Bndn Tiwri, Gunlin Ye,*, Minggung Li, Usm Khlid, Sntosh Kumr Ydv,b

a Department of Civil Engineering and State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

b Department of Civil Engineering, IOE, Pulchowk Campus, Tribhuvan University, Lalitpur, 44700, Nepal

Keywords:Deep sands in Shanghai Laboratory tests Shear strength Dilatancy Relative density

A B S T R A C T With rapid development of infrastructures like tunnels and open excavations in Shanghai,investigations on deeper soils have become critically important.Most of the existing laboratory works were focused on the clayey strata up to Layer 6 in Shanghai, i.e. at depth of up to 40 m. In this paper, Layers 7, 9, and 11,which were mostly formed of sandy soils at depth of up to 150 m,were experimentally investigated with respect to physico-mechanical behaviors.The stress-strain behaviors were analyzed by the consolidated drained/undrained (CD/CU) triaxial tests under monotonic loading. One-dimensional (1D) oedometer tests were performed to investigate the consolidation properties of the sandy soils. Specimens were prepared at three different relative densities for each layer. Also, the micro-images and particle size analyzers were used to analyze the shape and size of the sand grains.The influences of grain size,density,and angularity on the stress-strain behaviors and compressibility were also studied. Compared to the other layers, Layer 11 had the smallest mean grain size (D50), highest compressibility, and lowest shear strength. In contrast, Layer 9 had the largest mean grain size, lowest compressibility, and highest shear strength. Layer 7 was of intermediate mean grain size, exhibiting more compressibility and less shear strength than that of Layer 9.Also,the critical state parameters and maximum dilatancy rate of different layers were discussed.

1. Introduction

Shanghai is located in the southern bank of the Yangtze River delta. Geologically, Shanghai consists of marine Quaternary sediments that were deposited in the last 3 million years with an average thickness of 300-400 m having one phreatic aquifer group and five artesian aquifers (Xu et al., 2009). Based on depositional history physico-mechanical characteristics, and other factors, soils in Shanghai can be generally divided into 12 different layers according to local geotechnical design codes (DGJ08-11-2002 and DGJ08-37-2008) (Wu et al., 2015). Among them, Layers 2-6 at depths of 30-40 m mainly consist of soft marine clay. Alternate layers of sandy and clayey soils are deposited below 40 m.Most of the researches focusing Shanghai soils are generally within the depth of 40 m(Gong et al.,2009;Hong et al.,2015;Ye and Ye,2016;Wu et al.,2017;Ye et al.,2018).To date,studies on soil layers below 40 m are still rare.

Over the years,studies have been extensively reported on Layer 4 of soil in Shanghai (Li et al., 2012; Ye and Ye, 2016; Khalid et al.,2018; Zhang et al., 2018a,b; Khalid et al., 2019). At the same time,excavation has gone deeper with a larger scale due to the rapid expansion of the tunnels and other underground infrastructures(Li et al.,2018,2019;Zhang et al.,2013).For example,the underground construction of the Shanghai World Finance Center reached a depth of 83 m and the diaphragm walls for subway line 4 reached a depth of 65.5 m(Jia et al.,2019).For some high-rise buildings in Shanghai,the depth of piles can even reach the depth of 100 m.This has raised the importance of researches on deep soils(Chen et al.,2014).In the literature, the studies on the mechanical behavior of soils below Layer 6 are still insufficient. For this, this study tries to investigate the mechanical behaviors of deep soils in Shanghai.The deep sandy soils at Layers 7, 9, and 11 were selected,with the depth ranges of 41.4-49.8 m, 72.9-98.9 m, and 122.4-150 m, respectively. Basically, these layers are of sandy soils with different physical characteristics.

Grain shape and size basically play a dominant role in influencing mechanical behaviors of sandy soils. For this, numerous researches have been conducted since the 1950s in order to evaluate the influence of physical parameters on the strength of granular soils. However, the effects of particle shape and size on the shear behavior are still not well known. Kolbuszewski and Frederick (1963), Zolkov and Wiseman (1965), and Zelasko et al.(1975) observed that the shearing resistance increased with increase of grain size.Kirkpatrick(1965)concluded that the angle of shearing resistance and maximum and minimum void ratios were independent of grain size and grading; it only depended upon mineralogy and surface roughness of the material. Chattopadhya and Saha (1981) concluded that fabric of granular materials controlled the grain size and decrease in the grain size resulted in increase of the maximum void ratio. Cola and Simonini (2002)introduced a new grain size index (IGS) with which the influence of grading and mean grain size on critical state line (CSL) parameters was studied. Santamarina and Cho (2004) discussed the fabrics anisotropy effects on the deformation and strength behaviors of sands by decreasing the stiffness and residual friction angle.Wang et al. (2013) performed direct shear box and triaxial tests with a focus on grain size distribution(GSD)on the shear strength of soil and they suggested that the angle of shearing resistance increased with increases of mean grain size and gravel content.Ovalle et al. (2014) experimentally observed that particle size greatly affected the crushing strength of rock aggregates.

In addition, with increase in the particle size of coarser materials,decrease in shear strength due to increase in particle breakage tendency has also been investigated.Islam et al.(2011)conducted a series of direct shear tests and concluded that with increase in the grain size,the internal frictional angle increased and shear strength was also enhanced. Xiao et al. (2017) reported that with the increase of non-plastic angular fine grains, the peak friction angle increased, which could further increase the shear strength of mixture. Xiao et al. (2019) investigated the variations of strength,dilatancy, and stress-dilatancy of sand with particle shape by mixing different proportions of glass beads and concluded that,with decrease in overall regularity of mixture,the critical and peak state friction angle increased.

Various studies have been conducted to observe the effect of grain shape on behaviors of sands (e.g. Mair et al., 2002;Georgiannou 2006; Yang and Wei, 2012; Senetakis and Sandeep,2017). Holtz and Gibbs (1956) performed a series of triaxial tests on the mixture of gravel and sand, and indicated that, compared with the sub-angular and sub-rounded river sands, the angular materials of quarry had higher shear strengths. Mair et al. (2002)reported that increase of grain angularity could lead to increasing shearing resistance, as the ratio of rolling to sliding contacts decreased.Nouguier-Lehon et al.(2003)found that assembly of the rounded grains showed better softening behavior in comparison with that of angular or elongated grains which required more shear stresses in order to change its initial fabrics anisotropy and reach the critical state line. By adding 2.5% of silt, Georgiannou (2006)found that round silt particles had a more stable response than platy silt particles. Moreover, the shape of a fine grain had a significant effect on the mechanical behaviors of sands, especially on liquefaction.Cho et al.(2006)analyzed the relationships among the packing density,grain shape,stiffness,and strength of crushed and natural sands. They revealed that critical state friction angle,maximum void ratio (emax), minimum void ratio (emin), and their difference(Ie)increased with increase in irregularity of the particle.Yang and Wei (2012) explained that the fine grains with round shape exhibited higher potential of liquefaction than that with angular shape and the critical state friction angle can be increased remarkably with the increment of the angular fine grains.Similarly,Shin and Santamarina (2012) found the mobility of particles was affected by angularity which can result in higher friction angle and lower density using the oedometer tests in Ottawa and Blast sand.Cabalar et al.(2013)performed the drained and undrained triaxial tests on different natural sandy soils under monotonic and dynamic loadings and found that the sand specimens with more round particles exhibited strong dilation property whereas that with more angular-shape particles exhibited contraction property.

In this study, the physico-mechanical behaviors of deep sandy soils in Shanghai were investigated. The detailed physical characteristics were determined by performing different laboratory tests including microscopic test, maximum and minimum density test,and particle size analysis.One of these natural sandy soils,Layer 11 sand,had more than 50%of fine grains.Then,one-dimensional(1D)oedometer tests were conducted to investigate their compressibility. Moreover, a series of consolidated undrained (CU) and consolidated drained (CD) triaxial tests was performed to investigate the stress-strain and dilatancy behaviors of sandy soils at different relative densities with different mean grain sizes.

2. Materials and methodology

2.1. Materials

In this study, sandy soils were sampled using deep borehole method. Layer 7 was extracted from Gucui Road, Pudong New District,Shanghai,with a depth range of 41.4-49.8 m.Layers 9 and 11 were extracted from Nanchen Road,Baoshan District,Shanghai,with the depth ranges of 72.9-98.9 m and 122.4-150 m,respectively.

The GSD curves of sandy soils determined by particle size analyzer are shown in Fig.1.The sand fractions of Layers 7,9,and 11 were 90.5%,89.5%,and 43%,respectively;while the silt fractions of Layers 7, 9, and 11 were 9.5%, 11.65%, and 57%, respectively. The mean grain sizes (D50) of Layers 7, 9, and 11 were 0.125 mm, 0.2 mm, and 0.057 mm, respectively. The detailed physical characteristics of all layers are presented in Table 1.D50is the average particle diameter of the soil, and has been correlated with other property index, e.g. void ratio, crushability index, angle of repose, and maximum and minimum void ratios.

2.2. Specimen preparation and test procedure

Fig.1. GSD curves for different layers of deep sands in Shanghai.

Table 1 Physical properties of different sand layers.

The maximum and minimum dry densities of the specimens were measured according to the method by Japanese Geotechnical Society (JIS A1224:2009). The measurement of the maximum density(ρdmax)was performed by striking the side wall of mold by 100 times with a wooden hammer.Similarly,the minimum density(ρdmin)was determined by pouring the heap of specimen from the center of a funnel into the mold at a constant speed. The relative density (Dr) was calculated by

where e,emax,and eminare the void ratio,maximum void ratio,and minimum void ratio of the soil,respectively.In order to investigate the mechanical behavior of grain size of deep sandy soils, specimens were prepared at three relative densities(Dr)of 40%(loosely dense),60%(averagely dense)and 80%(highly dense)from all three layers for the oedometer, CD and CU triaxial tests. The triaxial specimen was prepared by the moist tamping method.

2.3. Methods

2.3.1. Particle size analyzer

GSDs of all the specimens from different layers were determined using the dry method by a laser particle size analyzer (OMEC LS-909, Shanghai, China). The measuring range is 0.1-2100 μm. In order to obtain consistent results, three specimens for each layer were used. The OMEC LS-909 apparatus consists of high-quality He-Ne laser emitters with advanced data collecting and processing technology, which depends upon the scattering angle. Specifically, when the lasers reached the grains, transmission routes of lights deviated to different scattering angles according to the physical size and orientation of the grains. The grain size was determined by measuring the scattering angles. Larger deviation angle means a smaller grain size, and vice versa. Based on the Fraunhofer theory (Endoh et al.,1998), this device can be used to measure the grain size.

By using Leica DM4000 M (German), the micro-images of different layers of sand specimens in Shanghai were obtained, as shown in Fig. 2. The micro-images can clearly calibrate the result obtained from particle size analyzer. The results showed that the mean grain size of Layer 9 was the largest,whereas Layer 11 was the smallest. The angularities of the different sand specimens were measured using the method of Miura et al. (1997), and the twodimensional (2D) angularity (A2D) of the grain was estimated using the table defined by Lees (1964a,b) (see Fig. 3). From the enlarged photo of the micro-image for each layer, 20 sand grains were considered with grain size of around D50,whose outlines were further traced. Using the following table, A2Dvalues can be estimated.The result shows that the grains of Layer 9 had the highest A2Dvalue of around 750 in comparison to Layers 7 and 11 with values of 470 and 350, respectively.

Fig. 2. Micro-images of deep sands in Shanghai from (a) Layer 7, (b) Layer 9, and (c)Layer 11.

2.3.2. One-dimensional (1D) consolidation tests

The 1D consolidation tests were conducted for different sandy layers with three different relative densities.The specimens were prepared by dry tamping method. The soil was fitted tightly into the cylindrical ring so that no lateral strain occurred. The height and diameter of specimen were 20 mm and 61.58 mm, respectively. The cylindrical ring was enclosed inside a metal ring with porous stones placed at the top and bottom of the specimen.When a predetermined static vertical load was applied on the specimen, the settlement versus time was recorded in the form of gage reading.At each loading stage,the load was double of the previous one, and the settlement induced by each load was recorded.The maximum load of 1600 kPa was applied at the final stage.

Fig. 3. Table proposed by Lees (1964a,b) for estimate of A2D value.

2.3.3. Triaxial tests

A series of CU and CD triaxial tests was performed in an automated triaxial apparatus. Specimens with diameter of 50 mm and height of 100 mm for the triaxial tests were prepared by moist tamping method to prevent segregation. For each required relative density, the predetermined weight of ovendried sand was mixed with de-aired water (10% by weight).The rubber membrane was flipped over the copper mold with a ferrule and vacuum pump.The filter paper was initially placed at the end of the mold followed by loading of a sand specimen and a tamping rod was used to press it. Specimens of different densities were divided into five equal layers. The weight of sand for preparing the specimen was divided into five equal parts, and one part means one layer. For a better contact between adjacent layers, the surface was scratched before the next layer layout. To ensure that the specimen was homogeneous, a Vernier caliper was used to measure the height of each layer.For example,while preparing the first layer of sand, the distance between top layer of sand and the top of the mold was 80 mm; for each layer,equal compaction was performed to ensure the uniformity of each layer. Moreover, the energy applied on each layer remained constant to ensure the uniformity of the specimen. This test procedure to control the specimen’s density has also been successfully applied to the triaxial test for granular materials in our laboratory (e.g. Ye et al., 2019).

To ensure saturation of specimen, the carbon dioxide was initially supplied in an upward direction for 30 min in order to remove the air trapped in pores.Meanwhile,by flushing de-aired water from bottom to top of specimen with some back pressure and maintaining the effective confining stress at 20 kPa, the specimen was fully saturated. After saturation, the specimen underwent pre-consolidation stage. The Skempton’s B-value was obtained to be no less than 0.95 to ensure that the specimen was fully saturated according to JGS-0523-2000 and ASTM D 4767-92-2002. After the pre-consolidation stage, the confining pressure was increased and the back pressure was kept constant. The consolidation was carried out under an effective confining pressure of 100 kPa. During consolidation, the volume change of the specimen was measured. Following the consolidation stage, the strain-controlled axial load was applied to the specimen at a rate of 0.1 mm/min for both drained and undrained conditions.During the shearing stage of CU triaxial tests, the drainage valves were closed.The void ratio after consolidation was noted as initial void ratio (e0) of triaxial tests.

3. Results and discussion

3.1. Compressibility of deep sands in Shanghai

Fig. 4. Compression curves of deep sands in Shanghai at different relative densities from (a) Layer 7, (b) Layer 9, and (c) Layer 11.

Results of 1D consolidation tests for different layers with different relative densities are presented in Fig. 4. From the e-curves, the initial void ratio (e0) of Layer 7 at relative densities of 40%, 60%, and 80% were 0.87, 0.746, and 0.629,respectively. Similarly, the values of e0at relative densities of 40%,60%, and 80% are 0.691, 0.601, and 0.512 for Layer 9, and 1.205,1.038, and 0.872 for Layer 11, respectively. Layer 11 with the smallest value of D50underwent maximum compression with the highest compressibility index (Cc) values of 0.23, 0.199, and 0.169,corresponding to relative densities of 40%, 60%, and 80%, respectively;whereas Layer 9 underwent minimum compression with the lowest compressibility index among all layers due to large value of D50, and Ccvalues were 0.082, 0.069, and 0.059, corresponding to the relative densities of 40%,60%,and 80%,respectively.Among all layers, Layer 7 had intermediate Ccvalues of 0.128, 0.0877, and 0.066 at relative densities of 40%, 60%, and 80%, respectively. The detailed compression properties of all layers are presented in Table 2.The result showed that compressibility was dependent on the mean grain size of the sandy soils and suggested that compression index decreased with increasing mean grain size,and vice versa.

3.2. Stress-strain and excess pore water pressure under undrained condition

In this section, the stress-strain behavior and excess pore water pressure were discussed for the three layers of deep sandy soils. As aforementioned, all the experiments were conducted under the same effective confining stress of 100 kPa for different layers at various relative densities. Fig. 5 shows the CU triaxial test results of Layer 7. Mfis the slope of the critical state line(CSL) in Figs. 5c, 6c and 7c. With increasing relative density, the peak deviatoric stress(q) and mean effective stress (p′)increased and the specimens demonstrated a behavioral change from strain-softening to strain-hardening. The peak excess pore water pressure (u) initially increased; whereas upon subsequent shearing, u decreased and showed a dilative tendency for specimens at high relative densities.Similar mechanical behavior was also observed for Layer 9 at different relative densities (see Fig. 6). For Layer 7 at a relative density of 80%, it had a strainhardening behavior (see Fig. 4b and c) where the excess pore water pressure decreased after reaching the peak. The stress paths at relative densities of 40% and 60% showed a strainsoftening behavior when deviatoric stress and constant excess pore water pressure decreased after reaching the peak value at 2% axial strain. The stress paths of Layer 9 showed a strainsoftening behavior only at relative density of 40%; while at relative density of 60% and 80%, it showed a strain-hardening behavior with decreasing excess pore water pressure (see Fig. 6b and c). The stress paths of Layer 11 showed a distinctive strain-softening behavior when relative density is less than or equal to 60%.However,at relative density of 80%,it demonstrated a strain-softening behavior up to critical state line, but after that,a small strain-hardening was observed (see Fig. 7c).

Table 2 Compression properties of different layers of sand.

Fig.5. CU triaxial test results of Layer 7 at different relative densities:(a)q-εa;(b)u-εa;and (c) q-p′.

Fig.6. CU triaxial test results of Layer 9 at different relative densities:(a)q-εa;(b)u-εa;and (c) q-p′.

With the increase in the mean grain size, at the higher relative densities,transition of the behavior from strain-softening to strainhardening showed a decreasing trend in excessive pore water pressure for Layers 7 and 9. But for Layer 11, there was no such change.The variation in the grain size is related to the modification of soil fabrics which induces the difference in the void ratio and alters the stress-strain behavior(Islam et al.,2011).Therefore,this variation may be attributed to the changes in grain shape,size,and fine grains content.Layer 9 had the highest mean grain size and the most angular grain than that of Layers 7 and 11(Fig.1).Due to the increase in angularity, grain interlocking was enhanced and resulted in an increase of deformation resistance. Also, the number of grain contact increased and resulted in high shear strength which altered the initial fabrics of soils. However, as the Layer 11 was composed of round grains with the smallest D50, more rolling and sliding scenario occurred leading to decrease in the interlocking among the grains.Hence a smaller deviatoric stress was required to change initial soil fabrics. As Layer 11 had a higher percentage of fine grains(Fig.1),the inter-granular contact between coarse grains was reduced which increased the fragility of sand (Thevanayagam et al., 2002).

Fig. 7. CU triaxial test results of Layer 11 at different relative densities: (a) q-εa; (b) uεa; and (c) q-p′.

3.3. Stress path comparison of different layers

Fig. 8. Comparison of different layers’ stress paths at relative densities of (a) 40%, (b)60%, and (c) 80%.

The comparison of the stress paths for different layers at different relative densities is shown in Fig.8.As shown in Fig.8a,all the layers exhibit strain-softening behaviors at relative density of 40%.Similarly,for specimens with relative density of 60%,Layers 7 and 11 show strain-softening behaviors with a gradual reduction of deviatoric stress after reaching the critical state, while Layer 9 exhibits a strong strain-hardening behavior with increases of deviatoric stress and mean effective stress values.At a relative density of 80%, Layer 7 showed diverse behaviors. At the initial stage, it appeared to be strain-softening but with increasing vertical stress,at the verge of reaching the critical state, it turned to strainhardening (see Fig. 8c). Layer 9 also showed the strain-hardening behavior at relative density of 80%, while Layer 11 demonstrated a strain-softening property.

3.4. Stress-strain and volumetric strain behavior under drained condition

In this section, the CD triaxial test results were presented for different layers at relative densities of 40%, 60%, and 80%. The variations in deviatoric stress (q) and volumetric strain (εv) with the axial strain (εa) were discussed for each layer. For Layers 7 and 11,with increasing relative density, there was an increment in the deviatoric stress value with a decrease in the corresponding volumetric strain value (see Figs. 9 and 10). When the deviatoric stresses reached the peak values,the specimens of Layers 7 and 11 showed a rapid contraction rate of the volumetric strain.However,after the peak,there was almost no change in the deviatoric stress and the volumetric strain. For Layer 9, with an increase of relative density from 40% to 80%, the peak deviatoric stress also increased(see Fig. 11). The volumetric strain only showed a contractive behavior during the whole shearing process at relative density of 40%. However, at the relative densities of 60% and 80%, the volumetric strain showed an initial contraction behavior for about 2%of axial strain;upon further shearing,a dilative behavior was detected(see Fig.11b).

3.5. Comparison of dilatancy of different layers

Comparisons of axial and volumetric strains for different layers at various relative densities are presented in Fig.12 a-c. For all the three relative densities, Layer 9 with the largest D50showed the least volumetric contraction effect, whereas Layer 11 with the smallest D50and the highest percentage of silt content performed the most prominent volumetric contraction effect.Also,at relative density of 80%, Layer 9 underwent dilation. However, only the contractive behaviors were observed for other layers.

Fig.9. CDtriaxialtest results for Layer 7 at different relative densities:(a)q-εa;and(b)εv-εa.

Fig.10. CD triaxial test results for Layer 11 at different relative densities: (a) q-εa;and(b) εv-εa.

During the shear deformation stage at low density, the intergrain coordination was low and the rotational movement with chain buckling and packing densification was high,which resulted in higher volumetric contraction (Cho et al., 2006). However, at high density, there was a higher inter-grain coordination which reduced the rotational movement and dissipated the applied energy in either dilation or frictional slippage(Cho et al.,2006).With increases in angularity and anisotropy, dilatancy was enhanced with obstruction of grain rotations.Such behavior was observed for Layer 9. Grains underwent dilation at high relative densities because of the presence of higher grain angularity than that of other layers.

Fig. 13 shows the relationships of maximum volumetric contraction (εvcv), secant modulus (E′50), and axial stress at peak stress (εap) with the mean grain size (D50) at different relative densities for all sandy soils. These variables were estimated from CD triaxial tests results. It can be clearly observed that: (1) εvcvand εapdecreased with increase in the dilative tendency and E′50increased with increasing relative density; and (2) the influences of relative density on the three variables became more prominent as the D50increased. For higher D50, the maximum volumetric contraction decreased and started to show a dilative behavior at higher relative densities,especially in Layer 9.E′50was increasing with increment of relative density,indicating the increase of stiffness.With increasing relative density and mean grain size, the brittle behavior of sandy soils was enhanced as the εapvalue decreased.

Fig.11. CD triaxial test results for Layer 9 at different relative densities: (a) q-εa; and(b) εv-εa.

3.6. Maximum dilatancy rate

The parameter“maximum dilatancy rate”is used to describe the contractive and dilatancy behaviors of sandy soils (Bolton, 1986;Cola and Simonini, 2002). The maximum dilatancy rates,（dεv/dεa）max,at different relative densities for different deep sandy soils in Shanghai are predicted in Fig. 14 (Bolton, 1986). The contraction was represented by the negative direction and the dilation was signified by the positive direction. For Layer 11, the effect of relative density on maximum dilation was insignificant and it showed a contractive behavior (see Fig. 14). The value of maximum dilatancy rate of Layer 7 would turn to positive after relative density of 96%. Similarly, the value of maximum dilatancy rate of Layer 9 would be positive at around 68%relative density.In Fig.14, the contraction behaviors at relative densities of 40% and 60% are clearly displayed.

3.7. Critical state friction angle and CSL from triaxial testing

Fig. 12. Comparisons of volumetric and axial strains for different layers at various relative densities: (a) 40%, (b) 60%, and (c) 80%.

After the soil was entirely destructed,the soil underwent critical state of deformation with constant volume,shear stress and effective mean stress at a constant shear rate which was considered to be only dependent on the effective stress and the composition(Mitchell and Soga,2005).The plots of deviatoric stress and mean effective stress at the critical state for different layers are shown in Fig.15.The friction angle associated with the critical state is known as critical state friction angle. There have been diverse opinions on the dependence of critical state friction angle on the coefficient of uniformity, grain shape, density, and mean grain size (e.g. Kokusho et al., 2004;Simonini et al.,2007).However,in this study,the critical friction angle was found to be independent upon the relative density and the drainage conditions. Similar observations were reported by Murthy et al. (2007) and Yang and Luo (2018). From the slopes of the bestfit lines for different layers, Layers 7 and 11 were found to have almost the same critical state friction angle; for Layer 9,the critical friction angle was slightly higher than that for other layers.Layer 9 is composedof thelargestmeansizegrainamongthethree layers,while Layer 11 had the smallest mean grain size,with the highest coefficient of uniformity(Cu)and coefficient of gradation(Cz)(see Fig.1).

Fig.13. Relationships of mean grain size (D50) with (a) maximum volume contraction(εvcv), (b) secant modulus (E′50), and (c) axial strain at peak stress (εap).

The plot of e-log10p′from the CU and CD triaxial tests for different layers is shown in Fig.16.For the CU triaxial test,as there was no volumetric change,the void ratio did not change.However,in CD triaxial test, void ratio changed during the shearing.Distinctive relationship exists between the void ratio and mean effective stress in the critical state, commonly known as CSL(Roscoe et al.,1958; Schofield and Wroth,1968; Been et al.,1991;Riemer and Seed, 1997). From previous studies (e.g. Been et al.,1991; Verdugo and Ishihara, 1996; Kang et al., 2019), it is recognized that the CSLs for both drained and undrained conditions are identical. Hence the CSL is deduced following the trend under undrained condition. The test results might have not reached the CSL as the specimen might have not undergone ultimate shearing with steady shear stress and volume.Also,load distribution among the whole volume was assumed to be uniform during shearing,which was practically impossible in the macro-observation due to the local discontinuities that may result in this discrepancy(Salvatore et al., 2017).

Fig.15. Critical stress states of different layers of deep sands in Shanghai.

From Fig.16a-c, it can be observed that the dilatancy of sands depends on the relative position between the initial state and the CSL. When the initial state lies above the CSL, it means it is looser than the critical state. Then the soil will show negative dilatancy during shearing.When the initial state lies beneath the CSL,it means it is denser than the critical state. Then the soil will show positive dilatancy during shearing. From Fig. 16d, it can be seen that the position of CSL changes with the particle size(grading)and particle shape.The CSL moved upward as the particle size decreased,and the slope of CSL may have become gentle as the angularity of particle decreased.In addition,Fig.15 indicates that the critical friction angle may decrease as the angularity decreases.For more angular particles,the number of contact surface will increase and interlocking will be higher resulting in larger shear strength. These findings are in agreement with previous studies(e.g.Been et al.,1991;Miura et al.,1997;Cho et al.,2006;Yang and Luo,2018).

4. Conclusions

In this study,laboratory tests were conducted to investigate the physico-mechanical behaviors of deep sandy soils in Shanghai, i.e.Layers 7, 9, and 11. We focused the effect of grain size on the strength and dilatancy of sands measuring the same relative densities. These findings are as follows:

(1) The effect of relative density significantly depended on the mean grain size. The effect was very slight for small mean grain size (i.e. Layer 11, D50= 0.057 mm) without any distinctive behavioral change. However, for large D50(i.e.Layer 9,D50= 0.2 mm)with the angular edges,the behavior of specimen changed from strain-softening to strainhardening under CU condition. Whereas under CD condition, the specimens showed contractive to dilative behavior with increasing relative density.

Fig.16. Determination of critical state lines (CSLs) on the e-log10p’ plane for different layers of deep sands in Shanghai: (a) Layer 7, (b) Layer 9, (c) Layer 11, and (d) all layers.

(2) The oedometer test showed that compressibility was dependent on the D50of the sandy soils, indicating that the compression index decreased with increasing D50, and vice versa.

(3) In the CD triaxial test,with increases in relative density and mean grain size, the axial contraction at peak strength and maximum volumetric contraction decreased, and secant modulus increased, resulting in increasing brittleness and stiffness.

(4) The relative density and the drainage condition did not influence the critical state friction angle. However, the critical state friction angle increased with grain angularity.

The test results and the investigation on the effect of grain size and particle size will be helpful for understanding the fundamental properties of deep sands in Shanghai.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The financial support of the National Natural Science Foundation of China (Grant Nos. 42072317 and 41727802) is gratefully acknowledged.