J. Cent. South Univ. (2020) 27: 2394-2407

DOI: https://doi.org/10.1007/s11771-020-4457-0

Dilatancy and liquefaction behaviour of clean sand at wide range of confining stresses

GU Lin-lin(顾琳琳)¹, WANG Zhen(王振)², HOSOYA Asa-hiro³, ZHANG Feng(张锋)³

1. Department of Civil Engineering, Nanjing University of Science and Technology, Nanjing 210094, China;

2. School of Mechanical Engineering, Nanjing University of Science and Technology,Nanjing 210094, China;

3. Department of Civil Engineering, Nagoya Institute of Technology, Nagoya 4668555, Japan

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract: The state of clean sand was mainly dependent on its void ratio (density) and confining stress that greatly influenced the mechanical behavior (compression, dilatancy and liquefaction) of clean sand. Confirming whether the confining stress was a state variable of sand required precise element tests at different confining stress, especially the tests under very low confining stress whose test data were very limited. In this study, static-dynamic characteristics of clean sand was comprehensively investigated by a unified test program under low and normal confining stress ranging from 5 to 98 kPa, under monotonic/cyclic and drained/undrained conditions, together with the literature available data under confining stress of 1.0 to 3.0 MPa. For monotonic loading tests, the contraction/dilation phase transition was observed for loose sand at low confining stress, and dilatancy angles were stress-dependent. In addition, the liquefaction resistance was observed to increase with reducing of confining stress, and the axial strain varied from compressive to dilative when confining stress increased. Special attention was also paid to the enhancement effect of membrane, and it was observed that its influence on the test results was limited. In addition, the experimental results were proved reliable by reproducibility.

Key words: void ratio; confining stress; monotonic/cyclic loading; drained/undrained triaxial test; state variable of sand

Cite this article as: GU Lin-lin, WANG Zhen, HOSOYA Asa-hiro, ZHANG Feng. Dilatancy and liquefaction behaviour of clean sand at wide range of confining stresses [J]. Journal of Central South University, 2020, 27(8): 2394-2407. DOI: https://doi.org/10.1007/s11771-020-4457-0.

1 Introduction

Basic factors influencing the mechanical behavior of clean sand had been studied over the years. One of these fundamental factors, or state parameters, was the void ratio, which was usually used to judge the state of sand. For instance, whether sand liquefied or not when subjected to quick vibration loading depended on relative density, confining stress and stress history and so on. Clean sand exhibited various mechanical properties at different confining stresses. However, the research about the influence of confining stress on compression and liquefaction behavior of clean sand was quite limited, as it was difficult to control and measure in low stress condition. The behavior of soil at low stress level was significant for the design of shallow foundation, slope, shallow buried tunnels and so on. Thus a comprehensive understanding of the influence of confining stress on the static-dynamic property of geomaterials was urgent.

PONCE et al [1] conducted triaxial loading tests at the cell stress of 1.4 to 240 kPa, and experimental results illustrated that expansive volume strain happened for loose sand in the shearing. FUKUSHIMA et al [2] pointed out that friction angle was not confining stress dependent and deformation characteristics only varied when the value under 10 kPa in the drained triaxial loading test. Experimental results in undrained monotonic triaxial loading (Mono-CU) illustrated that sand behaved in a dense manner with low confining stress, while it behaved in a loose manner with high confining stress [3-7]. CHAKRABORTY et al [8] proposed that dilation rate for sand decreased with the increase of confining stress based on triaxial compression test results. Under cyclic loading, it was easy for sand to liquefy with increase of confining stress [9-13]. For model test and element test in the microgravity environment, sand showed very large friction and dilatancy angles [14, 15]. The mechanical properties of sand under high confining stress was also studied by some researchers. KOLYMBAS et al [16] proved that friction angle of medium dense sand reduced when confining stress increasing from 50 to 1000 kPa. UDDIN et al [17] noticed that peak strength of cemented sand with fiber increased by 20% under confining stress of 50 kPa, while it increased by only about 1% at confining stress of 10 MPa.

Based on above literature survey, it was easy to find that although many researches had been done on mechanical behavior of clean sand, most of the researches only focused on the tests under limited conditions, did not cover wide range of confining stresses, different void ratios, different shear stress ratios and different hydraulic conditions. Further studies about dilatancy and liquefaction behaviors of loose sand and dense sand at low confining stresses were absolutely needed. To research the influence of low confining stress levels on the compression, dilation and liquefaction behavior of clean sand (Toyoura sand), a series of cyclic/monotonic triaxial experiments under undrained/drained condition were carried out in the present research. In the whole experimental program, the testing equipment with very high precision especially designed for low cell stress condition was employed to fully describe the mechanical behavior of clean sand.

2 Test program

First of all, void ratio dependency and confining stress dependency of loose sand (D_r=25%) and medium-dense sand (D_r=68%) at four disparate confining stresses (5, 10, 20, 98 kPa) were investigated. According to confining stress data of CHAKRABORTY et al [8], three ranges were also defined: σ_m0≤49 kPa (low); 49 kPa≤σ_m0≤1 MPa (normal) and σ_m0>1 MPa (high). In these tests, two different membranes of 0.15 and 0.20 mm thickness were used to examine membrane effect on test results. Test results were integrated with the test data of Mono-CU tests under high confining stress (1-3 MPa) carried out by ISHIHARA [3]. In this way, compression and dilatancy properties of clean sand were completely analyzed.

2.1 Apparatus for triaxial test

Cyclic undrained triaxial (Cyc-CU) tests, as well as monotonic drained triaxial (Mono-CD) and Mono-CU tests were conducted at various confining stresses with strain control loading equipment displayed in Figure 1. Individual components of testing equipment were illustrated in Figure 2. Electronic-controlled pneumatic regulators in an accuracy of 0.10 kPa for vertical stress and 0.04 kPa for confining stress were applied to get command of the vertical and lateral loading, confining stress and back stress in the shearing. Thus, it is possible to control the pressures even while maintaining a very low confining stress.

The axial loading was measured by inner-pressure loading cells connected with the top cap. In order to achieve high accuracy of the measurement, four load cells in different measuring ranges (0.1, 0.5, 2 and 5 kN) were applied to satisfy axial loading in wide stress ranges. All of these cells had an accuracy of 0.2% for each maximum range. For instance, the vertical load cell in a maximum range of 0.1 kN could offer the maximum stress of 50 kPa, manifesting that it was accurate to approximately 0.10 kPa if the area of the specimen was approximately 20 cm². It is also worth mentioning that at very low confining stress, the vertical load was also very small. Therefore, the total weight of loading parts including the load cell, the rod and the connecting parts, could not be neglected and a counter weight made of bronze copper was hung on the opposite side of the loading parts to reduce the unnecessary dead load as shown in Figure 2 (Part 12).

Figure 1 Triaxial test apparatus for monotonic/cyclic loading under drained/undrained condition

Figure 2 Pressure cell and loading parts of triaxial testing apparatus:

The axial displacement was measured by an external displacement sensor. The loading strain rate was steady at 0.04%/min during monotonic loading, and loading frequency of 0.01 Hz was employed in Cyc-CU experiments according to the work of GU et al [18]. The measured values for vertical load, displacements in vertical and horizontal directions, volumetric change and pore water pressure distribution were collected by computer through a switching box (TML ASW-30A) and data logger (TML TDS-300), which could be measured accurately. In this way, the axial strain and excess pore water pressure were able to be measured accurately. In the tests, the axial strain was measured by displacement transducers attached to the cell cap, and the volumetric strain was measured by a dual-burette volumetric transducer based on pressure difference meter installed on one side of the apparatus.

2.2 Preparation for test specimens

The sample was prepared to 10 cm high with diameter of 5 cm, with the mechanical variables listed in Table 1. The specimen mold could be divided into two parts and be fitted together on the base. The specimen was carefully prepared in the membrane, which was rolled over the cap and sealed by O-ring. The air between the mold and the membrane was discharged from a vacuum pump by two small holes on the two sides of mold.

Table 1 Physical properties of Toyoura sand

In the tests, both loose and medium dense sand were prepared by water pluviation method. During preparation process of a medium dense sand sample, compacting energy was applied by hammering a steel rod on the layer 15 times before the next layer was reclaimed. Before the preparation, the sand was immersed in de-aired water subjected to at least one-week vacuum condition to assure that B value of the specimen was greater than 0.98. Employing these methods, loose specimen of an average relative density of 25% and medium dense specimen with an average relative density of 68% were obtained with quite small deviations. Because whether the state of sand was loose or dense was not only judged by the void ratio but also by confining stress, the nomenclature used in this paper was such that the ‘loose sand’ was referred to sand of high void ratio, while ‘medium dense sand’ was referred to sand of small void ratio.

2.3 Testing procedure

There were 8 cases for Mono-CU tests and Mono-CD tests, and 48 cases for Cyc-CU tests. For Cyc-CU tests, 24 sets for both loose sample and medium-dense sample, and four various cell stresses of 5, 10, 20 and 98 kPa with three different stress ratios of 0.15, 0.20 and 0.25 were used. Membranes with two different thicknesses of 0.15 and 0.20 mm were also used to identify the influence of thickness at low confining stresses. For all the experiments, each sample was in isotropical consolidation to a specific cell stress and then the static or cyclic loading was applied. For Cyc-CU experiments, double-amplitude axial strain ε_DA of 5% was used as the evaluation criterion to define the state of steady flow or liquefaction for clean sand. Therefore, the cycles (N_c) required to reach double-amplitude axial strain 5% was recorded to elaborate on the development of axial strain.

3 Void ratio dependency

3.1 Results from monotonic loading

Results for loose sand and medium-dense sand subjected to monotonic triaxial loads under drained/ undrained conditions at confining stresses of 5, 10 and 20 kPa are shown in Figures 3 and 4. In the tests, D_r was considered a major factor to influence the monotonic compressive strength for the sand. The effective stress paths in undrained triaxial tests for loose sample and medium-dense sample are displayed in Figure 3, in which the mean effective stress decreased slightly at first but then increased until the stress paths reached the critical state, going through phase transition [19]. The phase transition was a transient state in which volumetric strain changed from contraction to dilation. It was not strange to find that mean effective stress for loose sand went down even more than medium-dense sand during undrained monotonic triaxial loading.

The stress-strain-dilatancy relation for sand at low confining stress in Mono-CD tests is illustrated in Figure 4. The peak strength for medium-dense sand was larger, and it came earlier than that of loose sand. During the shearing, dilatating behavior occurred after a low contraction for both samples, while positive dilatancy developed approximately two to three times larger than loose sand. In general, both loose sample and medium-dense sample at low confining stress behaved like dense sample at normal confining stress (49-1000 kPa). Loose sample at low confining stress bulged noticeably at very small axial strain, which could be attributed to over-consolidation property at this low level of stress.

Figure 3 Effective stress paths in Mono-CU tests:

Figure 4 Stress-strain-dilatancy relationship in Mono- CD tests:

3.2 Results from cyclic loading

Results for clean sand with different void ratios in Cyc-CU experiments with shear stress ratio q/(2σ_m0)=0.20 at confining stress of 20 kPa are shown in Figure 5. The results showed that both loose sand and medium-dense sand liquefied in the model of cyclic mobility at low cell stress (20 kPa) under cyclic loading, but the N_c value of the double-amplitude axial strain 5% was varied a lot for them. N_c for loose sand was 1.95, much smaller than that of dense sand (N_c=17.1). It was evident that loose sand generally much more easily liquefied, exhibiting strong void ratio dependency.

Figure 5 Void ratio dependency on mechanical behavior of sand in Cyc-CU (q/(2σ_m0)=0.20)

4 Confining stress dependency

4.1 A state variable in monotonic drained/ undrained tests

It is known from the results obtained in previous section that void ratio and confining stress acted as the state parameters that influenced the mechanical behavior of sand. On the other hand, test results reported by VERDUGO et al [20] and ISHIHARA [3] showed that critical state line (CSL) was unaffected by initial particle fabric as long as the soil mass was homogeneous. Thus, CSL was a unique reference line unaffected by the type of soil deposition, initial density and confining stress. It was also independent of the hydraulic condition, that was, drained or undrained.

It was illustrated in Figure 6 that all the data obtained in this research showed good agreement with the CSL of Toyoura sand in e-p′ plane reported by VERDUGO et al [20] and YANG et al [21]. BEEN et al [22] put forward the state variable δ, defined as the void ratio difference between the initial sand state and critical state under the same mean effective stress. This variable δ combined the effect of the void ratio with confining stress. Its concept and determination had been well described and would not be described in detail here. Table 2 illustrates the value of δ in drained/ undrained monotonic triaxial test of Toyoura sand. It showed that there was dilation during the shearing under low confining stresses of 5, 10, 20 and 98 kPa, which also could be seen in Figure 7. This phenomenon was consistent with the conclusion by BEEN et al [22]. The variable δ, combining void ratio with confining stress in a special form for sand material, had been proved to be a state parameter, while, in this study, their effect on the mechanical property of clean sand needed to be discussed separately. As is known to all that void ratio (relative density) was a state parameter, and the experimental results showed that the mechanical property was confining stress dependent and therefore it was much better to be considered another state variable.

Figure 6 Critical state line of Toyoura sand in monotonic loading tests

Table 2 Parameter δ in monotonic triaxial tests

Figure 7 Stress-strain-dilatancy relationship of Toyoura sand in Mono-CD tests

4.2 Dilation behaviors in monotonic drained/ undrained tests

Figure 7(a) illustrates the stress-strain- dilatancy relationship for loose sand with initial D_r of 25% at four confining stresses of 5, 10, 20 and 98 kPa. It was evident that loose sample just underwent compression at the start, and then great dilation followed by at these four low confining stresses. With the confining stress decreasing, the shear stress ratio and dilation increased accordingly. For the medium-dense sample (D_r=68%), the volumetric strain was almost uniform during drained monotonic loading, exhibiting great dilation at all four values of confining stresses, as illustrated in Figure 7(b). According to the definition of dilatancy angle φ, that is, tanφ=-(dε_v/dε_a), the maximum dilatancy angle φ_max with low confining stresses for several sands was displayed in Figure 8. The dilatancy angle decreased when confining stress increased. For dense sand, larger dilatancy values were observed with great effect on confining stress.

The effective stress paths and corresponding stress and strain relationships obtained from Mono-CU loading are shown in Figure 9, from which it was known that the loose sand had a peak stress in the shearing stress ratio-strain relationship at low cell stresses of 5 kPa and 10 kPa. Although there was a great discrepancy in stress and strain relations during initial stage of monotonic loads, all the samples came up to the identical ultimate strength in the critical state, which was the same as the behavior obtained by previous research [20].

Figure 8 Influence of confining pressure on φ_max for Toyoura sand and Hostun sand adapted from LANCELOT et al [4]

Figure 9 Stress-strain relationship and effective stress paths of Toyoura sand in Mono-CU tests

For the effective stress paths shown in Figure 9, there was an initial decrease followed by an increase and then moved to the same CSL, despite of the values of low confining stress. An explicit trend with respect to effective stress path was obvious given that, at lower stress level, the mean effective stress ratio reduced much more in the initial loading stage, prior to the phase transition from compression to dilatation.

The effective stress path of loose sand in Mono-CU experiments in very large range stress level from 5 kPa to 3 MPa is illustrated in Figure 10. It was observed that, under any confining stress condition, the mean effective stress for loose sample first reduced because of contraction and increased as dilation occurred and finally the stress path got to the CSL. Figure 10(b) from the work of ISHIHARA [3] illustrates that, when cell stress was large enough, the clean sand behaved as loose sample, and it showed compression behavior during the shearing; whereas if confining stress was small, it behaved as dense sample with dilation, which was known as confining stress dependency. At large stress level, the sand only showed compressive characteristics before the arrival to CSL. The steady state, was first described by CASTRO [23] as shown in Figure 10(b), which was a transient state in which the volumetric change shifted from contraction to dilation. The fundamental notion for steady state set for sand was basically the same as the critical state defined for clayey soil in the work of SCHOFIELD et al [24]. The gradient M of CSL was acquired just by the internal frictional angle,and the value was equal to 1.24 with the angle of 31° for Toyoura sand.

Figure 10 Effective stress paths of sand with large void ratio in Mono-CU tests:

4.3 Liquefaction behavior in cyclic undrained triaxial test

Figures 11 and 12 show the effective stress path, stress-strain relationship and the development of axial strain for the loose sample (D_r=25%) and dense sample (D_r=68%) in Cyc-CU tests in the range of confining stress of 5, 10 and 20 kPa with a shear stress ratio q/(2σ_m0)=0.25. The effective stress path entered the cyclic mobility stage with mean effective stress decreasing a lot before liquefaction occurred. Similar Cyc-CU experiments results from STURE et al [25] also illustrated that both loose sample and medium-dense sample liquefied at low stress. The trend of axial strain with time changed gradually with the increasing of confining pressures, that was, from compressive dominant to tensile dominant.

Figure 13 illustrates the cyclic numbers required for liquefaction in different shear stress ratios to produce double-amplitude shear strain (D_a) of 5%. With the confining stress increasing, the cyclic numbers required for liquefaction decreased accordingly. For both loose sample and medium-dense sample, the cycles added up to at least 50% with confining stress reducing from 98 kPa to 5 kPa. It was concluded that the resistance to liquefaction increased when confining stress decreased accordingly.

Figure 11 Results of Toyoura sand with large void ratio in Cyc-CU tests under different confining pressures:

Figure 12 Results of Toyoura sand with small void ratio in Cyc-CU tests under different confining pressure:

Figure 13 Liquefaction resistance curves for Toyoura sand:(D_a: Double amplitude shear strain)

Based on above discussions on the test results, it was very clear that confining stress dependency was also prominent in the similar way as that in the monotonic loading. With the decrease of confining stress, loose sand behaving like dense sand became more and more difficult to liquefy.

5 Reproducibility of test results and membrane thickness effect

5.1 Reproducibility of experimental results

Reproducibility of experimental results is one of the most important factors for assessing the validity of any laboratory test. Variation or error occurring in repeated tests under the same conditions may be caused by various operation methods or apparatus being employed, different manipulators for the tests, or measurements carried out over days during which the parameters might experience inevitable variations [26]. Thus, for a rigorous or sensitive test, some scattering in test results may be observed, even though the experiments were carried out by the only one laboratory technician in the same overall conditions.

To determine the reproducibility of the experiment results in this work, all Cyc-CU tests were conducted twice. The results for loose sample and the medium-dense sample were compared according to effective stress paths and the stress- strain relationship at cell stress of 20 kPa, as shown in Figure 14. In the same situation, there was no significant discrepancy, no matter loose or medium-dense samples, or even the test operators who conducted the tests at different years. The fact that both loose sand and the medium-dense sand at low stress level liquefied with cyclic mobility, was completely reproductive. In this way, the experimental results from this test device and relevant testing technology were considered to be reliable and had relatively high reproducibility.

Figure 14 Reproducibility of Cyc-CU tests results (confining stress=20 kPa,q/2σ_m0=0.20, membrane thickness=0.15 mm):

5.2 Influence of membrane thickness

In order to reduce any possible enhancement effect of membrane at low stress, the thickness of membrane was concerned about in this research and very thin membranes with thickness of 0.15 and 0.20 mm were employed contrast with 0.30 mm- thick membrane generally used for experiments at normal confining stress. As is known that there might be membrane penetration effect for a thin membrane, such that lateral penetration into test specimen can affect either the volumetric strain during drainage tests or the pore water pressure in non-drainage tests. It was affected by particle size, confining stress, rigidity and membrane thickness. BALDI et al [27] indicated that it was mainly influenced by grain size and confining stress and that membrane thickness had a little effect at normal confining stress. At low confining stress, the membrane penetration effect was neglectable, while the enhancement effect of membrane when the sample dilated could convincingly be great. In this research, there was limited data available based on this issue. Hereafter, the enhancement effect at low confining stress condition became simply known as membrane effect.

This membrane effect was studied by use of membranes with two thicknesses of 0.15 mm and 0.20 mm. As indicated in Figure 15, there did exist some discrepancy in the normalized effective stress paths and the stress-strain relationship for different thicknesses. The membrane effect had larger influence on the loose sample than on the medium-dense sample. A quantitative evaluation on the enhancement effect was able to be assessed easily if taking a short look in Figure 15(b), in which a negative effective stress with the value of 0.5-1.0 kPa occurred in cyclic mobility stage. Because saturated sand could never provide negative excessive pore water pressure, it must be caused by the membrane effect. It was reasonable to conclude that the membrane enhancement effect does exist and might give influence to the test results under low confining stress somehow but the degree was quite limited. Even in the condition of quite low cell stress of 5 kPa, using 0.15 mm-thick membrane would be possible to acquire accurate test results.

Figure 15 Influence of membrane thickness on mechanical behavior of sand (Confining stress=5 kPa, q/(2σ_m0)=0.20) in Cyc-CU tests:

6 Conclusions

In this paper, monotonic/cyclic triaxial experiments were carried out to study systematically the mechanical properties of Toyoura sand, a Japanese clean silica sand. Void ratio dependency and confining stress dependency were comprehensively investigated. The following main conclusions in this research were given out:

1) When subjected to drained/undrained monotonic loading, loose sample did behave as dense sample at low confining stress (5, 10 and 20 kPa), and medium-dense sample behaved as loose sample at very high confining stress (1-3 MPa). Under low stress condition, dilation appeared soon after a small compression during the shearing for loose sand; furthermore, the dilatancy angles were stress-dependent. The smaller the confining stress was, the larger the dilatation angle became. The state of clean sand, loose or dense, depended both on void ratio (density) and confining stress in respect with ultimate (steady) state.

2) In Cyc-CU tests, if the void ratio was the same, then smaller confining pressure was, and the larger loading cycles would be. Referred to the possibility of liquefaction, loose sand also behaved as dense under very low confining stress, that is, the liquefaction resistance increased with the reduction in the confining stress. Confining dependency was still prominent and similar way as that in monotonic loading. It was firstly confirmed that with increasing of confining stress, the trend of time history of strain changed gradually from compressive predominant to tensile predominant in both loose and medium-dense states.

3) Enhancement effect of membrane, mainly the influence of the thickness, had been investigated thoroughly and it was found that the influence on the test results in low confining stress did exist but the degree was limited. A membrane with thickness of 0.15 mm was enough to get an accurate test result at very low confining stress. Meanwhile, experimental results from the triaxial loading equipment and corresponding test technology were creditable with relatively good reproducibility.

4) This study presented a systematic study on the monotonic/dynamic behavior of sand under low confining stresses. It could be concluded that confining stress was another state parameter that strongly controlled the loose or dense state of sand, besides of void ratio. Future study should focus on the quantitative relationship between confining stress and the loose/dense state.

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(Edited by YANG Hua)

中文导读

低围压至高围压下砂土的剪胀性和液化性分析

摘要：砂土的状态主要取决于孔隙比(密实度)和围压大小，它们极大地影响了砂土的力学特性(压缩性、剪胀性和液化性)。为研究低围压至高围压范围内砂土相对密度和围压对土体强度和变形特性的影响，对2种不同相对密实度砂土试样在低至高围压下(5～3 MPa)进行常规三轴固结排水剪切试验、常规三轴固结不排水试验和动三轴非排水试验，对砂土的静、动变形特性及静、动强度特性进行研究。试验结果表明：在单调加载条件下，在低围压范围(5～20 kPa)，体积应变由剪缩向剪胀转变，且剪胀角具有明显的应力依存性，随着围压的减小而增大；在高围压范围(1～3 MPa)，试样体积逐渐趋于剪缩；在循环加载条件下，砂土试样抵抗液化能力随着围压的减小而增强，轴向应变伴随着围压的增大从压缩状态向膨胀状态转变。同时，试验结果表明，应用文中的试验方法，橡皮膜的约束效应对低围压的试验结果影响较小。

关键词：孔隙比；围压；单向/循环加载；排水/不排水三轴试验；砂土状态变量

Foundation item: Projects (51908288, 41627801) supported by the National Natural Science Foundation of China

Received date: 2020-02-26; Accepted date: 2020-06-04

Corresponding author: WANG Zhen, PhD, Lecturer; Tel: +86-13016950388; E-mail: wangzhen2012@njust.edu.cn; ORCID:https:// orcid.org/0000-0002-8081-2003