respectively; 2) the undrained shearing mode–TC for triaxial compression, TE for triaxial extension and Cyc for cyclic loading; 3) the amplitude of cyclic deviatoric stress.
Fig. 2. Monotonic shear response of sand under isotropic consolidation: (a) effective stress path; (b) stress-strain curve.
Fig. 3. Monotonic shear response of sand with drained loading path: (a) effective stress path; (b) stress-strain curve.
4
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Fig. 4. Monotonic shear response of sand with drained loading-unloading path: (a) effective stress path; (b) stress-strain curve. Fig. 5. Undrained stiffness varied with axial strain for sand with drained loading-unloading history in (a) triaxial compression and (b) triaxial extension.
response as characterized by the “butterfly” stress paths in Fig. 6(a), the S–shaped hysteresis curves in Fig. 6(b), the double–amplitude (DA) strain development in Fig. 6(c), and fully PWP buildup in Fig. 6(d). Following Hyodo et al. [12] and Yang and Sze [20], this specimen is regarded as failure at N = 26 according to the strain criterion of DA = 5%. The similar cyclic mobility type behavior can also be observed for sand with a loading–unloading history, as shown in Figs. 7 and 8. Applying the same failure criterion of DA = 5%, it can be seen that the specimens preloaded in compression and extension fail at N = 20 and N = 106, respectively. Compared to the sample without preloading, the sand is less prone to failure after an extensional loading–unloading cycle, while the compressional loading–unloading history only slightly reduces the cyclic resistance to liquefaction. This finding is consistent with the conclusions presented by Oda et al. [21] and Wei and Wang [47], who found that the drained stress or strain history in compression tended to reduce the liquefaction resistance of cohesionless soil. Moreover, the effective stress paths in Figs. 7(a) and 8(a) show a clear difference between the two types of preloading history, particularly during the first loading cycle. In fact, the specimen preloaded in compression behaves slightly elastically in the first half–cycle (the compression segment), but contracts considerably during the subsequent extension segment. Consequently, the excess PWP generated in the extension segment is higher than that in the compression segment, as shown in the inset of Fig. 7(d). In contrast, the extensional loading–unloading history provides a beneficial gain: pronounced contraction in the first half–cycle followed by negligible development of the PWP, as shown in Fig. 8(d). To illustrate the cyclic response of sand with stress anisotropy due to preloading, two typical results with varying amplitudes of the cyclic deviatoric stresses are presented in Figs. 9 and 10 for drained compressional and extensional loading, respectively. To simplify the presentation, only the effective stress paths and stress–strain curves are
illustrated. The typical residual deformation accumulation failure can be inferred from the stress–strain curves for the tests shown in both Figs. 9(b) and 10(b), and the stress paths shown in Figs. 9(a) and 10(a) appear to be stable with a negligible reduction in the effective stress. To provide a unified comparison of the cyclic resistance determined from different types of behavior, the criterion for the liquefaction or failure of sand in non-symmetric cyclic tests is defined as a 5% single–amplitude (SA) axial strain [14,17,48]. According to this strain criterion, the specimen with drained compressional loading fails at N = 69 on the compression side, while the specimen with drained extensional loading fails at N = 11 on the extension side. Although the test results in Figs. 9 and 10 indicate excessive accumulated residual deformation in both cases, apparent differences can still be observed. For instance, cyclic flow behavior, synchronized with an abrupt development in axial strain, is observed in the first loading cycle in Fig. 10(b), while the rate at which the cyclic strain increases in Fig. 9(b), is shown to be more moderate.
4.2. Effect of preloading on cyclic resistance and pore pressure The test results shown above indicate that the type of cyclic failure mode depends solely on the stress state of the specimen prior to the undrained shearing, i.e., cyclic mobility for the sand in an isotropic stress condition and residual deformation accumulation failure for the sand with stress anisotropy. Nevertheless, the drained preloading history also plays an important role in the cyclic resistance of sand. Fig. 11 summarizes the strain criterion–based cyclic resistance under various preloading conditions for the imposed cyclic stress ratio (CSR) in terms of the number of cycles required to attain axial strain of 5% (Nf,5%). In 5
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Fig. 6. Cyclic response of sand under isotropic consolidation (ICyc_40): (a) effective stress path; (b) stress-strain curve; (c) axial strain; (d) excess PWP.
than that in the subsequent extensional half-cycle. In contrast, for the cases with drained loading–unloading paths, the opposite trend is observed: the mean values are 0.3 for the UCyc(C) tests and 7.0 for the UCyc(E) tests. Thus, it can be concluded that the effect of a drained loading–unloading path on the pore pressure generation is closely related to whether the drained preloading and subsequent undrained cycling are in the same or opposite directions. When the cyclic loading is on the same side as the preloading, e.g., both in compression, the generated pore pressure is relatively small. However, when the specimen is preloaded in the opposite direction of the cyclic loading, the pore pressure is built up more rapidly. Moreover, as shown in Fig. 12, the specimens subjected to drained compressional or extensional loading have negative values of uC/uE; the mean values are −0.5 for the LCyc(C) tests and −0.6 for the LCyc(E) tests. This is caused by the dilative tendency of the sand that was sheared from an anisotropic stress state, as shown in Figs. 9 and 10.
general, for a given CSR, the required Nf,5% varies under different preloading conditions. Clearly, the CSR versus Nf,5% trends obtained from the LCyc(C) and LCyc(E) tests constitute the upper and lower bounds in this diagram. This signifies that the drained compressional loading can markedly enhance the resistance to liquefaction failure, while the effect of drained extensional loading on the cyclic resistance is detrimental, compared to the case without a preloading history (ICyc). The direction–dependent influence is also found in the sand subjected to compressional and extensional loading–unloading paths. The observed CSR versus Nf,5% trends for tests UCyc(E) and UCyc(C) are located above and below that for isotropically consolidated sand, respectively, indicating beneficial and adverse effects from extensional and compressional loading–unloading histories, respectively. Nevertheless, it is worth noting that the data points for these three cases fall within in a narrow band, indicating that the influence of the preloading history on sand cyclically sheared from an isotropic stress state tends to be far less significant than for sand with stress anisotropy. As shown in Figs. 7 and 8, one of the most notable features in the sand response is the dramatic difference in the generation of pore pressure during the incipient stage of cycling. Fig. 12 presents a summary interaction diagram showing the pore pressure coefficient (uC/uE) determined from cyclic tests with various combinations of preloading history and CSR. Herein, uC and uE denote the residual excess PWP developed on the triaxial compression and extension side in the first undrained cycle, respectively, as shown in the insets of Figs. 7(d) and 8(d). It should be noted that in this diagram, the data points for each preloading condition are somewhat scattered, and the mean values of uC/uE for all of the considered preloading cases are provided and indicated by the figures nearby. For example, the mean value of uC/uE for the ICyc tests is approximately 3.0, implying that the residual pore pressure generated during the first compressional half–cycle is greater
5. Link between monotonic and cyclic responses The flow behavior of sand during cyclic loading is thought to be intimately related to the sand responds to monotonic loading [11,20,49]. Fig. 13 shows two typical examples of flow behavior in the cyclic tests. The first example shows cyclic mobility, in which the cyclic stress path evolves rapidly to a near–zero effective stress state (Fig. 13(a)), and an abrupt deformation followed by a large DA strain results in the failure of the sand (Fig. 13(c)). In the second example, the sample is sheared from an anisotropic stress state on the extension side (Fig. 13(b)), and cyclic flow with a considerably larger strain occurs during the incipient cycling, resulting in a gradual and moderate accumulation of residual SA strain in the subsequent cycles (Fig. 13(d)). In Fig. 13(a) and (b), the monotonic TE effective stress paths (dashed 6
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Fig. 7. Cyclic response of sand with compressional loading-unloading path (UCyc(C)_40): (a) effective stress path; (b) stress-strain curve; (c) axial strain; (d) excess PWP.
Fig. 8. Cyclic response of sand with extensional loading-unloading path (UCyc(E)_40): (a) effective stress path; (b) stress-strain curve; (c) axial strain; (d) excess PWP. 7
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Fig. 9. Cyclic response of sand with compressional loading path (LCyc(C)_90): (a) effective stress path; (b) stress-strain curve.
lines) are superimposed with identical initial conditions, and the instability region bounded by the instability line (IL) and phase–transformation line (PTL) can thus be determined. The IL refers to the line connecting the origin and the IS prior to the strain–softening [9,50]; the PTL is the line that separates the contraction and dilation zones in the p′–q plane [7,43]. As illustrated in these diagrams, when the cyclic stress path approaches the IL defined in the monotonic tests, flow behavior characterized by a sudden increase in the axial strain is activated. Thus, it is expected that for the sand sheared from either an isotropic stress state or an anisotropic stress state with drained extensional loading, the cyclic flow behavior will always occur on the extension side, as the stress state of the cyclic loading lies in the instability region in the corresponding TE test. However, for the sand subjected to drained compressional loading, the cyclic stress path is significantly shifted toward the compression side, and no instability is observed in the corresponding monotonic TC test. This implies that the effective stress path during cyclic loading can never reach the monotonic instability region, and thus only residual deformation accumulation failure without flow behavior can occur for sand with a high stress anisotropy due to the compressional preloading, as shown in Fig. 9. On the triggering of cyclic flow, as marked by the arrows in Figs. 6(c) and 7(c) and 8(c) and 10(b), the strain development accompanied by a sudden acceleration can immediately satisfy the strain–based failure criterion for cyclic mobility, or even lead to drastic consequences owing to the relatively high magnitude of the abrupt residual deformation. In contrast to the conventional failure criteria in terms of specified strain thresholds (e.g., 5% DA or SA), the triggering of cyclic flow can also be considered as the failure state of sand, from which an estimation of the cyclic resistance on the safe side can be obtained. Fig. 14(a) shows the relationship between the CSR and the number of cycles required to trigger cyclic flow (Nf,flow). Similar to the trends
Fig. 11. Number of cycles to attain axial strain of 5% (Nf,5%) with respect to CSR under various preloading conditions.
based on strain criteria shown in Fig. 11, the required Nf,flow for a given CSR varies with the preloading condition. Similarly, the CSR versus Nf,flow curves for the UCyc(E) and UCyc(C) tests are located above and below that of the ICyc tests, respectively. This indicates that the drained extensional loading–unloading path can delay the occurrence of cyclic flow, while the compressional loading–unloading path has a somewhat detrimental effect on the resistance to cyclic flow. It should be noted that in Fig. 14(a), the data for the sand subjected to drained compressional loading are excluded, as no cyclic flow behavior is observed in the LCyc(C) tests. However, for the sand sheared from an anisotropic stress state due to extensional loading, the cyclic resistance is significantly decreased, as flow behavior is triggered in the very beginning of the shearing in the LCyc(E) tests.
Fig. 10. Cyclic response of sand with extensional loading path (LCyc(E)_30): (a) effective stress path; (b) stress-strain curve. 8
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example, the drained compressional loading is beneficial and greatly enhances the strength of the sample in TE tests, while its effect is detrimental and reduces the strength of the sample in the TC tests. In Fig. 14(b), the flow criterion–based cyclic resistance shown in Fig. 14(a) is normalized relative to the corresponding monotonic shear strength at IS. In the resulting diagram, the data for the sands sheared after isotropic consolidation and drained preloading collapse on a single line, irrespective of the type of preloading history and the amplitude of the cyclic stress. These results confirm the validity of the approach for relating cyclic flow to the instability behavior under monotonic shear. Therefore, for sand exhibiting a strain–softening response under monotonic loading, the undrained resistance to cyclic flow can be predicted from the shear strength at IS in the corresponding monotonic tests. In fact, based on experimental work with isotropically consolidated sand, Hyodo et al. [12] and Porcino et al. [51] proposed an approach to predict the cyclic strength of sand exhibiting either strain–softening or strain–hardening monotonic responses by relating the strain criterion–based cyclic resistance to the monotonic shear strength at PTS. To verify the validity of such an approach, the cyclic strength data in Fig. 11 normalized by the shear strength, SPT, are shown in Fig. 14(c). Note that the data for the LCyc(C) tests, which were not included in Fig. 14(a) and (b), have also been normalized by the SPT value obtained from the LTC(C) test and are presented in Fig. 14(c). Clearly, a unique trend exists for the sand undrained sheared from an isotropic state, regardless of the presence of a loading–unloading history. However, the data points for the sand subjected to drained compressional or extensional loading (solid symbols) are scattered and deviate significantly above the isotropic trend, suggesting that the traditional approach correlating the cyclic resistance and monotonic strength at PTS should take into account the stress state of the sand prior to the cyclic loading. Comparing Fig. 14(b) and (c) indicates that the IS, rather than the PTS, determined in monotonic shear tests is more suitable for evaluating the susceptibility of sand to undergo liquefaction due to cyclic loading, especially when cyclic flow behavior has been triggered. The new approach developed in this study for relating cyclic flow with monotonic instability, along with the obtained quantitative findings of the drained preloading effect, may provide insights to assess cyclic resistance of sand with varying initial stress states. Noting that the shear resistance at instability state is a sound unique parameter in
Fig. 12. Pore pressure coefficient (uC/uE) with respect to CSR during the first loading cycle.
Given the clear correspondence between cyclic flow and monotonic instability, further investigation is necessary to determine the relationship of the shear strength between the monotonic and cyclic tests. Following the work by Hyodo et al. [16] and Yang and Pan [11], the normalized shear strength of sand at IS (SIS) or PTS (SPT) under monotonic loading can be defined as follows:
SIS = qIS − q0 / p0′
or
SPT = qPT − q0 / p0′
(1)
where q0 is the initial deviatoric stress prior to the undrained shearing, and qIS and qPT are the deviatoric stresses at IS and PTS, respectively. Table 3 summarizes the values of SIS and SPT for sand in both TC and TE tests under various drained preloading conditions. Overall, for the sand tested in TC, no SIS exists owing to the absence of an instability response; however, SPT can be obtained in almost all of the tests, except for the UTC(C) test, in which dilation is dominant. It is found that under either TC or TE conditions, although the samples sheared from an isotropic stress state have similar SIS or SPT, further inspection indicates that the drained preloading on one side slightly strengthens the sample during subsequent loading on the same side, but results in lower strength in the sample during loading on the other side. However, for the sand sheared from an anisotropic stress state, the test data summarized in Table 3 appear to indicate an opposite tendency. For
Fig. 13. Schematic illustration of the correspondence between cyclic flow behavior and instability region during monotonic loading. 9
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6. Conclusions A series of monotonic and cyclic triaxial tests on medium–dense Toyoura sand were performed to investigate the influence of drained preloading on the liquefaction behavior of sand during subsequent undrained shearing. The strain development, pore pressure generation, and strength characteristics were presented, and the underlying correspondence between the monotonic and cyclic shear responses was explored. The main conclusions drawn from this study can be summarized as follows: 1. The monotonic shear behavior of sand depends on both the drained preloading type and the undrained shearing mode: a) in triaxial compression, the response is stable and predominately strain–hardening and dilative, whereas instability with strain–softening is triggered in extension; b) either drained compressional or extensional loading can decrease the shear strength of sand during undrained shearing in the same direction but strengthen the sample during undrained shearing in the other direction; c) a drained loading–unloading history on one side renders the sand stiffer during the incipient stage of subsequent shearing on the same side, but results in a more contractive and softer response during shearing on the other side. 2. Two different types of cyclic behavior are identified, i.e., cyclic mobility and residual deformation accumulation failure, depending on the stress state prior to the cyclic loading. Cyclic mobility dominates in sand sheared from an isotropic stress state and is accompanied by excessive DA cyclic strains. Residual deformation accumulation failure is observed in specimens with an initial shear stress and is characterized by the progressive development of SA residual strains. 3. Based on a failure criterion defined in terms of a specified strain threshold (e.g., 5%), the influence of the preloading history on the cyclic resistance of sand sheared from an isotropic stress state tends to be far less significant than for sand with stress anisotropy. Nevertheless, further inspection indicates a beneficial effect of an extensional loading–unloading history on increasing the cyclic resistance, but an adverse effect of a compressional loading–unloading history on the cyclic resistance. This direction–dependent influence was also observed for the pore pressure generation in sand during the first undrained loading cycle. 4. Cyclic flow behavior, characterized by a sudden strain development, occurs when the effective stress path during cyclic loading meets the instability region determined in the corresponding monotonic shear test. Based on a failure criterion defined in terms of triggering flow behavior, normalization of the cyclic strength with respect to the monotonic strength at the instability state provides a promising approach for correlating the undrained responses between the monotonic and cyclic shear conditions, irrespective of the drained preloading history.
Fig. 14. (a) Relationship between CSR and the required number of cycles to trigger cyclic flow (Nf,flow); (b) Relationship between Nf,flow and the normalization of cyclic strength to monotonic strength at instability state (CSR/SIS); (c) Relationship between Nf,5% and the normalization of cyclic strength to monotonic strength at phase-transformation state (CSR/SPT). Table 3 Undrained shear strength at characteristic states. Test
ITC/ITE
LTC(C)/ LTE(C)
LTC(E)/ LTE(E)
UTC(C)/ UTE(C)
UTC(E)/ UTE(E)
SIS SPT
Null/0.27 0.41/0.28
Null/0.66 0.08/0.64
Null/0.07 0.62/0.02
Null/0.25 Null/0.21
Null/0.33 0.36/0.35
Acknowledgements The research described was funded by the Natural Science Foundation of China (Grant Nos. 51825803, 51578499, 51761130078), and the National Key R & D program of China (No. 2016YFC0800200). Appendix A. Supplementary data
evaluating the liquefaction susceptibility, it can be determined in a simple way from isotropically consolidated sand tested under monotonic loading conditions. Nevertheless, more studies involving in–situ soils and case histories are required in the future to validate the approach developed in this paper, such that it can be applied in the practical designs and analyses with reliable and confident outcome.
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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Liquefaction of sand under monotonic and cyclic shear conditions: Impact of drained preloading history
T
K. Pana, Y.Q. Caia,b, Z.X. Yangb,*, X.D. Pana a b
College of Civil Engineering and Architecture, Zhejiang University of Technology, Hangzhou, Zhejiang, 310014, China Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou, Zhejiang, 310058, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Preloading history Monotonic loading Cyclic loading Liquefaction Shear strength Cyclic resistance Correspondence
In-situ sand deposits inevitably undergo a preloading history caused by factors such as overlying structures, adjacent construction work, or repeated sedimentation and erosion; this will in turn affect their mechanical behavior and liquefaction susceptibility during subsequent loading. An experimental program was developed to explore the potential influence of the drained preloading history on the undrained response of sand subjected to both monotonic and cyclic loadings. The results indicate that the shear strength, dilatancy, and stiffness characteristics in monotonic tests depend on the relative directions of the drained preloading and subsequent undrained shearing. Two typical types of behavior are observed and identified in the cyclic tests, i.e., cyclic mobility and residual deformation accumulation failure, depending on the stress state prior to the undrained cycling. The cyclic resistance is quantified based on a failure criterion defined in terms of the triggering of flow behavior, and it is compared to that determined using a criterion of specified strain threshold. In particular, the direction–wise (compressional or extensional) influence of the preloading history on the liquefaction resistance and pore pressure generated in sand during cyclic loading agrees well with that observed during monotonic loading. Furthermore, a correspondence between the cyclic and monotonic tests can be derived, and a unified approach is proposed to evaluate both the monotonic and cyclic responses, irrespective of the drained preloading history.
1. Introduction The terms liquefaction or liquefaction failure describe a phenomenon whereby a saturated cohesionless soil undergoes a substantial loss of strength and stiffness in response to an applied stress, typically accompanied by the development of excessive deformation and high pore pressures. A comprehensive laboratory study of the undrained responses of sandy deposits is of vital importance for assessing their susceptibility to liquefaction and the potential for related catastrophic damage, such as the sinking of structures on the surface, spreading of embankments, and lateral displacement of the ground [1–5]. Numerous experimental results have demonstrated that liquefaction phenomena can be classified into flow liquefaction and cyclic mobility based on the different triggering mechanisms [6–8]. Flow liquefaction, which is characterized by tremendous instabilities (known as a strain–softening response) in loose or contractive sand, can be induced under either monotonic or cyclic shear conditions [9–11]. However, for dense or dilative sand, cyclic mobility accounts for the excessive strain development and progressive stiffness degradation when the sand
*
experiences transient states of zero effective stress during cyclic loading [12–14]. In addition to the initial state of the sand, the liquefaction behavior is also influenced by the preloading history prior to the application of undrained monotonic or cyclic shear stress. In practical engineering, in–situ soils may experience a preloading history, such as the driving static shear stress that is imposed on subsoils beneath sloping ground or underneath structures. The existence of a static shear stress and its influence on the undrained responses of sands have been extensively studied [15–18]. These experimental results suggested that the static shear may enhance the liquefaction resistance and would be beneficial to dilative sand, but it tends to be detrimental when the static shear stress increases for contractive sand. Triaxial experimental tests conducted by Sivathayalan and Ha [10] and Pan et al. [19] indicated that the presence of static shear may increase the possibility of strain–softening of soil under subsequent monotonic shearing. Under cyclic loading conditions, Hyodo et al. [16], Yang and Sze [20], and Pan and Yang [14] found that the failure of sand with a large initial shear stress can be attributed to gradually accumulated residual deformation, rather
Corresponding author. E-mail addresses: [email protected] (K. Pan), [email protected] (Y.Q. Cai), [email protected] (Z.X. Yang), [email protected] (X.D. Pan).
https://doi.org/10.1016/j.soildyn.2019.105775 Received 9 April 2019; Received in revised form 24 June 2019; Accepted 25 July 2019 0267-7261/ © 2019 Elsevier Ltd. All rights reserved.
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Abbreviations CSR Dr Eu e0 Nf,5% Nf,flow p0’ q0
qcyc qIS, qPT
cyclic stress ratio relative density of sand undrained secant Young's modulus initial void ratio prior to undrained shearing number of cycles required to attain axial strain of 5% number of cycles required to trigger cyclic flow initial mean normal effective stress initial deviatoric stress prior to undrained shearing
SIS, SPT uC, uE
εa
than the flow liquefaction or cyclic mobility that is usually observed in sands without an initial shear stress. Moreover, soils in the field may have experienced excavation, refilling, and repeated sedimentation and erosion, and thus involve an unloading stress path in addition to the initial sustained shear stress; therefore, a loading–unloading cycle of shear stress is usually applied prior to the subsequent shear tests [21–23]. Since the pioneering work of Finn et al. [24], many studies have been conducted to assess the effect of an undrained preloading cycle followed by reconsolidation on the liquefaction susceptibility of soils. Previous studies performed by Ishihara and Okada [25], Suzuki and Toki [26], and Bouferra et al. [27] indicated that the undrained preloading at small stress or strain amplitude can delay the occurrence of liquefaction failure, while a preloading cycle with large amplitude usually weakens the liquefaction resistance. However, the effect induced by the drained preloading history, which can also be encountered in field conditions [28–30], on the liquefaction behavior of sand has not been adequately elucidated and should be investigated further. In particular, to quantify the drained preloading effect, it is necessary to analyze the respective influences of the loading and unloading processes of the initial shear stress and their interaction on the subsequent undrained response of sand in a systematic manner. It has long been recognized that the soil fabric or inherent anisotropy is an important factor governing its mechanical behavior; for example, sand under triaxial compression exhibits enhanced dilation and much stiffer response than sand under triaxial extension [31,32]. It should be noted that the inherent anisotropy formed during the deposition process of natural sands may undergo further alteration due to the preloading history, which is known as the stress–induced fabric anisotropy. The existing experimental data from monotonic and cyclic shear tests have focused primarily on the induced fabric or stress anisotropy caused by a compressional preloading path. For example, Gajo and Piffer [28] and Finge et al. [33] examined the effect of a compressional preloading cycle on the undrained responses of sand, and concluded that the induced anisotropy may significantly affect the elastic deformation characteristics and shear resistance during subsequent loadings. However, few studies have considered the anisotropy induced by preloading in extension, which also often occurs in soil deposits under field conditions, as described by Yoshimine and Hosono [34], Andersen [35], and Yang and Pan [11]. Furthermore, there is still no consensus regarding the impact of inherent and induced anisotropy that can be determined based on the correspondence between the undrained responses of sand under monotonic and cyclic loading conditions. Mao and Fahey [36], Baki et al. [37], and Li et al. [38] confirmed that the stress path of a monotonic test defines a boundary surface for the corresponding cyclic behavior, which implies that flow failure with abrupt deformation could be triggered when the cyclic stress path is
cyclic deviatoric stress deviatoric stresses at instability state and phase–transformation state, respectively normalized shear strengths at instability state and phase–transformation state, respectively residual pore pressure components developed in compression and extension segments of the first cycle, respectively axial strain
close to or beyond the stress path of the monotonic test under the same initial conditions. On the other hand, it has also been argued that cyclic flow occurs when the stress state in the cyclic tests meets the instability line determined in the corresponding monotonic test [16,39,40]. Hence, it seems reasonable to explore the liquefaction behavior of sand under both compressional and extensional preloading paths through a sophisticated experimental program, and to further establish the correlation between the undrained responses during monotonic and cyclic loadings. In summary, the primary aim of this study is to assess the influence of induced anisotropy created by varying the drained preloading history on the undrained strength, deformation, and pore pressure responses of sand through monotonic and cyclic triaxial tests. Dramatic differences in the influence of the imposed compression and extension preloading paths on the monotonic and cyclic responses can be observed, depending on the relative direction between the drained preloading and subsequent undrained shearing. Based on failure criteria defined as a specified strain magnitude or the triggering of flow behavior, the effect of the preloading history on the cyclic resistance of sand can be determined. Remarkably, this effect is much more significant when the samples are sheared from the anisotropic stress state than the isotropic stress state. Moreover, by normalizing the cyclic strength to the corresponding monotonic strength, a unified approach can be developed to quantify the correspondence between the undrained responses under monotonic and cyclic shear conditions. The experimental observations and quantitative findings for the preloading effect obtained in this study can offer insight into the correlation between the undrained monotonic and cyclic responses of sand, and thus provide useful guidance for the practical design of engineering projects.
2. Test procedures The experiments in this study were conducted using an automated triaxial system capable of performing both monotonic and cyclic loading tests, as described by Pan and Yang [41]. Toyoura sand was employed as the test material, as it has been extensively characterized in the literature; Table 1 lists the physical properties of Toyoura sand [32]. Ample experimental evidence has indicated that the fabric anisotropy of a sample prepared for laboratory testing is strongly dependent on the preparation technique [1,32,39]. In this study, the dry deposition method was used to prepare the reconstituted samples, mimicking the gravitational deposition process of sand in the field. The samples have a diameter of approximately 70 mm and a height of 140 mm. Fully saturated samples with Skempton's B-values > 0.96 are obtained through backpressure saturation facilitated by preceding circulation of carbon dioxide.
Table 1 Index properties of the test material. Mean particle diameter, D50: mm
Uniformity coefficient, Uc
maximum void ratio, emax
minimum void ratio, emin
specific gravity, Gs
0.17
1.7
0.977
0.597
2.65
2
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The saturated samples were first isotropically consolidated to a mean effective stress of p0’ = 100 kPa. They were then preloaded to the desired initial stress state along a constant p’ stress path prior to the undrained shearing tests. As illustrated in Fig. 1, four preloading paths were considered in this study: drained compressional loading with a magnitude of 80 kPa (‘O-A-C’), drained extensional loading with a magnitude of −60 kPa (‘O-A-E’), and drained compressional and extensional loading–unloading paths (‘O-A-C-A’ and ‘O-A-E-A’, respectively). In contrast to the first two paths, the latter two paths aim to examine the effect of induced fabric anisotropy caused by loading–unloading cycles and to isolate the influence of the initial stress anisotropy. Moreover, a sample subjected to isotropic consolidation (path ‘O-A’) without any preloading history was also tested as a benchmark for comparison. At the end of the drained preloading, the void ratios, e0, of all specimens ranged from 0.732 to 0.748 (relative density Dr = 59%–63%), and can thus be classified as medium–dense sand [19,42]. The small variation in the density of specimens is not expected to produce significant discrepancies in the results of the subsequent undrained shear tests, which include triaxial compression (TC), triaxial extension (TE), and cyclic loading (Cyc). In the monotonic tests, a strain rate of 0.1%/min was employed, while in cyclic tests, a sinusoidal waveform was applied at a frequency of 1 Hz. Table 2 summarizes the test details, such as the drained preloading types and undrained shearing modes.
significantly reduce the strength in TE, and vice versa. Second, the effective stress paths shown in Fig. 4(a) vary dramatically between these two preloading paths, especially in the incipient shearing stage of TC or TE. When the undrained shearing commences from the same direction as the drained preloading, i.e., the UTCC and UTEE tests, the mean effective stress changes only slightly during the incipient stage. When the undrained shearing is imposed in the opposite direction of the drained preloading, a dramatic decrease in the effective stress can be observed in the UTCE and UTEC tests. This scenario is in agreement with the shear test results reported by Yimsiri and Soga [44] and Gu et al. [45] from discrete element simulations, and provides evidence supporting the anisotropic elasticity interpretation described by De Gennaro et al. [39], Ye et al. [30], and Pan et al. [19]. The nonlinear stress–strain response shown in Fig. 4(b) indicates that the stiffness degradation of sand is also affected by the preloading history. Fig. 5(a) and (b) show the variations in the undrained Young's modulus (Eu), which is defined as the secant slope of the deviatoric stress–strain curve [19,46], with the development of axial strain under TC and TE loadings, respectively. In each plot, the stiffness characteristics of the sand subjected to the drained loading–unloading history are compared to those of isotropically consolidated sand. Broadly, a significant reduction in the secant Young's modulus with the strain is observed. Under the undrained TC condition, as shown in Fig. 5(a), the stiffness of the specimen subjected to the extensional loading–unloading path (UTCE) is lower than that of the specimen subjected to the compressional loading–unloading path (UTCC). The stiffness reduction curve for the sample without preloading (ITC) falls in between those for the UTCE and UTCC. However, when the samples were subjected to TE, the above trends were reversed, as shown in Fig. 5(b), in which the curve obtained in the UTEE test is above that obtained in the UTEC test, with the ITE curve in between. The results presented in Fig. 5 reveal that the drained loading–unloading history on one side can enhance the stiffness if the sample is subsequently subjected to undrained shear on the same side.
3. Undrained responses during monotonic loading Fig. 2(a) and (b) show the effective stress paths and stress–strain curves obtained from undrained TC and TE tests on isotropically consolidated sand (ITC and ITE). It is clear that the monotonic response of sand differs dramatically between TC and TE under otherwise identical testing conditions. The shear resistance increases monotonically and the strain–hardening response dominates in the ITC test, accompanied by significant dilation in the post phase–transformation state (PTS) stage [43]. In contrast, in the ITE test, the shear resistance initially increases to a negative maximum, known as the instability state (IS) [9], after which a strain–softening response prevails, with a reduction in shear resistance until the PTS stage. It is worth noting that to avoid the occurrence of cavitation due to the high negative pore pressure in TC or necking (severe non–uniform deformation) in TE, the axial strains imposed on the specimens during monotonic loading are not sufficient for the specimens to reach the critical state. The influence of the preloading history on the effective stress paths and stress–strain curves of sand is presented in Figs. 3 and 4 for the cases with drained loading and loading–unloading paths, respectively. It can be seen from Fig. 3(a) and (b) that the overall behavior of the sand exposed to drained compressional and extensional loading appears similar to that of the isotropically consolidated sand shown in Fig. 2(a) and (b), i.e., it exhibits predominately dilative behavior with stable strain–hardening in TC and an unstable response with slight strain–softening in TE. In particular, as shown in Fig. 3(b), under either TC or TE conditions, the stress–strain curve is shifted in the direction of the drained preloading (upward or downward). As a result, the shear stress at the PTS under TC is slightly higher for the LTCC test, while the peak resistance at the IS obtained under TE is lower for the LTEC test. The test results for samples with a drained loading–unloading path are shown in Fig. 4. It can be seen that unlike the strain–softening response observed in the TE condition, the undrained TC results exhibit strain–hardening and a more dilative response. For instance, as shown in Fig. 4(a), no discernible contraction is observed in the UTCC test. Although the initial stress state of the samples in Fig. 4 is the same as that subjected to isotropic consolidation alone (Fig. 2), some key differences in the responses due to the drained preloading can be identified. First, as shown in Fig. 4(b), the loading–unloading history on the compression side may enhance the undrained shear strength in TC but
4. Undrained responses during cyclic loading 4.1. Typical types of cyclic behavior Figs. 4 and 5 show that the drained loading–unloading path has a significant influence on the dilative response and stiffness degradation of sand. To examine the influence of the loading–unloading history on the cyclic behavior of sand, the results of three typical tests, illustrated by the effective stress paths, the stress–strain curves, and development of the axial strain and excess PWP with the number of cycles, are presented in Figs. 6–8. These tests were conducted with an equal magnitude of the cyclic deviatoric stress, qcyc = 40 kPa, but with different preloading histories. Fig. 6 shows the cyclic behavior of isotropically consolidated sand without any preloading history, which is the typical cyclic mobility
Fig. 1. Schematic diagram for drained preloading path. 3
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Table 2 Summary of monotonic and cyclic triaxial tests. Series
Preloading type
Shearing mode
e0
q0 (kPa)
qcyc (kPa)
CSR
Test IDa
I
I(O-A) I(O-A) I(O-A) I(O-A) I(O-A) I(O-A) I(O-A) L(O-A-C) L(O-A-C) L(O-A-C) L(O-A-C) L(O-A-C) L(O-A-E) L(O-A-E) L(O-A-E) L(O-A-E) L(O-A-E) U(O-A-C-A) U(O-A-C-A) U(O-A-C-A) U(O-A-C-A) U(O-A-C-A) U(O-A-E-A) U(O-A-E-A) U(O-A-E-A) U(O-A-E-A) U(O-A-E-A)
TC TE Cyc Cyc Cyc Cyc Cyc TC TE Cyc Cyc Cyc TC TE Cyc Cyc Cyc TC TE Cyc Cyc Cyc TC TE Cyc Cyc Cyc
0.739 0.735 0.742 0.741 0.737 0.744 0.740 0.748 0.746 0.740 0.742 0.739 0.737 0.739 0.732 0.741 0.741 0.738 0.747 0.744 0.737 0.741 0.739 0.733 0.740 0.742 0.736
0 0 0 0 0 0 0 80 80 80 80 80 −60 −60 −60 −60 −60 0 0 0 0 0 0 0 0 0 0
/ / 30 35 38 40 45 / / 70 80 90 / / 15 25 30 / / 30 35 40 / / 35 40 50
/ / 0.15 0.175 0.19 0.2 0.225 / / 0.35 0.4 0.45 / / 0.075 0.125 0.15 / / 0.15 0.175 0.2 / / 0.175 0.2 0.25
ITC ITE ICyc_30 ICyc_35 ICyc_38 ICyc_40 ICyc_45 LTC(C) LTE(C) LCyc(C)_70 LCyc(C)_80 LCyc(C)_90 LTC(E) LTE(E) LCyc(E)_15 LCyc(E)_25 LCyc(E)_30 UTC(C) UTE(C) UCyc(C)_30 UCyc(C)_35 UCyc(C)_40 UTC(E) UTE(E) UCyc(E)_35 UCyc(E)_40 UCyc(E)_50
II
III
IV
V
Note: e0, initial void ratio prior to undrained shearing, q0, qcyc, initial and cyclic deviatoric stresses, respectively; CSR, cyclic stress ratio (the ratio of the cyclic shear stress amplitude to that of the initial mean effective stress, CSR=qcyc/(2p0’)). a The designation identifies: 1) the drained preloading type–I for isotropic consolidation, L for loading, U for loading-unloading, (C) and (E) for preloading in compression and extension, respectively; 2) the undrained shearing mode–TC for triaxial compression, TE for triaxial extension and Cyc for cyclic loading; 3) the amplitude of cyclic deviatoric stress.
Fig. 2. Monotonic shear response of sand under isotropic consolidation: (a) effective stress path; (b) stress-strain curve.
Fig. 3. Monotonic shear response of sand with drained loading path: (a) effective stress path; (b) stress-strain curve.
4
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Fig. 4. Monotonic shear response of sand with drained loading-unloading path: (a) effective stress path; (b) stress-strain curve. Fig. 5. Undrained stiffness varied with axial strain for sand with drained loading-unloading history in (a) triaxial compression and (b) triaxial extension.
response as characterized by the “butterfly” stress paths in Fig. 6(a), the S–shaped hysteresis curves in Fig. 6(b), the double–amplitude (DA) strain development in Fig. 6(c), and fully PWP buildup in Fig. 6(d). Following Hyodo et al. [12] and Yang and Sze [20], this specimen is regarded as failure at N = 26 according to the strain criterion of DA = 5%. The similar cyclic mobility type behavior can also be observed for sand with a loading–unloading history, as shown in Figs. 7 and 8. Applying the same failure criterion of DA = 5%, it can be seen that the specimens preloaded in compression and extension fail at N = 20 and N = 106, respectively. Compared to the sample without preloading, the sand is less prone to failure after an extensional loading–unloading cycle, while the compressional loading–unloading history only slightly reduces the cyclic resistance to liquefaction. This finding is consistent with the conclusions presented by Oda et al. [21] and Wei and Wang [47], who found that the drained stress or strain history in compression tended to reduce the liquefaction resistance of cohesionless soil. Moreover, the effective stress paths in Figs. 7(a) and 8(a) show a clear difference between the two types of preloading history, particularly during the first loading cycle. In fact, the specimen preloaded in compression behaves slightly elastically in the first half–cycle (the compression segment), but contracts considerably during the subsequent extension segment. Consequently, the excess PWP generated in the extension segment is higher than that in the compression segment, as shown in the inset of Fig. 7(d). In contrast, the extensional loading–unloading history provides a beneficial gain: pronounced contraction in the first half–cycle followed by negligible development of the PWP, as shown in Fig. 8(d). To illustrate the cyclic response of sand with stress anisotropy due to preloading, two typical results with varying amplitudes of the cyclic deviatoric stresses are presented in Figs. 9 and 10 for drained compressional and extensional loading, respectively. To simplify the presentation, only the effective stress paths and stress–strain curves are
illustrated. The typical residual deformation accumulation failure can be inferred from the stress–strain curves for the tests shown in both Figs. 9(b) and 10(b), and the stress paths shown in Figs. 9(a) and 10(a) appear to be stable with a negligible reduction in the effective stress. To provide a unified comparison of the cyclic resistance determined from different types of behavior, the criterion for the liquefaction or failure of sand in non-symmetric cyclic tests is defined as a 5% single–amplitude (SA) axial strain [14,17,48]. According to this strain criterion, the specimen with drained compressional loading fails at N = 69 on the compression side, while the specimen with drained extensional loading fails at N = 11 on the extension side. Although the test results in Figs. 9 and 10 indicate excessive accumulated residual deformation in both cases, apparent differences can still be observed. For instance, cyclic flow behavior, synchronized with an abrupt development in axial strain, is observed in the first loading cycle in Fig. 10(b), while the rate at which the cyclic strain increases in Fig. 9(b), is shown to be more moderate.
4.2. Effect of preloading on cyclic resistance and pore pressure The test results shown above indicate that the type of cyclic failure mode depends solely on the stress state of the specimen prior to the undrained shearing, i.e., cyclic mobility for the sand in an isotropic stress condition and residual deformation accumulation failure for the sand with stress anisotropy. Nevertheless, the drained preloading history also plays an important role in the cyclic resistance of sand. Fig. 11 summarizes the strain criterion–based cyclic resistance under various preloading conditions for the imposed cyclic stress ratio (CSR) in terms of the number of cycles required to attain axial strain of 5% (Nf,5%). In 5
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Fig. 6. Cyclic response of sand under isotropic consolidation (ICyc_40): (a) effective stress path; (b) stress-strain curve; (c) axial strain; (d) excess PWP.
than that in the subsequent extensional half-cycle. In contrast, for the cases with drained loading–unloading paths, the opposite trend is observed: the mean values are 0.3 for the UCyc(C) tests and 7.0 for the UCyc(E) tests. Thus, it can be concluded that the effect of a drained loading–unloading path on the pore pressure generation is closely related to whether the drained preloading and subsequent undrained cycling are in the same or opposite directions. When the cyclic loading is on the same side as the preloading, e.g., both in compression, the generated pore pressure is relatively small. However, when the specimen is preloaded in the opposite direction of the cyclic loading, the pore pressure is built up more rapidly. Moreover, as shown in Fig. 12, the specimens subjected to drained compressional or extensional loading have negative values of uC/uE; the mean values are −0.5 for the LCyc(C) tests and −0.6 for the LCyc(E) tests. This is caused by the dilative tendency of the sand that was sheared from an anisotropic stress state, as shown in Figs. 9 and 10.
general, for a given CSR, the required Nf,5% varies under different preloading conditions. Clearly, the CSR versus Nf,5% trends obtained from the LCyc(C) and LCyc(E) tests constitute the upper and lower bounds in this diagram. This signifies that the drained compressional loading can markedly enhance the resistance to liquefaction failure, while the effect of drained extensional loading on the cyclic resistance is detrimental, compared to the case without a preloading history (ICyc). The direction–dependent influence is also found in the sand subjected to compressional and extensional loading–unloading paths. The observed CSR versus Nf,5% trends for tests UCyc(E) and UCyc(C) are located above and below that for isotropically consolidated sand, respectively, indicating beneficial and adverse effects from extensional and compressional loading–unloading histories, respectively. Nevertheless, it is worth noting that the data points for these three cases fall within in a narrow band, indicating that the influence of the preloading history on sand cyclically sheared from an isotropic stress state tends to be far less significant than for sand with stress anisotropy. As shown in Figs. 7 and 8, one of the most notable features in the sand response is the dramatic difference in the generation of pore pressure during the incipient stage of cycling. Fig. 12 presents a summary interaction diagram showing the pore pressure coefficient (uC/uE) determined from cyclic tests with various combinations of preloading history and CSR. Herein, uC and uE denote the residual excess PWP developed on the triaxial compression and extension side in the first undrained cycle, respectively, as shown in the insets of Figs. 7(d) and 8(d). It should be noted that in this diagram, the data points for each preloading condition are somewhat scattered, and the mean values of uC/uE for all of the considered preloading cases are provided and indicated by the figures nearby. For example, the mean value of uC/uE for the ICyc tests is approximately 3.0, implying that the residual pore pressure generated during the first compressional half–cycle is greater
5. Link between monotonic and cyclic responses The flow behavior of sand during cyclic loading is thought to be intimately related to the sand responds to monotonic loading [11,20,49]. Fig. 13 shows two typical examples of flow behavior in the cyclic tests. The first example shows cyclic mobility, in which the cyclic stress path evolves rapidly to a near–zero effective stress state (Fig. 13(a)), and an abrupt deformation followed by a large DA strain results in the failure of the sand (Fig. 13(c)). In the second example, the sample is sheared from an anisotropic stress state on the extension side (Fig. 13(b)), and cyclic flow with a considerably larger strain occurs during the incipient cycling, resulting in a gradual and moderate accumulation of residual SA strain in the subsequent cycles (Fig. 13(d)). In Fig. 13(a) and (b), the monotonic TE effective stress paths (dashed 6
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Fig. 7. Cyclic response of sand with compressional loading-unloading path (UCyc(C)_40): (a) effective stress path; (b) stress-strain curve; (c) axial strain; (d) excess PWP.
Fig. 8. Cyclic response of sand with extensional loading-unloading path (UCyc(E)_40): (a) effective stress path; (b) stress-strain curve; (c) axial strain; (d) excess PWP. 7
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Fig. 9. Cyclic response of sand with compressional loading path (LCyc(C)_90): (a) effective stress path; (b) stress-strain curve.
lines) are superimposed with identical initial conditions, and the instability region bounded by the instability line (IL) and phase–transformation line (PTL) can thus be determined. The IL refers to the line connecting the origin and the IS prior to the strain–softening [9,50]; the PTL is the line that separates the contraction and dilation zones in the p′–q plane [7,43]. As illustrated in these diagrams, when the cyclic stress path approaches the IL defined in the monotonic tests, flow behavior characterized by a sudden increase in the axial strain is activated. Thus, it is expected that for the sand sheared from either an isotropic stress state or an anisotropic stress state with drained extensional loading, the cyclic flow behavior will always occur on the extension side, as the stress state of the cyclic loading lies in the instability region in the corresponding TE test. However, for the sand subjected to drained compressional loading, the cyclic stress path is significantly shifted toward the compression side, and no instability is observed in the corresponding monotonic TC test. This implies that the effective stress path during cyclic loading can never reach the monotonic instability region, and thus only residual deformation accumulation failure without flow behavior can occur for sand with a high stress anisotropy due to the compressional preloading, as shown in Fig. 9. On the triggering of cyclic flow, as marked by the arrows in Figs. 6(c) and 7(c) and 8(c) and 10(b), the strain development accompanied by a sudden acceleration can immediately satisfy the strain–based failure criterion for cyclic mobility, or even lead to drastic consequences owing to the relatively high magnitude of the abrupt residual deformation. In contrast to the conventional failure criteria in terms of specified strain thresholds (e.g., 5% DA or SA), the triggering of cyclic flow can also be considered as the failure state of sand, from which an estimation of the cyclic resistance on the safe side can be obtained. Fig. 14(a) shows the relationship between the CSR and the number of cycles required to trigger cyclic flow (Nf,flow). Similar to the trends
Fig. 11. Number of cycles to attain axial strain of 5% (Nf,5%) with respect to CSR under various preloading conditions.
based on strain criteria shown in Fig. 11, the required Nf,flow for a given CSR varies with the preloading condition. Similarly, the CSR versus Nf,flow curves for the UCyc(E) and UCyc(C) tests are located above and below that of the ICyc tests, respectively. This indicates that the drained extensional loading–unloading path can delay the occurrence of cyclic flow, while the compressional loading–unloading path has a somewhat detrimental effect on the resistance to cyclic flow. It should be noted that in Fig. 14(a), the data for the sand subjected to drained compressional loading are excluded, as no cyclic flow behavior is observed in the LCyc(C) tests. However, for the sand sheared from an anisotropic stress state due to extensional loading, the cyclic resistance is significantly decreased, as flow behavior is triggered in the very beginning of the shearing in the LCyc(E) tests.
Fig. 10. Cyclic response of sand with extensional loading path (LCyc(E)_30): (a) effective stress path; (b) stress-strain curve. 8
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example, the drained compressional loading is beneficial and greatly enhances the strength of the sample in TE tests, while its effect is detrimental and reduces the strength of the sample in the TC tests. In Fig. 14(b), the flow criterion–based cyclic resistance shown in Fig. 14(a) is normalized relative to the corresponding monotonic shear strength at IS. In the resulting diagram, the data for the sands sheared after isotropic consolidation and drained preloading collapse on a single line, irrespective of the type of preloading history and the amplitude of the cyclic stress. These results confirm the validity of the approach for relating cyclic flow to the instability behavior under monotonic shear. Therefore, for sand exhibiting a strain–softening response under monotonic loading, the undrained resistance to cyclic flow can be predicted from the shear strength at IS in the corresponding monotonic tests. In fact, based on experimental work with isotropically consolidated sand, Hyodo et al. [12] and Porcino et al. [51] proposed an approach to predict the cyclic strength of sand exhibiting either strain–softening or strain–hardening monotonic responses by relating the strain criterion–based cyclic resistance to the monotonic shear strength at PTS. To verify the validity of such an approach, the cyclic strength data in Fig. 11 normalized by the shear strength, SPT, are shown in Fig. 14(c). Note that the data for the LCyc(C) tests, which were not included in Fig. 14(a) and (b), have also been normalized by the SPT value obtained from the LTC(C) test and are presented in Fig. 14(c). Clearly, a unique trend exists for the sand undrained sheared from an isotropic state, regardless of the presence of a loading–unloading history. However, the data points for the sand subjected to drained compressional or extensional loading (solid symbols) are scattered and deviate significantly above the isotropic trend, suggesting that the traditional approach correlating the cyclic resistance and monotonic strength at PTS should take into account the stress state of the sand prior to the cyclic loading. Comparing Fig. 14(b) and (c) indicates that the IS, rather than the PTS, determined in monotonic shear tests is more suitable for evaluating the susceptibility of sand to undergo liquefaction due to cyclic loading, especially when cyclic flow behavior has been triggered. The new approach developed in this study for relating cyclic flow with monotonic instability, along with the obtained quantitative findings of the drained preloading effect, may provide insights to assess cyclic resistance of sand with varying initial stress states. Noting that the shear resistance at instability state is a sound unique parameter in
Fig. 12. Pore pressure coefficient (uC/uE) with respect to CSR during the first loading cycle.
Given the clear correspondence between cyclic flow and monotonic instability, further investigation is necessary to determine the relationship of the shear strength between the monotonic and cyclic tests. Following the work by Hyodo et al. [16] and Yang and Pan [11], the normalized shear strength of sand at IS (SIS) or PTS (SPT) under monotonic loading can be defined as follows:
SIS = qIS − q0 / p0′
or
SPT = qPT − q0 / p0′
(1)
where q0 is the initial deviatoric stress prior to the undrained shearing, and qIS and qPT are the deviatoric stresses at IS and PTS, respectively. Table 3 summarizes the values of SIS and SPT for sand in both TC and TE tests under various drained preloading conditions. Overall, for the sand tested in TC, no SIS exists owing to the absence of an instability response; however, SPT can be obtained in almost all of the tests, except for the UTC(C) test, in which dilation is dominant. It is found that under either TC or TE conditions, although the samples sheared from an isotropic stress state have similar SIS or SPT, further inspection indicates that the drained preloading on one side slightly strengthens the sample during subsequent loading on the same side, but results in lower strength in the sample during loading on the other side. However, for the sand sheared from an anisotropic stress state, the test data summarized in Table 3 appear to indicate an opposite tendency. For
Fig. 13. Schematic illustration of the correspondence between cyclic flow behavior and instability region during monotonic loading. 9
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6. Conclusions A series of monotonic and cyclic triaxial tests on medium–dense Toyoura sand were performed to investigate the influence of drained preloading on the liquefaction behavior of sand during subsequent undrained shearing. The strain development, pore pressure generation, and strength characteristics were presented, and the underlying correspondence between the monotonic and cyclic shear responses was explored. The main conclusions drawn from this study can be summarized as follows: 1. The monotonic shear behavior of sand depends on both the drained preloading type and the undrained shearing mode: a) in triaxial compression, the response is stable and predominately strain–hardening and dilative, whereas instability with strain–softening is triggered in extension; b) either drained compressional or extensional loading can decrease the shear strength of sand during undrained shearing in the same direction but strengthen the sample during undrained shearing in the other direction; c) a drained loading–unloading history on one side renders the sand stiffer during the incipient stage of subsequent shearing on the same side, but results in a more contractive and softer response during shearing on the other side. 2. Two different types of cyclic behavior are identified, i.e., cyclic mobility and residual deformation accumulation failure, depending on the stress state prior to the cyclic loading. Cyclic mobility dominates in sand sheared from an isotropic stress state and is accompanied by excessive DA cyclic strains. Residual deformation accumulation failure is observed in specimens with an initial shear stress and is characterized by the progressive development of SA residual strains. 3. Based on a failure criterion defined in terms of a specified strain threshold (e.g., 5%), the influence of the preloading history on the cyclic resistance of sand sheared from an isotropic stress state tends to be far less significant than for sand with stress anisotropy. Nevertheless, further inspection indicates a beneficial effect of an extensional loading–unloading history on increasing the cyclic resistance, but an adverse effect of a compressional loading–unloading history on the cyclic resistance. This direction–dependent influence was also observed for the pore pressure generation in sand during the first undrained loading cycle. 4. Cyclic flow behavior, characterized by a sudden strain development, occurs when the effective stress path during cyclic loading meets the instability region determined in the corresponding monotonic shear test. Based on a failure criterion defined in terms of triggering flow behavior, normalization of the cyclic strength with respect to the monotonic strength at the instability state provides a promising approach for correlating the undrained responses between the monotonic and cyclic shear conditions, irrespective of the drained preloading history.
Fig. 14. (a) Relationship between CSR and the required number of cycles to trigger cyclic flow (Nf,flow); (b) Relationship between Nf,flow and the normalization of cyclic strength to monotonic strength at instability state (CSR/SIS); (c) Relationship between Nf,5% and the normalization of cyclic strength to monotonic strength at phase-transformation state (CSR/SPT). Table 3 Undrained shear strength at characteristic states. Test
ITC/ITE
LTC(C)/ LTE(C)
LTC(E)/ LTE(E)
UTC(C)/ UTE(C)
UTC(E)/ UTE(E)
SIS SPT
Null/0.27 0.41/0.28
Null/0.66 0.08/0.64
Null/0.07 0.62/0.02
Null/0.25 Null/0.21
Null/0.33 0.36/0.35
Acknowledgements The research described was funded by the Natural Science Foundation of China (Grant Nos. 51825803, 51578499, 51761130078), and the National Key R & D program of China (No. 2016YFC0800200). Appendix A. Supplementary data
evaluating the liquefaction susceptibility, it can be determined in a simple way from isotropically consolidated sand tested under monotonic loading conditions. Nevertheless, more studies involving in–situ soils and case histories are required in the future to validate the approach developed in this paper, such that it can be applied in the practical designs and analyses with reliable and confident outcome.
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