Experimental Study on Horizontal Resistance Parameter of Gravelly Soil Considering Slope Gradient Factor

Abstract

Horizontal resistance can be significantly different for gravelly soil slope sites with different gradients. The impact of slope gradient on the horizontal resistance of soil based on a three-dimensional physical simulation test has been investigated, and the displacement of the pile top and soil pressure for four piles under various gradients (slope gradient 0–45°) was analyzed. The research reveals that ① The soil resistance exhibits a linear increase stage, non-linear steep increase stage, and gradually stabilizing stage with the increase in load. ② The ultimate soil resistance is significantly affected by depth and displacement, and hyperbolic variation characteristics related to the displacement stage. It has a slope weakening effect, and the steeper the slope gradient, the lower the ultimate soil resistance of the pile sides, which effect is negligible when the depth exceeds 0.6–0.7 times that of the pile buried depth. ③ Based on the characteristics of horizontal ultimate resistance-displacement-depth variation in soil, a gradient factor, which is only related to the slope gradient, was used to describe the impact of gradient on the soil resistance modulus (k_ini) and ultimate resistance (p_u). k_ini is reduced close to the ground surface and gradually increases with depth until it becomes equal to the value of level ground. The ratio between p_u in slope ground and level ground was determined for slope angles. The above horizontal resistance parameters were expressed as a function based on the test data to calculate the lateral ultimate bearing capacity of gravelly soil considering the slope gradient factor. The research results developed the theory of foundation design for building structures, promoting the reliability evaluation of pile soil systems towards a more scientific and rigorous direction.

1. Introduction

When pile foundations are in slope terrain grounds, the pile–soil interaction caused by pile deformation can generate soil horizontal resistance. If the soil resistance is too small to prevent slope deformation, the slope can be unstable and destroyed. The effect of the slope gradient on the horizontal resistance and the safety and stability of the structure is important in the design of foundations.

Coulomb’s soil pressure theory considers the oblique state soil surfaces [1]. The passive soil pressure is determined through an equilibrium condition. However, if the form of the assumed slip surface is not consistent with the actual situation, the degree of this discrepancy is proportional to the internal friction angle [2,3]. The distribution mode of soil resistance in the front of the pile is commonly based on elastic theory, combined with relevant data from modeling tests and actual measured results of pile tests [4]. The calculations are based on stressing deformation characteristics and soil types [5]. For the construction of structural foundations (piles) located on steep slopes, geographic and geomorphic conditions are major impact factors which affect the distribution of soil resistance [6,7,8,9]. An empirical reduction coefficient for the resistance of compacted sand soil with various gradients has been developed using model experiments and 3-D simulation [10,11]. Current standards in China estimate the horizontal resistance of soil using an m value [12,13], and the m value is unsuitable for similar diameter piles. Therefore, it needs to be adapted to the level of the load and the allowable displacement. The relationship between the resistance coefficient of soil and the displacement of the pile top can be expressed using an empirical or semi-empirical method for calculating the m value [14,15,16]. By changing the dimensions of the pile and the strength of the soil around the pile, the relationship between the m value and the coefficient of soil compression and the displacement of the mud surface of the pile can be calculated. However, the existing distribution patterns or calculation methods for soil resistance are based on relatively homogeneous soil, cohesive soil, sand soil foundation, and a limited number of small-scale pile foundation field test results [17,18,19,20,21]. At present, research shows that the resistance distribution of similar soils varies greatly [22,23,24,25,26]. Therefore, when adopting any distribution pattern for soil resistance, the assumed conditions are consistent with the soil and the pile foundation of the slope site will be considered. Some investigators [27,28,29,30,31,32] have proposed parameters, with consideration of gradient correction, to calculate the resistance of slope soil; their accuracy depends on the values of relevant parameters, and it is still unknown whether they meet the actual distribution of soil resistance (which has not been tested in practice), especially for slope sites with non-semi-infinite spatial bodies. The failure mechanism of the pile in slope mainly depends upon the soil–structure interaction, which varies between the pile in slope and horizontal ground, so the magnitude of horizontal resistance varies significantly with the slope gradient. As most of the literature discusses the behavior of the soil–structure interaction of pile in slope ground, study towards the horizontal resistance parameter of gravelly soil considering slope gradient factor is not discussed elaborately.

This paper presents results from a three-dimensional physical simulation test in the laboratory, and the impact of slope gradient on the distribution of the horizontal resistance of soil was evaluated. Four types of gravel soil slopes, with different gradients, were designed. The distribution characteristics of soil horizontal resistance and pile–soil deformation were studied. The impact of soil horizontal resistance with depth, displacement, and slope on the characterization parameters of soil horizontal resistance under different slope gradients was discussed. The flow chart introduces the research logic, as shown in Figure 1.

2. Similarity Ratio of Test Model

Manual excavation of the pile foundation is usually used for construction in southwest China if the foundation has a relatively thick soil cover (thickness than 3 m). This is especially appropriate for construction in steep slope situations within mountainous areas. More than 90% of the transmission tower foundations in the southwest mountainous area have used constructed piles. The tower is in an area of steep topography with a slope gradient >30°, and the length of the pile foundation section ranges from 0.8 to 1.2 m. The total pile length ranges from 8 to 10 m and is dominated by square or circular piles.

The design of the model test pile considered the characteristics of the gravel soil slope sites in southwest China, and the laboratory test was conducted in the three-dimensional geological simulation laboratory of the State Key Laboratory of GeoHazard Prevention and GeoEnvironment Protection (SKLGP). The testing platform was 3 m × 2 m × 1.5 m (length × width × height). For the laboratory test model, the test similarity ratio was designed according to the size of the prototype pile and the size of the test tank. The prototype pile had a pile diameter of 1 m and a length of 10 m. The geometric similarity ratio of the model pile to the prototype pile in the test was determined to be 10 (similarity refers to the similarity in length, width, and height). Thus, the pile had a cross-section dimension of 0.1 m × 0.1 m, length of 1 m, and square cross-section, and the concrete was C30. Four slopes with 0°, 15°, 30°, and 45° gradients were considered, with one test pile for each slope gradient, as shown in Figure 2. To meet the need of boundary constraint conditions in the test, the laboratory model test was conducted so that the tank chosen had 8–12 times and 3–4 times the pile width in and to the direction of loading, to ensure it was free from the zone of influence [6]. Thus, the constructed model was 1.5 m long, 1.0 m wide, and 1.3 m high, and was free from edge effect. Figure 2 illustrates the plane and sections of the proposed model.

3. Modeling

3.1. Pile Model

The model pile specimen was constructed using Code GB50010 [33], and the cement mortar ratio was determined to be 1:1.76:0.32 for cement–sand–water. The pile foundation model was constructed using four 6 mm diameter steel bars as the main reinforcement and 2 mm diameter steel wire as a ring with a 10 cm spacing. The prepared model pile is shown in Figure 3.

3.2. Soil Model

The gravel soil was collected from the field and models were prepared indoors. The particle size distribution curve of the tested soil was obtained by measuring 2000 g to 5000 g of soil sample for the soil screening test [34,35], as seen in Figure 4. We took the average value of the natural grading of soil, and used the equivalent substitution method to replace soil particles with particle sizes exceeding 60 mm by 5–60 mm. For particles less than 5 mm, we mixed them according to the natural grading value to obtain the substitute grading for testing. According to the alternative grading, the laboratory’s existing crushed stone and cohesive soil were designed for proportioning. To achieve the best compaction state of the crushed stone containing soil, 2.7% water was added into the soil (as the optimal moisture content of the crushed stone containing soil used in this simulation experiment was measured to be 9%, while the moisture content of the soil was 6.3%), and stirred to obtain a reshaped soil sample. Then, the soil sample was mixed evenly.

The test soil was constructed in layers, with each layer consisting of 20 cm of thick loose soil which was then compacted by a concrete block (0.2 m × 0.2 m × 0.2 m for length × width × height). After the completion of soil filling, the models were uniformly brushed to the required slope gradients. The physical and mechanical parameters of the soil were tested, and the results are presented in

Table 1. Physical mechanical parameters of gravel soil.

Soil Properties	Physical Mechanical Parameter		Test Curve
Gravel soil	γ (kg/m3)	22.7
	C (kPa)	7–10
	φ (°)	42
	Cu	13.8

.

3.3. Monitoring Elements

Two dial gauges were used to measure the displacement near the top of the model pile. Strain gauges were arranged at 15 cm intervals below the mud surface in the front and back of the pile, for a total of 12 strain gauges. The soil pressure box was arranged in the front of the pile with spacings of 15 cm, 10 cm, 10 cm, 15 cm and 15 cm downside from the 10 cm of the pile top (As seen in Figure 5). The depth was approximately the same as the depth of the strain gauges of the pile. Three pressure boxes were installed upward from the bottom of the pile at distances of 10 cm and 15 cm at the backside of the pile.

The loading device was the Jack of the high precision static servo hydraulic press. The frame of the loading system of 3D geo-mechanical simulation test was used as the counterforce frame. A slow, load-maintaining method was used for loading. The loading increment of each load step was 0.3 kN. The loading was kept in static state for 5 min at each step of loading, and then the next load step was applied after the dial gauge meter reading stabilized. The test process was stopped when the displacement of the pile top exceeded 40 mm. Test loading model can be seen in Figure 6.

4. Data Analysis

4.1. Horizontal–Displacement Relationships of Pile–Soil Interaction

The displacement–loading curves of the test model are shown in Figure 7. The pile–soil deformation stage can be further divided into the three stages:

• Linear deformation stage. At this stage, the top displacement under each step of loading was relatively small. With increased loading, the displacement of the pile top increased in an approximately linear law. When the loading increased in increments of 0.3–0.5 kN, the pile top displacement increased by around 0.2–0.4 mm compared to the prior loading step.
• Non-linear deformation stage. The pile top load was between critical and ultimate loads. As loading increased by intervals of 0.3–0.5 kN, the displacement of pile top increased by around 0.5–10 mm compared to the prior loading step and the pile top loading exhibited non-linear variation in displacement.
• Accelerated deformation stage. The pile top loading enters the post-stage of ultimate loading. For identical loading increments, the displacement of the pipe top increases by approximately 2 cm compared to the prior loading step. At this time, the displacement, with loading, tends to increase.

As the load acting on the pile top increases, the pile–soil interaction will reflect a different displacement–horizontal load relationship, resulting in varying horizontal resistance in the soil at different stress–strain stages. The relationship between the horizontal load and pile head displacement divides the stress–strain stages of the pile soil system into three phases, as shown in Figure 8.

As shown in Figure 8:

(1)

Linear deformation stage: the displacement of the pile top under each level of load is relatively small. For every 0.3–0.5 kN increase in load, the displacement of the pile top increases by about 0.2–0.4 mm relative to the previous level of load. At this point, there are no obvious cracks in the soil around the pile.

(2)

non-linear deformation stage: the pile head load is between the critical and ultimate loads. For every increase of 0.3–0.5 kN in load, the pile top displacement increases by about 0.5–10 mm relative to the previous level of load. At this stage, there is an increase in the number and size of micro cracks in the soil around the pile.

(3)

Accelerated deformation stage: when the pile top load enters the ultimate load stage, under the same load increment conditions, the displacement of the pile top increases by about 2 cm relative to the previous level load, and the displacement shows an accelerating trend with the load. The cracks in the soil have undergone a qualitative change, and the soil behind the pile is separated from the pile. The crack develops rapidly and accelerates step by step with the load. The crack extends towards a certain angle in front of the pile, but it has not yet penetrated.

4.2. Soil Horizontal Resistance under Various Loading Grades

The relationship between soil resistance (p) and depth in different load–deformation stages for the pile–soil system is shown in Figure 9.

At the linear deformation stage (Figure 9a), with increased depth the soil resistance (p) exhibits a convex profile being smaller at the top and bottom, and maximum in the upper part. The soil resistance at the slope surface was relatively small expect for level grounds, and it gradually increases with depth. It reached a minimum value (about 0 kPa) at a depth of 0.6 m, and then gradually increased at the backside of the pile from a zero value to the pile bottom.

At the non-linear deformation stage (Figure 9b), the variation in soil resistance with depth was approximately similar to the linear deformation stage, but the soil resistance value was larger than that of the prior stage. The maximum soil resistance levels, with the soils of four slope gradients, were 100 kPa, 200 kPa, 300 kPa, and 400 kPa, respectively.

At the accelerated deformation stage (Figure 9c), the variation mode of soil resistance with depth had no obvious deformation, but the magnitude of soil resistance increase was not as apparent as in the prior stage. Comparison of Figure 9b,c shows that after the pile–soil enters non-linear deformation, and the maximum value of the soil resistance under various slope gradients did not increase with an increased load.

Comparing the three figures, we found that there is a difference between the maximum soil resistance and the effectiveness of the soil resistance that the soil can provide. After the non-linear stage, the soil resistance at a certain depth (approximately 0.2–0.5 m depth) close to slope surface did not increase further. Below the depth of 0.2–0.5 m, the soil resistance continues to increase until the accelerated deformation stage. There is a depth at which the soil resistance did not increase with increased displacement. The maximum soil pressure for 15°, 30°, and 45° slopes occurred in the range of 0.3, 0.4–0.5, and 0.4–0.5 m, respectively. This means that the soil resistance of various depth has a slope gradient-related effect.

5. Soil Horizontal Resistance Distribution Laws of Slope Soil

5.1. Soil Horizontal Resistance Parameters

The p-y curves of the pile depth were derived from the indoor test to analysis the soil horizontal resistance parameters.

Table 2. Soil resistance parameters in different depths of piles.

Depth	0°		15°		30°		45°		Soil Pressure–Displacement Curve
	kini	pu	kini	pu	kini	pu	kini	pu
0.15 m	9.5	40	4.8	30	2.99	20	1.66	8
0.25 m	17.7	146	12.4	103	5.75	45	4.32	25
0.4 m	26	200	19.7	150	7.56	100	6.61	30
0.5 m	34.3	254	27	197	9.37	155	8.9	35	For buried depth below 0.4 m, only the calculated results are listed in the table.
0.7 m	42.6	308	39	299	37	300	37	250

shows the variation curve of the soil pressure parameters with load at different depths (0.15 m, 0.25 m, and 0.45 m) in the front of the pile. k_ini is soil initial modulus and p_u is ultimate resistance of soil; their definitions can be found in the literature [17].

The pile displacement was proportional to the resistance of soil around the pile but tended to stabilize after reaching a certain value (Table 2). The resistance of soil on the side of the pile did not increase substantially with an increase in displacement. The p-y curve variation tendency exhibits the change characteristics of a hyperbolic curve. At the non-linear stage, the shallow soil reaches the ultimate resistance state first, and then with the further conversion of pile-soil stress and strain, the medium and the soil at greater depths gradually reach the maximum state of soil resistance.

Both the soil initial modulus k_ini and ultimate resistance of soil p_u increased with increased pile depth and decreased with increased slope gradient. Therefore, the steeper the slope gradient, the lower the ultimate soil resistance of the pile sides. A comparison of the values of the p-y curve at a depth of 2 m under various slope gradients showed that the ultimate soil resistance around the pile sides for a 30° slope was 15% less than that of 15° slope, and 30% less than that of a 45° slope. This impact decreased with the increase in soil depth, especially for soil depths exceeding 4 to 5 times the pile diameter, where the impact was minimal. The relationship between the pile displacement under various slope gradients and depth and soil resistance was similar.

5.2. Proposed Distribution Mode of Soil Resistance

The distribution and variation in horizontal resistance of soil can be caused by different pile–soil stress and strain stages. The distribution of soil resistance with depth was approximately the same. The distribution of soil resistance with depth in each pile–soil stress and strain stage is shown in Figure 10.

Figure 10 shows that the horizontal resistance of soil is smaller on the ground surface and increases with soil depth, and then decreased gradually after reaching the maximum depth (L₂) of resistance. It reached the minimum value at the resistance neutral point (L₁). The resistance of the soil body had a certain value behind the pile at the resistance neutral point, gradually increased with increased depth, and reached a maximum value at the bottom of the pile (L₃). Specifically:

(1)

PhasesⅠ: When the horizontal load is small (less than the critical load), the soil in front of the pile is in the linear deformation stage and the soil horizontal resistance (p_u1) of the pile side is smaller than the ultimate soil resistance along the pile (Figure 10b).

(2)

PhasesⅡ: When the load further increases and is greater than the critical load, but less than the ultimate load, the soil in the upper section above the neutral point of the pile enters a non-linear deformation stage while the lower part remains in the linear deformation stage (Figure 10c). At this time, the soil at the depth above the resistance neutral point of soil first reaches the ultimate resistance state (p_u2) and the depth gradually increases with increased load.

(3)

PhasesⅢ: The horizontal load is greater than the ultimate load (pu3). The soil above and below the resistance neutral point of soil gradually approaches the ultimate resistance state of soil (Figure 10d).

Figure 10e: with an increase in slope gradient, the location with the maximum value of soil pressure in the pile sides is shifted toward the pile bottom. Meanwhile, under the same loading condition, the maximum soil pressure in front of the pile decreased with increased slope. With a slope gradient increasing every 15°, the maximum variation value of pressure in front of the pile under identical load decreased by 33–40%, according Figure 9.

After a period of loading, the resistance of the soil at a certain depth near the slope will not continue to increase and it will reach the ultimate resistance of soil. Under that buried depth, the resistance of the soil continues to increase until the acceleration stage. The depth at which the resistance of the soil does not increase with the increase in displacement has a certain extension. This means that the soil resistance at various depths has a certain temporal effect. The shallow soil at the non-linear stage reaches the ultimate resistance state and then, with the further conversion of pile–soil stress and strain, the soil at medium and deep depths gradually enters a stable resistance state. For this reason, according to the soil depth, the variation laws of the resistance–displacement of soil were divided.

(1)

Because shallow (<2 m) soil is affected by the slope gradient and other conditions, the proportion of the resistance loss is large and the soil enters the accelerated deformation stage under the action of a small thrust.

(2)

The depth of soil can provide relatively large resistance to the deformation caused by thrust, and the resistance is relatively larger than that of shallow soil.

(3)

The transmission depth of thrust is limited. Although the soil at medium and shallow buried depth has entered a linear or non-linear deformation stage, the soil at that depth may still be in the range of linear deformation and may not reach its ultimate resistance state.

6. Discussion

6.1. Soil Initial Modulus k_ini

The initial foundation reaction modulus of soil is given by the slope of the initial straight line from the field experiment p-y curve (the ratio of the maximum soil resistance to the corresponding displacement). This test represents a static load test for slope pile foundation. If the k_ini is calculated only based on ground surface data, then the estimate of the internal deformation and rigidness of soil could be erroneous. The degree of the estimation error will increase with an increase in soil depth.

k_ini gradually increases with the increase in pile depth, and the depth z has a significant impact on the k_ini value. There is a relationship between the calculation of the initial modulus k_i0 for the horizontal site p-y curve of foundation soil and the strength parameters of the soil around the pile. For the experimental results from the model test, we calculated the initial modulus of the p-y curve foundation soil for the pile foundation with a pile length of 1 m and diameter of 0.1 under a slope gradient of 15°, 30°, and 45°, and we compared these results with those calculated and tested from horizontal sites. The results are compared in Figure 11. Figure 11 shows that the impact of the slope gradient θ on the initial modulus of foundation soil can be approximated by Equation (1). When the slope surface of the pile exceeds 0.6–0.7 times that of the pile buried depth, the slope gradient has little impact on the initial modulus k_ini of gravel soil p-y curve foundation soil and its value is similar to the results calculated and tested from the horizontal site. When the slope surface is within 0.7 times that of the pile buried depth, the ratio of k_iniθ/k_i0 exhibits an approximately linear decrease, and the degree of impact increases with the increase in the slope gradient. The relation of k_iniθ/k_i0 and slope gradient θ is represented by Equation (1).

$$\mathsf{\vartheta }={\displaystyle \frac{{\mathrm{k}}_{\mathrm{i}\mathrm{n}\mathrm{i}\mathsf{\theta }}}{{\mathrm{k}}_{\mathrm{i}\mathrm{n}\mathrm{i}}|\mathsf{\theta }=0°}}={\displaystyle \frac{z}{5\mathrm{b}}}\times (1+\cos \mathsf{\theta })\times {\displaystyle \frac{1}{1+\tan \mathsf{\theta }}}$$

(1)

where k_ini is soil initial modulus; k_iniθ is soil initial modulus for any slopes; z is pile diameter; θ is slope angle; $\mathsf{\vartheta }$ is the ratio between k_iniθ and k_i0.

6.2. Ultimate Resistance of Foundation Soil p_u

We compared the ultimate resistance of pile–soil under different slope gradients obtained from the test with the resistance of the underground pile–side soil in a horizontal site. The p_u of the pile side of slope θ on the pile-side soil resistance is shown in Figure 12.

Figure 12 shows that the ratio of p_uθ for each slope gradient to p_u under the horizontal site is approximately constant. This ratio seems unrelated to pile depth and only related to slope gradient. When the slope gradient was 0°, 15°, 30°, and 45°, the ratio was 1, 0.79, 0.63, and 0.5, respectively, and approximately the same as calculated using Equation (2).

$${\mathrm{N}}_{\mathrm{S}\mathrm{C}\mathrm{C}}={\displaystyle \frac{{\mathrm{p}}_{\mathrm{u}\mathsf{\theta }}}{{\mathrm{p}}_{\mathrm{u}}}}={\displaystyle \frac{1}{1+\tan \mathsf{\theta }}}$$

(2)

where p_uθ is ultimate resistance of soil for any slopes; p_u is ultimate resistance of soil for level ground; z is depth; θ is slope angle; h is the maximum valve range of soil resistance; N_scc is the ratio between p_uθ and p_u.

Figure 12 shows that the ratio of soil resistance under various slope gradients to that of horizontal sites is approximately 1 and the corresponding depth ranges from 3 m, 5 m, and 6 m for slope angles from 15°, 30°, and 45° respectively. Due to the impact of slope gradient in the front of the pile above that depth, the ability of pile side soil to resist the deformation of the pile body is weakened.

7. Conclusions

The variation in the horizontal resistance of gravel soil along the depth of slope soil and the variation characteristics of soil resistance with displacement of the pile body were studied by using a three-dimensional physical simulation test. When soil is subjected to a horizontal thrust from the foundation (pile), the soil deformation can be divided into a linear deformation stage, non-linear deformation stage, and the accelerated deformation stage, related to the variation in the displacement. The level of resistance exhibits a convex profile that is small on the top and bottom and large in the middle, with hyperbolic variation characteristics related to the displacement stage. When the buried depth of pile exceeds 0.6 to 0.7 times that of the pile depth, the slope has almost no impact on the initial modulus kini of the gravel soil p-y foundation. The ratio of p_uθ under each slope gradient to p_u under horizontal sites is approximately a constant, is only related to the slope gradient, and the corresponding depth ranges from 3 m, 5 m and 6 m for slope angle from 15°, 30°, and 45°, respectively. This observation indicates that due to the impact of the slope gradient in front of the pile above that depth, the ability of pile side soil to resist the deformation of the pile body is weakened. After the so-called slope effect occurs, the soil cannot provide resistance similar to that in the horizontal site.

Overall, the research of this paper is on the horizontal resistance parameter of gravelly soil, considering the slope gradient factor for homogeneous gravel soil composition. However, the gravelly soil slopes in southwestern China have a complex genesis, for which soil stratification or heterogeneity is significant in the regions. Further research is needed to gather more experimental data to explore how different environmental factors affect the accuracy of the lateral ultimate bearing capacity of gravelly soil and to further revise the method of calculation.