Post-Cyclic Drained Shear Behaviour of Fujian Sand under Various Loading Conditions

Abstract

In offshore engineering, the sand beneath an embankment may be subjected to traffic loads, resulting in a series of engineering issues. The behaviour of the sand beneath the embankment may change under a long-term traffic load. A series of drained cyclic and post-cyclic monotonic triaxial tests were performed on Fujian sand with different relative densities. The drained strength and stress–dilatancy behaviours were studied. The results indicated that the normalised peak strength ratio after cyclic loading was greater than that without cyclic loading, depending on the cyclic stress amplitude, while the critical state strength seemed to be only slightly affected by the cyclic loading history. The dilative response of sand could also be influenced by cyclic loading-induced fabric. Under constant relative density conditions, the higher the cyclic stress amplitude applied to the sand sample, the larger the volume strain produced in the critical state. Furthermore, cyclic-induced fabric could be destroyed after 6% axial strain.

1. Introduction

Coastal reclamation projects frequently employ sand. The soil beneath an embankment can be subjected to traffic loads that can modify the soil fabric and the mechanical properties of the foundation soil [1,2,3,4,5]. The safety and serviceability of geotechnical structures can be impacted by the effects of cyclic loading and the mechanical properties of the foundation soil will be changed. Hence, it is critical to investigate the post-cyclic mechanical behaviours of subgrade sand.

Several studies have been conducted to investigate the post-cyclic behaviour of soil under undrained conditions [3,6,7,8,9,10,11,12]. Yasuhara [6] reported that the undrained strength and stiffness of low plasticity silt are degraded after undrained cyclic loading conditions. Kaya [3] discoveredwhether the post-cyclic strength of fine-grained soils decreased depending on the deformation levels during cyclic loading. Dai [7] performed a series of undrained post-cyclic monotonic shear tests on anisotropically consolidated soft marine clay and proposed an empirical prediction model of the post-cyclic anisotropic strength based on the definition of equivalent overconsolidation. Hyde [8] found that normally consolidated and lightly overconsolidated samples showed a reduction in strength after cyclic loading. Andersen [9] claimed that the dissipation of pore pressures leads tothe strength and deformation modulus to be higher than the initial ones before cyclic loading. Castro [10] tested undisturbed samples of three soils and discovered that ultimate undrained shear strength depended on the void ratio, irrespective of previous cyclic loading.

Considering the low permeability of soft clay, the long period of traffic loads, and the complexity of the permeation path in the subgrade soil, many studies have been performed to evaluate the dissipation of excess pore water pressure in specimens [1,4,13,14,15]. Wang [4] carried out undrained cyclic triaxial tests on Mississippi River Valley Silt under different initial consolidation conditions. The authors found that tested samples fully consolidated after cyclic loading had a higher post-cyclic undrained monotonic shear strength because tested samples became denser due to reconsolidation. Jhabc [1] performed variable confining pressure triaxial tests on lateritic clay under partially drained conditions. The cyclic loading-induced pore water pressure was allowed to dissipate in order to reach various reconsolidation degrees. The results indicated that the ratio of undrained strength with and without reconsolidation linearly increased with the reconsolidation degree. Wang [14] reported that the critical state line of reconstituted marine silty clay subjected to cyclic loading in the e-log p plane was not consistent with that of the specimens in directly static shear test, depending on cyclic stress amplitude and irrespective of the reconsolidation process. Wang [13] conducted cyclic triaxial tests on undisturbed marine silty clay and found a similar effect of cyclic loading on the critical state line of tested samples in the e-log p plane.

Due to their high permeability, sand embankments can be under full drainage conditions during traffic loads. Several studies have investigated sand’s cyclic behaviour under drained conditions [16,17,18,19,20,21]. The effect of the cyclic stress ratio on accumulated strain was investigated by Sun [16] and Cai [17]. The authors discovered that higher cyclic stress ratios lead to larger cumulative axial strains. Thakur [18] and Xu [19] analysed the influence of effective confining pressure on strain accumulation and found that increasing confining pressure reduced strain accumulation with a constant cyclic stress ratio. Liu [20] studied the effect of unloading on the drained cyclic behaviour of Sydney sand. The result implied that unloading leads to the enlargement of axial strain. However, in these studies, the drained monotonic behaviours of sand after drained cyclic loading have not been examined. There is a paucity of literature on static mechanical characteristics after traffic loads under full drainage conditions.

This paper reports the results of a series of drained cyclic and drained post-cyclic triaxial tests conducted on Fujian sand with various relative densities. The effects of the cyclic stress amplitude on the strength and dilatancy of the sand sample after cyclic loading are presented and discussed.

2. Experimental Apparatus and Procedures

2.1. Experimental Apparatus and Material

The tests were conducted at GuangXi University by cyclic triaxial equipment, which was manufactured by GDS Instruments Ltd., Hooke, UK. All tested samples were performed on Fujian sand. The specific gravity was 2.64. The maximum and minimum void ratios were 0.71 and 0.32, respectively. The grain size distribution curve of the sand is shown in Figure 1.

The specimens were prepared using the air pluviation method. The sand was slowly poured into a split mould and flushed with carbon dioxide and de-aired water. More detail about the adopted method can be found in the work of Liu [20]. In all the tests, a Skempton B-value of at least 0.96 was achieved.

2.2. Test Procedure

As illustrated in Figure 2, the samples were firstly isotopically consolidated at an effective confining pressure of 50 kPa. Thereafter, the specimens were anisotropically consolidated by increasing the deviatoric stress to 50 kPa and keeping confining pressure constant, resulting in a K (the ratio of horizontal effective stress to vertical effective stress) value of 0.5. After the completion of K consolidation, tests were performed on two series of specimens with different relative densities (D_r), moderately dense (0.49–0.56) and dense (0.73–0.81), in which D_r was calculated as follows:

$$D_r=\frac{e_{\max }-e}{e_{\max }-e_{\min }}$$

(1)

where e is the void ratio after anisotropic consolidation, and e_max and e_min are the maximum and minimum void ratios of Fujian sand, respectively.

Table 1. Programme of drained monotonic and cyclic test.

Test Series	Test ID	Relative Density Dr (%)	qd (kPa)	B Value	Density (g/cm3)
1	S54.67-0	54.67	0	0.963	17.64
	S55.93-0	55.93	0	0.974	17.70
	S65.32-0	65.32	0	0.982	18.14
	S74.33-0	74.33	0	0.970	18.59
	S78.35-0	78.35	0	0.965	18.80
	S80.10-0	80.10	0	0.968	18.89
2	DS53.43-20	53.43	20	0.972	17.58
	DS54.70-30	54.70	30	0.978	17.64
	DS52.15-30	52.15	30	0.982	17.52
	DS49.67-40	49.67	40	0.967	17.41
	DS55.60-40	55.60	40	0.984	17.68
	DS52.63-50	52.63	50	0.963	17.54
	DS73.27-40	73.27	40	0.965	18.54
	DS77.70-50	77.70	50	0.974	18.76
	DS78.44-60	78.44	60	0.969	18.80
	DS79.19-60	79.19	60	0.981	18.84
	DS78.07-70	78.07	70	0.970	18.78
	DS75.17-70	75.17	70	0.972	18.63
	DS74.72-80	74.72	80	0.978	18.61

Note: S represents the samples that were directly sheared without cyclic loading, DS represents the samples that were sheared after cyclic loading, and D_r represents the relative density of tested samples after consolidation.

summarises the programme of the drained monotonic and cyclic tests. The samples were named with the test series, relative density, and cyclic stress amplitude q_d. For example, the sample in series 2 with a relative density of 50.35% and a cyclic stress amplitude q_d of 20 kPa was named DS50.35-20. Sinusoidal cyclic loading under a frequency of 0.05 Hz was applied in the tests. The frequency was lower than the 0.1 Hz frequency recommended by Cai [17] to ensure that the samples were under drained conditions. After 500 loading cycles, the drained strain-controlled monotonic tests with a rate of 0.1%/min were conducted to study the post-cyclic behaviour of the Fujian sand. All tests ended at ε_a = 25%, as illustrated in Figure 2. In addition, test series 1 with a q_d of 0 representsthat the samples were monotonously sheared without cyclic loading.

3. Results and Discussion

3.1. Cyclic Behaviour of Fujian Sand

Figure 3 presents the axial and volume strain accumulation curves of moderately dense samples with different cyclic stress ratios. It can be seen that the axial strain accumulated rapidly in the first few cycles and then tended to be stable. At a relatively low cyclic stress amplitude, q_d = 20, 30, the permanent strain became almost stable after 400 cycles, whilst for a higher cyclic stress amplitude, q_d = 30, 40, the strain still tended to increase. Similar results have been observed by Qian [22,23] on ShangHai silty clay and Cai [17] on NanJing sand. Figure 3b shows the unapparent relationship between the accumulated volume strain and the cyclic stress amplitude. For example, after 500 loading cycles, the accumulated volume strain of DS53.63-50 became about 0.137%, which falls in the range of 0.099–0.310% of accumulated volume strain measured in DS54.70-30 and DS52.75-40. This can be attributed to the strain flow direction and is discussed in detail below.

Figure 4 shows the relationship between the accumulated deviatoric strain ε_q and the accumulated volume strain ε_v, where ε_q was calculated using:

$${\epsilon }_q=\frac{2}{3}\left({\epsilon }_1-{\epsilon }_3\right)$$

(2)

in which

$${\epsilon }_3=\frac{1}{2}\left({\epsilon }_v-{\epsilon }_1\right)$$

(3)

where ε₁, ε₃, and ε_v correspond to accumulated axial, lateral, and volume strain, respectively.

It can be seen in Figure 4 that with the increase in cyclic stress amplitude q_d, the slopes of the curves in the figure become larger, indicating that deviatoric strain became predominant with respect to volume strain. This is because increasing the cyclic stress amplitude q_d leads to the stress state moving towards the critical state line in the p-q plane. This finding agrees with those of Wichtmann [24,25] and Liu [20]. At the relative low cyclic stress amplitude q_d = 20, 30, although the slopes of the curves in Figure 4 are lower than that of q_d = 40, their accumulated volume strain was lower than that of sample DS49.67-40 due to the lower accumulated deviatoric strain. For the high cyclic stress amplitude q_d = 50, because the deviatoric strain became predominant with respect to volume strain, the sample accumulated a lower volume strain than sample DS49.67-40. This is the reason why there was no significant correlation between the deviatoric stress amplitude and the accumulated volume strain, as shown in Figure 3b.

3.2. Post-Cyclic Strength Characteristics of Fujian Sand

Figure 5 shows the trend of stress–strain curves for moderately dense and dense samples after cyclic loading with different cyclic stress amplitudes. The measured stress–strain curves of S52.67-0 and S80.10-0 are plotted in Figure 5a and 5b, respectively, to better compare the samples not subjected to cyclic loading. As can be seen, the deviatoric stress increased rapidly in the early stage of the shearing process and then reached peak stress. As the shearing process continued, the deviatoric stress began to decline, and the samples reached a critical state at ε_a = 25%. Figure 5a shows that the peak and critical state strength of moderately dense sand after cyclic loading were almost identical to those without cyclic loading. Obviously, for the dense sand specimens (Figure 5b), the peak strength after cyclic loading was still larger than that without cyclic loading, and their critical state strengths were roughly equal.

Figure 6 indicates the peak strength $S_{u0}^p$ and critical state strength $S_{u0}^c$ derived from all drained monotonic tests with cyclic loading. The linear growth in $S_{u0}^p$ and $S_{u0}^c$ with increasing relative density can be described by:

$$S_{u0}^p=2.1085\times D_r+23.506$$

(4)

$$S_{u0}^c=0.7762\times D_r+74.649$$

(5)

The values of $S_{u0}^p$ were considerably higher than those of $S_{u0}^c$ and exhibited a significant density dependence. The reason why the values of $S_{u0}^c$ also showed a slight density dependence is that the critical state was not fully reached at ε_a = 25% (the deviatoric stress in Figure 5 declines constantly at this value).

In order to eliminate the influence of different relative densities and cyclic stress amplitudes, as shown in Figure 7, the peak strength $S_u^p$ and the critical state $S_u^c$ derived from all drained monotonic tests after cyclic loading were normalised by $S_{u0}^p$ and $S_{u0}^c$, respectively. For the figure, Equations (4) and (5) were used to calculate $S_{u0}^p$ and $S_{u0}^c$, and D_r in the two equations corresponds to relative density after drained cyclic loading. The cyclic stress amplitude dependence of the normalised peak strength ratio is inspected in Figure 7. It can be seen that increasing the cyclic stress amplitude led to an increase in the normalised peak stress ratio. However, for the normalised critical state strength ratio, Figure 6 shows similar values ranging from 0.95 to 1.05, irrespective of the cyclic stress amplitude. This phenomenon implies that drained cyclic loading strengthens the fabric of the sand and results in variation in the normalised peak strength ratio. It can be observed that the larger the cyclic stress amplitude, the more substantial the adjustment in the microstructure and the greater the normalised peak strength ratio. Large deformation can destroy the fabric induced by cyclic loading; thus, the normalised critical state strength ratio values are almost 1.

3.3. Post-Cyclic Stress–Dilatancy Response of Fujian Sand

The diagrams in Figure 8 demonstrate the effect of the cyclic deviatoric stress amplitude on the volume strain–axial strain relationship. All curves that belong to the samples that experienced cyclic loading were located below those without cyclic loading, implying an improvement in stress–dilatancy. The relative density did not change considerably during drained cyclic loading, as shown in

Table 2. Results of drained cyclic and monotonic shear test.

Test ID	εa at 500th Cycles (%)	εv at 500th Cycles (%)	Dr after Cyclic Loading (%)	Peak Strength (kPa)	Critical State Strength (kPa)	φp (°)	φc (°)
S54.67-0	-	-	-	139.95	115.39	35.7	32.4
S55.93-0	-	-	-	142.56	120.87	36.0	33.2
S65.32-0	-	-	-	155.81	123.34	37.5	33.5
S74.33-0	-	-	-	184.45	128.36	40.4	34.2
S78.35-0	-	-	-	188.01	130.04	40.8	34.4
S80.10-0	-	-	-	192.00	139.74	41.1	35.7
DS53.43-20	0.332	0.060	53.86	137.60	119.47	35.4	33.0
DS54.70-30	0.545	0.099	55.34	138.88	110.19	35.5	31.6
DS52.15-30	0.989	0.343	53.37	138.84	118.88	35.4	32.9
DS49.67-40	1.864	0.310	50.78	142.67	113.51	36.0	32.1
DS55.60-40	1.029	0.214	56.37	146.93	122.35	36.6	33.4
DS52.63-50	2.371	0.137	54.10	143.82	114.46	36.1	32.3
DS73.27-40	0.129	−0.009	73.25	190.03	129.77	40.9	34.4
DS77.70-50	0.188	−0.005	77.68	205.02	132.19	42.2	34.7
DS78.44-60	0.295	−0.007	78.42	205.93	135.59	42.3	35.1
DS79.19-60	0.381	−0.032	79.09	204.12	134.78	42.2	35.0
DS78.07-70	0.536	−0.040	77.94	211.91	136.04	42.8	35.2
DS75.17-70	0.703	−0.116	74.78	199.04	128.85	41.7	34.3
DS74.72-80	1.084	−0.131	74.28	209.52	139.80	42.6	35.7

, but it affected the stress–dilatancy response significantly. This can be attributed to the fact that cyclic loading can change the texture of particles, resulting in an improvement in the sand samples’ fabric. However, the volume–axial strain curves in Figure 8 do not clearly correlate with the deviatoric stress amplitude. The critical state volume strain of sample DS54.30-40 subjected to a 40 kPa cyclic stress amplitude was -2.52%, which was close to that of DS50.35-20 (−2.47%) and smaller than that of DS54.70-30 of (−3.10%). The reason for this phenomenon can be attributed to the variation in the samples’ relative densities.

As the increase in the dilatancy response with an increasing density of samples is well-known [26], the relative density has significant effects on stress–dilatancy. In order to separate the effects of cyclic deviatoric stress amplitude and relative density, the volume strain at ε_a = 25% was plotted versus relative density. The cyclic stress amplitude dependence of the stress–dilatancy can be better judged on the basis of Figure 9. Considering a constant value of relative density, the increase in the cyclic stress amplitude raised the value of the volume strain at ε_a = 25%. The microstructure of specimens with larger cyclic stress amplitudes was adjusted more severely, resulting in a greater change in fabric and hence a greater response to stress–dilatancy.

Wang [13,14] reported that the critical state line of marine silty clay subjected to cyclic loading in the e-log p plane was inconsistent with that of the specimens subjected to static shear test directly, depending on the cyclic stress amplitude. On the other hand, samples subjected to undrained monotonic shear tests generate excess pore water pressure, resulting in the relaxation of average principal stress. The generation of excess pore pressure essentially reflects the plastic volume strain. The movement of the critical state line in the p-q plane is essentially the change in the plastic volume strain in the monotonic test. The volume strain under the drained monotonic test can be measured and calculated directly. As a result, the findings in Figure 9 agree with those of Wang [13,14].

Figure 10 shows the calculated curves of the ε_v/ε_q versus stress ratio. It can be seen that the stress ratio increased to the peak value at first, indicating that the samples reached the peak strength and then began to decrease slowly, suggesting that the samples approached a critical state. The data in Figure 10 demonstrate that the samples cut out after cyclic loads showed a more dilative response than those without cyclic loading. For example, the black curve in Figure 10a is mainly above the other curves, showing less volume strain in the sample without cyclic loading than in the sample after cyclic loading. It is worth noting that for all samples subjected to cyclic loading in Figure 10, once the axial strain reached 6%, the ε_v/ε_q values became almost coincident, implying that the cyclic loading-induced fabric would be destroyed around 6% axial strain, regardless of the cyclic stress amplitude and relative density. This is also the reason why the deviatoric stress–strain relationship curves show a similar trend beyond 6% axial strain in Figure 5.

4. Conclusions

The paper shows the results of a series of drained cyclic triaxial tests that were carried out on Fujian sand. The study was undertaken to investigate the post-cyclic monotonic drained shear behaviour of Fujian sand. On the basis of the aforementioned statements, the following conclusions can be drawn:

• Drained cyclic loading impacts the fabric of the sand sample, even if the relative density is hardly affected. The fabric induced by cyclic loading can improve the normalised peak strength ratio, depending on the cyclic stress amplitude. The critical state strength was almost consistent with that without cyclic loading because its fabric was destroyed due to the large deformation.
• Cyclic loading-induced fabric significantly affects the stress–dilatancy of sand samples on the basis of the cyclic stress amplitude. The greater the cyclic stress amplitude on the sand sample, the larger the volume strain produced at the critical state under the same relative density conditions.
• Stress–dilatancy enhanced by fabric is destructed with 6% axial strain. Changes in the stress–strain relationship and stress–dilatancy were observed before the axial strain reached 6%. Once such a strain threshold was approached, the effects of cyclic loading on the stress–strain and the dilative response of the sand specimens rapidly disappeared, regardless of cyclic stress amplitude and relative density.