Influence of Soil Fabrics and Stress State on the Undrained Instability of Overconsolidated Binary Granular Assemblies

Laboratory observations have consistently confirmed that two samples of sand prepared by different reconstitution methods to the same density may exhibit quite different index properties and mechanical responses when subjected to monotonic and cyclic loading conditions under otherwise similar conditions [25,26,27, 29, 33, 36]. The obtained differences can be attributed to the resulted microstructure induced by the different reconstitution techniques that can be identified by the spatial arrangement of sand particles and associated voids [5, 30]. How to take fabrics effects into account in geotechnical engineering analysis is becoming a veritable challenge and remains a difficult problem that attracts efforts on both theoretical and practical levels. Published literature reported that several techniques have been developed to reconstitute samples of granular soil in laboratory testing. Moist tamping and pluviation (through air or water) are amongst the most popular techniques. Numerous studies [7, 17, 20, 28, 29, 33, 35, 40] have shown that different sample preparation methods induce different soil fabrics and consequently different stress– strain responses of reconstituted samples subjected to a small to moderate shear strain levels. Studies conducted by [29] and [40] were amongst the first attempts to study the effects of the sample preparation method on reconstituted sand behaviour. [28] performed a series of stress-controlled cyclic triaxial tests and found that sand samples prepared by moist tamping exhibited a much higher resistance to liquefaction than their counterparts formed by air pluviation, with the liquefaction resistance of the samples formed by water pluviation being in between. [40] observed that the method of sample preparation significantly affected the cyclic shear strength of sand. Similarly, [28] reported that different sample preparation procedures significantly affected the liquefaction characteristics of sand in undrained stresscontrolled cyclic triaxial compression tests. [4, 6, 13, 20, 24] presented results showing that the samples prepared with dry funnel pluviation (DFP) are more resistant than those prepared with wet deposition (WD). [39] performed undrained triaxial compression tests on loose silty sands and found that the shear response depended significantly on the used sample preparation techniques. The soil may become unstable even before the stress state reaches failure; this has been observed by [21, 23] under undrained conditions. [8, 18] investigated instability line behaviour for saturated sands under monotonic undrained triaxial tests conditions. Analysis of the obtained results showed a trend line representing peak shear strength points that passes through the origin. The tests were performed on samples with similar void ratios and different effective confining pressures. [22] indicated that instability is not synonymous with failure, although both may lead to catastrophic events; moreover, he observed that loose fine sand under undrained conditions becomes unstable even before the stress state reaches failure. [9] stated instability as one of the failure mechanisms that lead to flow slides or collapse of granular soil slopes for loose to medium dense sand under strain-controlled conditions. [10] also indicated the observed instability by various instability lines. However, they suggested that the instability line obtained from undrained tests could be used to predict the instability observed under decreasing mean normal stresses. Similarly, [31] idealised the observed instability conditions by a straight line and named it the ‘failure initiation line’. [11] also stated that the obtained instability line is the same for conventional undrained triaxial tests for a given void ratio. [15] reported from triaxial compression test results on sand samples prepared using two fabric methods such as DFP and WD that the WD samples exhibited a contractive character leading to instable soil samples compared to those prepared by DFP. They claimed that this behaviour can be attributed to the role of water to confer to the soil a higher void ratio, which leads to easily compressible samples and consequently to very vulnerable soil sample structure to liquefaction. [16] found that the stress path (in p’–q plot) indicated clearly that the slope of the instability lines for both dry funnel pluviated and wet deposited samples increased with increasing in confining pressure. The instability zone for WD method is larger than that for DFP method. [34] presented the definition of the instability line, the steady-state line and the instability zone. The instability line is a line that connects the peak of a series of effective stress paths obtained from undrained compressions tests (Figure 1).

Figure 1

The objective of this study is to explore the effects of two depositional methods, DFP and WD, and confining pressure (P’_c = 100, 200 and300 kPa) on the shear behaviour and instability friction angle of normally consolidated and overconsolidated Chlef sand–silt mixture samples (OCR = 1 and 2), focusing on the influence of low plastic fines content (F_c = 0%, 20% and 40%). Factors such as degree of saturation, sample size and relative density have been kept constant. A detailed laboratory investigation has been presented in the subsequent sections.

Data from the present study (Figures 7–14) are reproduced in Figure 15 for the purpose of analysing the effects of the OCR (1 and 2) and fines content (F_c = 0%, 20% and 40%), 20% and 40%), considering two sample preparation methods (DFP and WD) on the undrained shear strength instability lines. It is observed from the plot that the slopes of instability lines (η) increases with the increase in the OCR (1 and 2) for the range of fines content and initial relative density under study (D_r = 52%). Moreover, the samples reconstituted using DFP are more stable and dilatant than those prepared using WD (slopes of the instability lines of dry funnel pluviated samples are greater than those of wet deposited samples). The results of this research work are in good agreement with the findings of [15, 16]; thus, they stated that DFP method appeared to exhibit a more dilative character or stable samples, whilst WD method appeared to induce a more contractive response or unstable samples. Moreover, it can be observed from Figure 15 that the slope of the instability lines (η) decreases with the increase in fines content for dry funnel pluviated samples and the inverse tendency was observed in the case of wet deposited samples.

Figure 15

For the purpose of analysing the effects of the presence of the low plastic fines fraction and depositional methods (DFP and WD) on the instability friction angle (ϕ’_ins) of normally consolidated and overconsolidated sand–silt mixture samples (OCR = 1 and 2) reconstituted with an initial relative density D_r = 52%, Figure 16 reproduces the test results obtained from the current study. It is clear from the plots that the instability friction angle decreases linearly with the increase in the fines content (0% ≤ F_c ≤ 40%) in the case of the dry funnel deposited samples. However, the inverse tendency was observed in the case of wet deposited samples. The observed instability friction angle trend is a result of the fact that the low plastic fines in combination with DFP and WD sample preparation techniques induce contractive and dilative character to the sand–silt mixture, respectively. The influence of the OCR on the ϕ’_ins is clearly observed for both depositional methods (DFP and WD). Moreover, it is clearly observed that the instability friction angle increases with the increase in the OCR for a given fines content. The following expressions are suggested to express instability friction angle (ϕ’_ins) in terms of fines content (F_c) for the range of the OCR under study by considering the two methods (DFP and WD):

Figure 16

ϕ<!-- ? -->ins′=b⋆<!-- ? -->(Fc)+a$$\begin{array}{} \displaystyle \rm \phi'_{ins}=b^{\star}(F_{c})+a \end{array}$$(2)

Table 4 illustrates the coefficients a and b and the corresponding coefficient of determination (R²) for the selected material under consideration.

Table 4

Coefficients a, b and R² for equation (2).

Figure 17 shows the variation of the DFP instability friction angle (ϕ’_{ins_DFP}) versus WD friction angle (ϕ’_{ins_WD}) of sand–silt mixture samples. It can be observed that the DFP instability friction angle decreases linearly with the increase in WD friction angle. For selected OCRs, the ϕ’_{ins_DEP} correlates very well (R² = 0.76 for OCR = 1 and R² = 0.95 for OCR = 2) with the ϕ’_{ins_WD} within the range of fines content (0% ≤ F_c ≤ 40%) under consideration. The instability friction angles of both DFP and WD increase with the increase in OCR (1 and 2). The following expression is suggested to correlate the DFP instability friction angle (ϕ’_{ins_DFP}) as a function of the WD friction angle (ϕ’_{ins_WD}) for the range of the OCR (1 ≤ OCR ≤ 2) under study:

Figure 17

ϕ<!-- ? -->ins−<!-- - -->DEP′=b⋆<!-- ? -->(ϕ<!-- ? -->ins−<!-- - -->WD′)+a$$\begin{array}{} \displaystyle \rm \phi'_{ins-DEP}=b^{\star}(\phi'_{ins-WD})+a \end{array}$$(3)

Table 5 illustrates the coefficients a and b and the corresponding coefficient of determination (R²) for the selected material under consideration.

Table 5

Coefficients a, b and R² for equation (3).

Figure 18 shows the variation of the overconsolidated instability friction angle (ϕ’_{ins_OC}) versus the normally consolidated instability friction angle (ϕ’_{ins_NC}) of Chlef sand–silt mixtures for both sample preparation techniques under consideration (DFP and WD). The samples were reconstituted with an initial relative density D_r = 52%. It can be noted from Figure 18 that the overconsolidated dry funnel pluviated sample’s instability friction angle increases linearly with the increase in the normally consolidated dry funnel pluviated sample’s instability friction angle for the range of fines content tested. However, the reverse trend was observed in the case of wet deposited sand–silt mixture samples. The WD sample reconstitution technique appears to produce important variation in the instability friction angle for the different tested OCR (1 and 2) and range of fines content (F_c = 0%, 20% and 40%) in comparison to the dry pluviation sample reconstitution technique. The following equation is suggested to express the overconsolidated instability friction angle (ϕ’_{ins_OC}) as a function of the normally consolidated instability friction angle (ϕ’_{ins_NC}) for both sample preparation techniques (DFP and WD):

Figure 18

ϕ<!-- ? -->ins−<!-- - -->OC=b⋆<!-- ? -->(ϕ<!-- ? -->ins−<!-- - -->NC′)+a$$\begin{array}{} \displaystyle \rm \phi_{ins-OC}=b^\star(\phi'_{ins-NC})+a \end{array}$$(4)

Table 6 illustrates the coefficients a and b and the corresponding coefficient of determination (R²) for the selected material under consideration.

Table 6

Coefficients a, b and R² for equation (4).

Figure 19 illustrates the evolution of the instability friction angle of the sand–silt mixtures with the instability friction angle of the clean sand for the two samples preparation techniques (DFP and WD) under consideration. It is observed from the plot that the instability friction angle of the sand–silt mixture increases with the increase in the instability friction angle of the clean sand for the two fines contens (F_c = 0% and 40%) and the range of OCR (1 and 2), considering the two sample depositional techniques under study (DFP and WD). The dry funnel pluviated and wet deposited samples are clearly affected by the presence of low plastic fines. However, the slope of DFP instabiliy friction angle of sand–silt mixtures versus DFP instability friction angle of clean sand is higher than that of WD instabiliy friction angle of sand–silt mixtures versus WD instability friction angle of clean sand.

Figure 19

Data from the present study (Figures 7–14) are reproduced in Figure 20 for the purpose of analysing the effects of the OCR (1, 2, 4 and 8), low plastic silty fines content (F_c = 0%, 20% and 40%) and sample fabric (DFP and WD) on the instability shear strength (q_ins) of sand–silt mixtures. The samples were subjected to three confining pressures (P’_c = 100, 200 and 300 kPa). It is observed from the plot that the instability shear strength (q_ins) generally decreases linearly with the increase in the fines content (0% ≤ F_c ≤ 40%) for the range of the OCR (1 and 2) and confining pressure under consideration in the case of the DFP. However, the reverse trend was observed in the case of WD. The observed instability shear strength tendency results is due to the fact that the low plastic fines in combination with DFP and WD induce contractive and dilative character to the sand–silt mixture, respectively. The influence of the OCR on the instability shear strength (q_ins) is clearly observed for the overconsolidated samples reconstituted by both depositional methods and fines content. Moreover, it can be observed that the instability shear strength increases with the increase in the OCR for a given fines content for both methods (DFP and WD) and all the confining pressures under study. The observed trend results from the role of the overconsolidation to increase the particle interlocking because of the existence of smaller silt particles between larger sand particles and the dilation phase of the sand–silt mixtures, leading to a more stable structure of the samples. It also shows that instability shear strength increases with the increase in confining pressure. The following equation is proposed to express the instability shear strength (q_ins) as a function of the fines content (F_c):

Figure 20

qins=b⋆<!-- ? -->(Fc)+a$$\begin{array}{} \displaystyle \rm q_{ins}=b^\star(F_{c})+a \end{array}$$(5)

Table 7 illustrates the coefficients a and b and the corresponding coefficient of determination (R²) for the selected material under consideration.

Table 7

Coefficients a, b and R² for equation (5).

Figure 21 presents the variation of the instability shear strength (q_ins) as a function of the instability friction angle (ϕ’_ins) of normally consolidated and overconsolidated sand–silt mixtures reconstituted with DFP and WD at different fines content (F_c = 0%, 20% and 40%) and subjected to three confining pressures (P’_c =100, 200 and 300 kPa). It is clear from Figure 21 that the instability shear strength (q_ins) increases as the instability friction angle increases (ϕ’_ins) for both dry funnel pluviated and wet deposited samples and the range of confining pressures under study. This increase becomes very pronounced for samples reconstituted by DFP compared to samples reconstituted by WD. Moreover, it is observed that the instability shear strength and instability friction angle friction angle decrease with the increase in fines content (F_c = 0%, 20% and 40%) in the case of the dry funnel pluviated samples and the inverse tendency was observed for the wet deposited samples. The slope of DFP instability shear strength (q_ins = f(ϕ’_ins)) is higher than the slope of the WD instability shear strength. The following equation is proposed to express the instability shear strength (q_ins) as a function of the instability friction angle (ϕ’_ins):

Figure 21

qins=b⋆<!-- ? -->(ϕ<!-- ? -->ins′)+a$$\begin{array}{} \displaystyle \rm q_{ins}=b^\star(\phi'_{ins})+a \end{array}$$(6)

Table 8 illustrates the coefficients a and b and the corresponding coefficient of determination (R²) for the selected material under consideration

Table 8

Coefficients a, b and R² for equation (6).

For the purpose of analysing the effect of the presence of the low plastic fines fraction and depositional method (DFP and WD) on the mobilised friction angle at instability lines (ϕ_s), Figure 22 reproduces the test results obtained from the current study. It is clear from the results that the mobilised friction angle at instability line (ϕ_s) decreases linearly with the increase in the fines content in the case of the dry funnel deposited samples. However, the reverse tendency was observed in the case of wet deposited samples. The observed mobilised friction angle trend results from the fact that the low plastic fines in combination with DFP and WD induce contractive and dilative character to the sand–silt mixture soil, respectively. The effect of the depositional methods (DFP and WD) on the mobilised friction angle at instability line (ϕ_s) is clearly observed for both OCR values (1 and 2) and that the mobilised friction angle increases with the increase in the OCR for a given fines content. The following expression is suggested to express the mobilised friction angle (sin ϕ_s) = 6^*η / (3+η)) in terms of fines content (F_c) for the range of the OCR under study, considering the two sample preparation techniques (DFP and WD):

Figure 22

ϕ<!-- ? -->s=b⋆<!-- ? -->(Fc)+a$$\begin{array}{} \displaystyle \rm \phi_{s}=b^\star(F_{c})+a \end{array}$$(7)

Table 9 illustrates the coefficients a and b and the corresponding coefficient of determination (R²) for the selected material under consideration.

Table 9

Coefficients a, b and R² for equation (7).

Figure 23 shows the relationship between the mobilised friction angle at instability lines (ϕ_s) and instability friction angle (ϕ’_ins) of the different dry funnel pluviated and wet deposited samples reconstituted at an initial relative density D_r = 52%, considering at once all the initial applied parameters under study (sample reconstitution, fines content, overconsolidation ratio and confining pressure). As it can be observed from Figure 23, the mobilised friction angle increases linearly with the increase in the instability friction angle and a good linear relationship (R² = 0.99) may represent their variation, confirming that both angles (mobilised friction angle or instability friction angle) are suitable for the mechanical response characterisation of sand–silt mixtures. The following equation is proposed to express the mobilised friction angle (ϕ_s) as a function of the instability friction angle (ϕ’_ins):

Figure 23

ϕ<!-- ? -->s=b⋆<!-- ? -->(ϕ<!-- ? -->ins′)+a$$\begin{array}{} \displaystyle \rm \phi_{s}=b^\star(\phi'_{ins})+a \end{array}$$(8)

Figure 24 illustrates the instability friction angle versus the initial global void ratio at different fines content of normally consolidated and overconsolidated sand–silt mixtures prepared using DFP and WD. It is clear from Figure 24 that the dry pluviation instability friction angle decreases as the initial global void ratio decreases and fines content increases for up to 20%. Beyond 20% of fines content, the dry pluviation instability friction angle continues to decrease with the increase in the global void ratio and fines content for both OCR values (1 and 2. The tendency inverse was generally observed for WD instability friction angle variation. The global void ratio appears to be a parameter not as pertinent in sand–fines mixtures as in clean sands for characterising the mechanical response because of the fact that the decrease in the global void ratio and increase in the fines content induce a decrement in the undrained shear strength and instability friction angle.

Figure 24

Data from the present study (Figures 7–14) are reproduced in Figure 25 for the purpose of analysing the effects of the intergranular void ratio and silty fines content on the instability friction angles of the dry funnel pluviated and wet deposited sand–silt mixture samples, considering the OCR parameter. It is observed from Figure 25 that instability friction angle decreases with the increase in the intergranular void ratio and fines content from 0% to 40 % for the both OCR values (1 and 2. However, the DFP instability friction angle variation with the intergranular void ratio is very significant for the range of fines content (F_c = 0–20%). The tendency inverse was observed in the case of the wet deposited samples, where the instability friction angle increases with the increase in intergranular void ratio of silty sand (Figure 25).

Figure 25

This article presents an experimental study including a series of saturated untrained monotonic triaxial tests to express the impact of depositional methods (DFP and WD), confining pressure, low plastic fines (F_c=0%, 20% and 40%) and OCR (1 and 2 on the instability shear strength behaviour of Chlef sand–silt reconstituted at a medium initial relative density of D_r = 52% and subjected to three confining pressures (P’_c =100, 200 and 300 kPa). The following conclusions can be drawn:

–

Undrained monotonic triaxial compression tests performed on reconstituted sand–silt mixture samples using two depositional methods (DFP and WD) showed that the low plastic fines, confining pressure and OCR control in a significant manner the instability friction angle and undrained instability shear strength of sand–silt mixture samples.