The Effect of the Nonplastic Fines on the Cyclic Resistance of the Saturated Sand-Fines Mixtures

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Introduction
Liquefaction is a special phenomenon wherein the excess pore pressure of a mass of soil increases and the shear resistance decreases when subjected to a monotonic, cyclic, or dynamic load. Te mass undergoes very large unidirectional shear strains; it appears to fow until the shear stress is as low as or lower than the reduced shear resistance [1]. Such a phenomenon leads to the lateral spreading of gently sloping ground, densifcation and vertical ground settlements, and slope instability. Te loss of life and damage to facilities and infrastructure due to liquefaction were very signifcant in past earthquakes, such as those in Kobe, Wenchuan, and east Japan [2][3][4]. For these reasons, soil liquefaction is one of the most important and complex issues studied in geotechnical earthquake engineering. Scholars have devoted themselves to the phenomenon's investigations, and many signifcant results have been achieved [5][6][7][8][9][10][11]. For many years, the phenomenon of liquefaction was thought to be limited to sand. Finer-grained soils were considered incapable of generating high pore pressures, which were commonly associated with soil liquefaction. Terefore, most of the previous research work on soil liquefaction has been focused on relatively clean sands [12][13][14]. However, natural sandy soils, though, contain fnes (passing sieve no. 200, particle size less than 0.074 mm) more or less. Natural sands are always mixed with fnes. Such combinations are called silty sands or sand-fnes mixtures. Historically, many cases of earthquake-induced liquefaction were observed to occur in silty sands. Field performance data during earthquakes indicated that liquefaction-related failures had also occurred at sites with silty sands and sandy silts. For example, liquefaction occurred in the sands induced by the Chi-Chi earthquake was with very high fnes content (FC) [15]. Terefore, the efect of FC on the liquefaction behavior of sand-fnes mixtures has elicited particular interest from scholars in the past few decades, and plenty of test data are available in the technical literature.
However, many data points and conclusions in the technical literature are seemingly contradictory, and the subject of the efect of FC on the liquefaction behavior of sand-fnes mixtures seems to be associated with confusion.
For the laboratory test, Amini and Qi [16], and Chang et al. [17], among others, found that the cyclic resistance ratio (CRR) of the sand-fnes mixtures increased with the increase of the FC, which meant the FC exerts a positive efect on the liquefaction resistance of the mixtures. However, Troncoso and Verdugo [18], Vaid [19], Chien et al. [20], and Papadopoulou and Tika [21], among others, found that the CRR decreased with the increase of the FC, which meant the FC exerts a negative efect on the liquefaction resistance of the mixtures. In addition, Dash et al. [22], Polito and Martin [23], Xenaki and Athanasopoulos [24], and Tevanayagam [25,26], among others, held the view that the CRR decreased frstly and then increased with the FC increasing from low to high, which meant the FC exerts a negative efect on the liquefaction resistance of the mixtures in the low FC but exerts a positive efect in the high FC. It is believed that the FC plays an important role in determining the sand structure and the consequent extreme void ratios. Tese, in turn, have signifcant infuences on the compressibility and liquefaction potential of a sand deposit [27]. Tere exists a threshold value of fnes content, FC th , which is not unique but it may depend on the characteristics of the coarse and fne grains, as well as on the value of the global void ratio (e) of the mixtures. Cabalar et al. [28] studied the compressional behavior of gravel and clay mixture and believed that the FC th is the boundary between fne-domination and coarse-domination of a mixture. Tevanayagam [26] proposed a conceptual framework by introducing intergranular and interfne void ratio to describe the contact state of the mixtures rather than e. Rahman et al. [29,30] proposed a semiempirical formula to calculate FC th . Cabalar and Hasan [31] and Monkul and Ozden [32] studied the compressional behavior of a sand and clay mixture. Te intergranular void ratio was used to express the compressive response of the mixture. Wei and Yang [33,34] proposed a critical state constitutive model for the silty sands to describe the mechanical behavior and studied the cyclic behavior and liquefaction resistance of silty sands with the presence of initial static shear stress. Furthermore, Yang et al. [35] believed that e was a better parameter to describe the contact and mechanical behavior of the sand-fnes mixtures than the skeleton void ratio. It was logically inconsistent with the assumption underlying the concept of the skeleton void ratio that fnes make no contribution to the force transfer.
With respect to the conficting conclusions in the technical literature and the confusion about the efect of the FC on the liquefaction behaviour of sand-fnes mixtures, a series of undrained cyclic triaxial test investigations were carried out to understand the cyclic behaviours of saturated sand-fnes mixtures, especially the CRR. Te infuences of FC, e, and D r were considered. A new index, D r /e, is proposed in this study for the dense state of the sand-fnes mixtures. A semiempirical model is proposed to evaluate the CRR of the sand-fnes mixtures using the parameters of D r /e and FC of the fnes based on the back analysis method. Te test results and proposed model are good references for engineering practice.

Undrained Cyclic Triaxial Tests
2.1. Testing Materials. Fujian sand was used as the host sand material. Fujian sand is one type of clean sand in China, which has been widely used in recent studies. Stone powder was used as nonplastic fnes. Te mixtures of Fujian sand and stone powder are called FS for convenience. Te FC of FS mixtures are 10%, 20%, 30%, 40%, and 50%. Te particle size distribution curves of FS mixtures under various FC are schematically illustrated in Figure 1. Te basic properties of the sand and fnes are listed in Table 1.

Testing Apparatus and Method.
Te undrained cyclic triaxial tests were carried out using a DYNTTS-type cyclic triaxial test system manufactured by GDS Instruments, UK. Te full view of the apparatus is shown in Figure 2. Te axial force, displacement, confning pressure, and back pressure of the test system can be independently controlled by the equipment, and monotonic or cyclic loads can be applied according to the test requirements. Te maximum dynamic load that can be applied in the test system is 10 kN and the frequency is 2 Hz. Te axial force and displacement are controlled by a servo motor in the base, which can apply sine, cosine, and other forms of loads or displacements with an accuracy of 0.1 kPa and 0.001 mm. Te confning pressure is applied using water. Te volume precision of the confning pressure and back pressure controller can reach 1 mm 3 and the pressure precision can reach 0.1 kPa (maximum value of 2 MPa). Te overall accuracy of the test system is high enough to meet the accuracy requirements of the tests.
Te cylindrical specimen has a diameter of 50 mm and height of 100 mm. Te specimen was prepared using a dry tamping method, which has previously been used by several scholars to test granular material [36,37]. Te well-mixed sand and fnes were tamped into a cylindrical specimen preparation device for four layers in the dynamic triaxial apparatus using the dry tamping method. Te presaturation was conducted after the specimen preparation. Te presaturation consists of 3 steps: (1) permeating the specimen with CO 2 for 30 minutes; (2) fushing with deaired water for 60 minutes; (3) and fushing all water lines. After the presaturation, the back pressure saturation was initiated. Back pressure was gradually applied and the Skempton B-value was checked until it was greater than 0.95, which guaranteed the saturation of the tested sample. Te saturated sample was consolidated under an efective target confning pressure until the variable quantity of the back pressure volume was smaller than 5 mm 3 every 5 minutes. Te sample was tested thereafter. Te undrained cyclic triaxial tests were performed in accordance with the ASTM D5311D/5311M standard [38].
Te infuences of the FC, e, and D r were considered to study the cyclic behaviours of saturated sand-fnes mixtures, especially the CRR. Te undrained cyclic triaxial tests were 2 Advances in Materials Science and Engineering conducted at various cyclic stress ratios (CSRs). Te CSR of the sample in an isotropic consolidation state is defned in where σ d is the applied sinusoidal cyclic axial stress amplitude. Te maximum and minimum global void ratios of FS with various FCs are shown in Figure 3. Te values were determined according to the ASTM D4253 and D4254 standards [40,41].
A series of undrained cyclic triaxial test investigations were carried out to understand the cyclic behaviours of saturated sand-fnes mixtures, especially the CRR. Te infuences of the FC, e, and D r were considered. Te detailed undrained cyclic triaxial test conditions are shown in Table 2. Te efective confning pressure (σ 0 ′ ) and loading frequency (f) of the test are 100 kPa and 0.1 Hz, respectively.

Liquefaction Criterion.
With respect to the liquefaction failure of the soil mass under cyclic load, Seed and Lee [5] deemed that the efective stress and shear strength of the soil Note. G s means specifc gravity; C u means coefcients of uniformity; C c means coefcients of curvature; e max and e min mean maximum and minimum global void ratio, respectively. ρ max and ρ min mean maximum and minimum dry density, respectively.   Advances in Materials Science and Engineering mass were 0 when liquefaction occur. However, Casagrande [42] focused on the fow characteristics of liquefed soil and suggested that liquefed soil had a steady-state shear strength and that damage was mainly manifested as excessive deformation, displacement, or strain. For the undrained cyclic triaxial laboratory test, the liquefaction criteria of clean sand in an isotropic consolidation state are divided into two types. Te frst type is the pore pressure criterion. Te pore pressure increment (∆u) of the sample is equal to σ 0 ′ , which means that the excess pore pressure ratio (R u � ∆u/σ 0 ′ ) under cyclic load is 1. Te second type is the deformation criterion. Te single amplitude strain (ε SA ) of the sample reaches 2%∼3%, and the double amplitude strain (ε DA ) reaches 5% under cyclic load. Considering that the specimen cannot be completely saturated and the excess pore pressure ratio cannot be 1, ε DA � 5% was selected as the initial liquefaction criteria in this study. Figure 4. Te N L is defned as the number of cycles required to lead to the initial liquefaction of the sample under a certain CSR. All samples were prepared at a D r of 50%. As shown in Figure 4, FC has signifcant efects on the CSR of the mixtures. Te CSR curves signifcantly difer with increasing FC. Te N L of a mixed sample with a certain FC increases with decreasing CSR. Te results show that the relationship between the CSR and N L of sandy soil can be described using the following equation [43]:

Cyclic Resistance Ratio Analysis. Te correlations between the CSRs of the FS mixtures with various FCs and the number of initial liquefaction cycles (N L ) are shown in
Te test data for the CSR and N L of various mixtures were ftted using this equation. Te ftting curves are shown in Figure 4.
Te CRR is defned as the CSR that leads to the initial liquefaction of the soil at a certain N L . Te N L was selected to be 15 in this study. Terefore, the CRR of various sand-fnes mixtures is represented by CRR 15 in this study. Te correlations between the CRR 15 and FC of FS mixtures prepared at a constant D r are shown in Figure 5. Figure 5 shows that the CRR 15 s of FS mixtures nonlinearly change with increasing FC. Te CRR 15 s frstly decrease and then increase, fnally stabilizing with increasing FC.
FC th , the threshold fnes content, is 20% when the samples are prepared at a constant D r .
Te correlations between the CSR of samples prepared at a constant e with various FCs and the N L are shown in Figure 6. Te e of the FS mixtures is 0.474. Te curves ftted using equation (2) are also shown in Figure 6. Te correlations between the CRR 15 and FC of FS mixtures prepared at a constant e are shown in Figure 7.
As shown in Figure 7, the CRR 15 s of the FS mixtures nonlinearly change with increasing FC. Te CRR 15 values decrease and then increase with increasing FC. Te FC th of FS mixtures prepared at a constant e is 30%.   It can be noted that the CRR 15 change trend of the mixture samples prepared at a constant e has both similarities and diferences compared with that of the samples prepared at a constant D r . Te CRR 15 of the two groups of samples frst decreases with increasing FC. Te reason for this decrease is that the fnes occupy the voids between the coarser particles, smoothen the roughness, and reduce the interlocking shear strength of the coarser particles with a low FC. Terefore, the CRR 15 frst decreases. Te CRR 15 increases with increasing FC when the samples are prepared at a constant e. Te reason is that the fnes become the skeleton to bear the load and the sands suspend in the fnes. Te fnes impede the relative movement of the coarser particles and lead to an increase in the CRR 15 . However, the e of the samples prepared at a constant D r increases with increasing FC, which leads to a decrease in the CRR 15 . Te CRR 15 of the samples prepared at a constant D r is stable under increasing e and FC. In addition, the FC th of FS mixtures prepared at a constant D r is 20%. However, the FC th of FS mixtures prepared at a constant e is 30%. Te FC th varies with the sample preparation standard. In a word, the correlations between the CRR 15 and FC of mixtures prepared at a constant D r difer from those of samples prepared at a constant e. It is signifcant to defne a constant D r or e before the test.
Te correlations between the CSR values of the FS mixture with an FC of 20% under various D r values and the N L are shown in Figure 8. Te curves ftted using equation (2) are also shown in Figure 8. As shown in Figure 8, the D r afects the CSR of the mixtures. Te CSR-N L curves shift upwards with the increase in the D r from 40% to 60%, which means that the CRR of the mixtures increases with increasing D r .
As shown in Figure 9, the CRR 15 s of FS mixtures increases almost linearly with the increasing D r . Te e of the Advances in Materials Science and Engineering mixtures decreases with increasing D r , which is not conducive to the development of excess pore pressure. Terefore, the CRR of the mixtures increases with increasing D r .  Te test data obtained in this study were ftted using equation (3). Te ftting results are shown in Figure 10. Te data obtained from the study of Dash et al. [22], Polito and Martin [23], and Sitharam et al. [44] are also ftted using the model to verify its applicability. Te ft results of the data from other studies are shown in Figure 10. Te ftted parameters for the test data of the study and other references are listed in Table 3.

Semiempirical Evaluation
It can be seen from Table 3

Conclusions
A series of undrained cyclic triaxial test investigations were carried out to understand the cyclic behaviours of saturated sand-fnes mixtures, especially the CRR. Te infuences of the FC, e, and D r were considered. A new index, D r /e, is proposed in this study to describe the dense state of the sand-fnes mixtures. A semiempirical model was proposed to evaluate the CRR of saturated sand-fnes mixtures based on the test results of this study and other references. Te following conclusions can be drawn: (1) Both the FC and D r (or e) afect the CRR of the sandfnes mixtures when the efect of the FC on the CRR is considered. It is important to defne a constant D r or e before the test. Te CRR of the sand-fnes mixtures frstly decreases and then increases, fnally stabilizing with increasing FC when the samples are prepared at a constant D r . Te CRR reaches its minimum when the FC is 20%. However, the CRR decreases and then increases with increasing FC when the samples are prepared at a constant e. Te CRR reaches its minimum when the FC is at 30%. Te CRR of the sand-fnes mixtures increases with increasing D r . (2) A single D r or e cannot describe the dense state of the mixture efectively. A new index, D r /e, is proposed in this study to describe the dense state of the sand-fnes mixtures. A semiempirical model is proposed to evaluate the CRR of the sand-fnes mixtures using the parameters of D r /e and FC of the mixture based on the back analysis method. Te applicability of the model is verifed by the test data from this study and other scholars.

Data Availability
Te data used to support the fndings of this study are available from the corresponding author upon request.

Conflicts of Interest
Te authors declare that they have no conficts of interest.