Model Test Study on Bearing Characteristics of Pile Foundation in Red Clay

Abstract

The physical and mechanical properties of red clay have a significant influence on the bearing characteristics of pile foundations. Therefore, this paper conducted model tests to study the influence of different red clay water content (16~−20%) and different compaction degrees (88~−92%) on the bearing characteristics of pile foundations. The results show that the load–displacement curves of the test pile generally exhibit a steep type. The ultimate bearing capacity of the test pile increases gradually with the compaction degree from 86% to 92%. However, the ratio of load borne by the side of the pile increases from 54.8% to 67.8%, while the ratio of load borne by the end decreases from 45.2% to 32.2%. The ratio of load borne by the pile end to that borne by the pile side also decreases gradually from 0.825 to 0.476. The ultimate bearing capacity of the test pile decreases gradually with the moisture content from 17% to 26%, showing a decreasing trend. However, the ratio of load borne by the pile side decreases from 69.5% to 51.9%, while the ratio of load borne by the end increases from 30.5% to 48.1%. The ratio of load borne by the pile end to that borne by the pile side also increases gradually from 0.439 to 0.927. This indicates that increasing the compaction degree or reducing the moisture content has a more significant effect on increasing the side resistance. In this paper, the ultimate bearing capacity of test piles are calculated by the Mohr–Coulomb criterion (M-CC) and Duncan–Chang hyperbolic model (D-CHM), respectively. The results show that M-CC and D-CHM methods can accurately calculate the bearing capacity of the pile foundation in red clay. The conclusion of this study can provide a reference for the design and construction of pile foundations in red clay areas.

1. Introduction

Red clay is widely distributed in the southwestern region of China, characterized by high shear strength, low compressibility, and significant shrinkage upon desiccation. Many scholars have researched pile foundations in red clay formations, yielding abundant results.

Zhong [1] enhanced the shear strength of silt soil and subsequently increased the ultimate bearing capacity of silt soil foundations by using direct and reverse electro-osmosis. Zhou et al. [2] conducted indoor model tests using a visualization apparatus, investigating the critical depth of end resistance and the gradient trend of side resistance in layered media with weak overlying layers and sand at the pile tip. Wang et al. [3] analyzed the distribution pattern of freezing force along the pile shaft through indoor single-pile extraction model tests, establishing the relationship function among freezing force, bearing capacity, and freezing temperature. Kou et al. [4] and Tang et al. [5] explored the relationship between the bearing characteristics of piles and time using interval load tests, revealing that the ultimate bearing capacity of pile foundations increases logarithmically over time, with side resistance being the primary component of the ultimate bearing capacity. Wang and Zhang [6] similarly conducted interval compression tests on saturated soft clay foundation piles, with results indicating that the increase in pile-bearing capacity is mainly due to the increase in side resistance. Song [7], to study the stress characteristics at the pile–soil interface, conducted indoor static pile tests using saturated red clay as the foundation material. The results showed that the pore water pressure, soil pressure, and effective stress at the pile–soil interface increased with increasing penetration depth, particularly exhibiting a linear increase followed by a sharp rise at the bottom of the pile. Liu Xiangpei [8] conducted single-pile static load model tests using both red clay and sand as the pile base material, revealing that the ultimate bearing capacity of the sand base was greater than that of the red clay base. Wang Jiaquan et al. [9,10] investigated the soil plug effect, bearing mechanism, and compaction effect of open-end driven piles in red clay through model tests, as well as the residual stress characteristics of statically pressed closed-end tubular piles. Zhao Xiushao et al. [11] found, through indoor cement–soil compaction pile impact tests, that the primary influencing factors on the compaction effect of compaction piles in red clay foundations were the number of impacts and the drop height. Li Chunhong et al. [12] established a constitutive model for the pile–red clay interface based on the principle of energy dissipation and considering the influence of temperature. Du et al. [13] used a scale model device to experimentally explore the load-bearing behavior of multi-tooth piles under different bearing layer conditions. Ng et al. [14] conducted model tests on steel piles, compacting soil profiles composed of non-cohesive or cohesive soils in a large sand well, and studied the impact of clay resistance on the model piles. Wang et al. [15] employed the self-balanced static load test to study the effects of combined grouting on the ultimate bearing capacity, shaft axial force, shaft side friction, pile tip resistance, and settlement reduction in bored cast-in-situ piles in cohesive soil. Peng et al. [16] employed the Finite Element Limit Analysis method to investigate the influence of slopes on the lateral bearing capacity of large-diameter single piles in cohesive soil nearshore. Bandyopadhyay et al. [17] utilized a three-dimensional numerical method to analyze the bearing characteristics of pile groups located in soil profiles that consist of both cohesive and non-cohesive layers. Jung et al. [18] conducted a study using the finite element analysis program Plaxis to calculate the p-y curves and Pm for both single piles and a 3 × 3 arrangement of pile groups in cohesive soil, investigating the behavior of pile foundations under larger horizontal loads.

The above studies mainly focus on the comprehensive effects of influencing factors on the bearing characteristics of pile foundations in clay. However, there is a lack of research on the effects of single factors on the bearing characteristics of pile foundations by controlling variables, especially under the condition of considering the combined effects of moisture content and compaction degree, whereas, in natural soils, there are differences in water content and compaction. For this purpose, in this study, the influence law and influence trend of different degrees of compaction and moisture content of red clay on the bearing characteristics of pile foundations were investigated by model tests, which made up for the shortcomings of existing research.

2. Model Test Overview

2.1. Piles and Soil Layers

The test site is located in Guilin, Guangxi, China. The local red clay has a natural moisture content of 23% and a compaction degree of about 88% as measured by indoor geotechnical tests. Therefore, to study the effects of compaction degree and moisture content on the bearing characteristics of pile foundations, the compaction degrees of the red clay in which the piles are embedded are designed to be 86%, 88%, 90%, and 92%, and the moisture contents are designed to be 17%, 20%, 23%, and 26%, respectively. ABS resin material has the advantages of uniform material, high strength and convenient production, which can effectively reflect the deformation of the material. The purpose of this study is to explore the influence law and trend of influencing factors on the bearing characteristics of pile foundations. Considering that the ABS material ensures accurate dimensions and ease of fabrication of model piles, the piles used in this model test were fabricated using ABS material via 3D printing, as illustrated in Figure 1.

The total length of the piles was 450 mm, with a cap length of 50 mm and a diameter of 35 mm, corresponding to 0.1 times the pile length, and they were embedded 350 mm into the red clay. The dimensions of the model box were 315*315*500 mm, with a distance of 4 times the pile diameter from the pile side to the side wall of the model box, meeting the requirements for boundary effects [19,20]. The profile of the soil layers for the model pile is shown in Figure 2.

The steps for preparing the soil samples for testing are as follows: 50 g of red clay is weighed into a weighing tray, and the sample and tray are then placed in an oven to dry at a temperature range of 105–110 °C for 8 h. After removal from the oven, the sample is placed in a desiccator to cool to room temperature, and then re-weighed to determine the moisture content after drying. The required amount of water to be added is calculated, and this is uniformly and repeatedly added to the dried red clay. After mixing, the sample is allowed to stand for 24 h. A small amount of the soil sample is taken before loading tests to ensure that the moisture content meets the experimental requirements. The soil sample needed for the corresponding compaction degree is calculated based on the maximum compaction degree, and the soil sample is then filled into the model box and compacted into ten layers.

The parameters of piles and red clay are summarized in

Table 1. Parameters of piles and red clay.

Pile No.	Diameter D (mm)	Embedded Depth z (mm)	Moisture Content (%)	Compaction Degree (%)	Cohesion/kPa	Internal Friction Angle/(°)
CDTP1	35	350	20	86	9.96	6.72
CDTP2/MCTP2	35	350	20	88	13.56	10.14
CDTP3	35	350	20	90	14.13	11.89
CDTP4	35	350	20	92	15.91	13.11
MCTP1	35	350	17	88	17.22	15.12
MCTP3	35	350	23	88	10.22	8.89
MCTP4	35	350	26	88	8.63	7.01

.

2.2. Test Device and Method

The loading equipment used in this experiment is the XS(082)F testing machine. The loading method adopts the constant rate of penetration loading method, with a loading rate of 1 mm/min (the minimum loading speed of the testing machine), loaded until the model pile load stabilizes or the pile top displacement reaches 15 mm, approximately 0.4 times the pile diameter. The loading system is shown in Figure 3.

Pile top displacement is measured using displacement transducers, and a miniature soil pressure box is installed at the pile base to measure the pile end load. Strain gauges are attached to multiple sections of the pile body to measure axial forces, and the arrangement of strain gauges on the model pile is shown in Figure 4.

3. Experimental Results and Analysis

3.1. Load–Displacement Curves

The load–displacement curve of the test pile top is shown in Figure 5.

As shown in Figure 5, the load–displacement curves of the seven piles exhibit an overall abrupt change type. In the initial loading stage (0~400 N), the pile top displacement increases linearly at a relatively constant rate with the load. As the applied downward load increases, the rate of increase in pile top displacement gradually accelerates. After reaching a certain load level, the rate of increase in pile top displacement stabilizes.

In this model test, the ultimate bearing capacity of the piles is taken as the load value when the pile top displacement reaches 10% of the pile diameter [21]. The experimental results are presented in

Table 2. Results of model pile tests.

Pile No.	Maximum Test Load/N	Maximum Pile Top Displacement/mm	Ultimate Bearing Capacity/N
CDTP1	900	15.00	648
CDTP2/MCTP2	1000	15.05	733
CDTP3	1030	15.00	757
CDTP4	1231	15.02	856
MCTP1	1500	15.00	1172
MCTP3	900	15.00	691
MCTP4	850	15.00	557

.

According to Table 2, the relationship between the ultimate bearing capacity and the compaction degree, and the moisture content of the red clay are shown in Figure 6 and Figure 7, respectively. As can be seen from Figure 6, as the compaction degree of red clay increases gradually from 86% to 92%, the ultimate bearing capacity of the test pile increases progressively, with an average growth rate of 4.91%. As shown in Figure 7, as the moisture content of the red clay increases gradually from 17% to 26%, the ultimate bearing capacity of the test pile also demonstrates a gradual decrease, with an average decreased rate of 10.43%.

In summary, the analysis indicates that with an increase in compaction degree, the cohesion and internal friction angle of red clay correspondingly increase, thereby enhancing the ultimate bearing capacity of pile foundations. Conversely, with an increase in moisture content, the cohesion and internal friction angle of red clay correspondingly decrease, leading to a reduction in the ultimate bearing capacity of pile foundations. This indicates that the cohesion and internal friction angle of red clay have a significant impact on the bearing characteristics of pile foundations.

3.2. Axial Force Curve and Side Resistance Curve of Pile

In this test, a strain gauge was used to measure the cross-sectional strain of the pile, and the axial force of the pile was calculated based on the measured strain. The average side resistance of the pile was calculated using the method in reference [22]. Based on the calculation results, the axial force-pile depth curve and the average side resistance-depth curve under each load level were plotted.

The axial force distributions of the pile are shown in Figure 8.

From Figure 8, it can be observed that the axial force of the pile progressively increases with the increase in downward load and gradually decreases with the increase in embedded depth. During the initial loading stage, the axial force at the bottom of the pile is approximately zero, indicating that the upper load is mainly borne by the side resistance of the pile. As the downward load increases, the pile end resistance gradually comes into play, while the side resistance tends to stabilize.

The Side resistance distributions of model piles under various load levels are shown in Figure 9.

From Figure 9, it is evident that with the increase in downward load, both side resistance and end resistance continuously increase, but the growth rate of end resistance is much higher than that of side resistance. Under the same load level, as the embedded depth of the pile increases, the side resistance gradually increases.

3.3. Analysis of Load Bearing Characteristics at Pile End and Pile Side

The ratios of load borne by the pile side and pile end relative to the pile head load under various load levels for the seven model piles are analyzed. Taking CDTP1 as an example, under a load of 100 N, the load transferred from the pile top to the pile end is 90 N. Therefore, the pile end bearing ratio is 90%, and the pile side bearing ratio is 10%. The curves of the load ratio at the pile side and pile end are plotted, as shown in Figure 10.

As can be seen from Figure 10, as the pile top load increases, the proportion of the load borne by the pile side gradually decreases, while the proportion of the load borne by the pile end gradually increases. Taking CDTP1 as an example, when the pile top load increases from 0 N to the ultimate load of 648 N, the pile end bearing ratio gradually increases from 0% to 45%. This shows that in the initial stage of pile top loading, the side resistance of the pile is first exerted, and in the later stage of loading, the synergistic effect with the pile end resistance is gradually exerted. Under the ultimate load at the pile top, the relationship between the bearing characteristics of the pile end and pile side and the compaction degree is shown in

Table 3. Statistical of load bearing by pile end and pile side under different compaction degrees.

Type	Pile No.
	CDTP1	CDTP2	CDTP3	CDTP4
Load bearing by pile end (N)	293 (45.2%)	291 (39.7%)	280 (37.0%)	276 (32.2%)
Load bearing by pile side (N)	355 (54.8%)	442 (60.3%)	477 (63.0%)	580 (67.8%
Ratio	0.825	0.658	0.587	0.476

and Figure 11, and the relationship with the water content is shown in

Table 4. Statistical of load bearing by pile end and pile side under different moisture content.

Type	Pile No.
	MCTP1	MCTP2	MCTP3	MCTP4
Load bearing by pile end (N)	357 (30.5%)	291 (39.7%)	287 (41.6%)	268 (48.1%)
Load bearing by pile side (N)	815 (69.5%)	442 (60.3%)	404 (58.4%)	289 (51.9%)
Ratio	0.439	0.658	0.713	0.927

and Figure 12.

From Table 3 and Figure 11, it is observed that as the compaction degree increases from 86% to 92%, the ratio of pile side load gradually increases from 54.8% to 67.8%, with an average growth rate of 4.58%; the ratio of pile end load decreases from 45.2% to 32.2%, with an average decrease rate of 5.31%; The ratio of the pile end bearing to the pile side bearing progressively decreases from 0.825 to 0.476.

From Table 4 and Figure 12, it is observed that as the moisture content increases from 17% to 26%, the ratio of pile side load gradually decreases from 69.5% to 51.9%%, with an average decrease rate of 4.59%; the ratio of pile end load increases from 30.5% to 41.8%, with an average growth rate of 8.42%. The ratio of the pile end bearing to the pile side bearing increases progressively from 0.439 to 0.927.

Through the above analysis, it is observed that as the compaction degree increases, the cohesion and internal friction angle of red clay correspondingly increase, thereby enhancing the lateral resistance of piles. With an increase in moisture content, the cohesion and internal friction angle of red clay correspondingly decrease, leading to a reduction in lateral resistance, indicating that the impact of cohesion and internal friction angle on pile side resistance is more significant compared to that on pile end resistance.

4. Ultimate Bearing Capacity Calculation

To supplement the model test, a theoretical method is introduced to investigate the calculation of pile-bearing capacity based on the results of the test. Based on the test results, it is found that the bearing capacity of the test pile is mainly borne by the pile side resistance and end resistance:

$$Q=Q_s+Q_e$$

(1)

where, $Q$ is the ultimate bearing capacity, kN; $Q_s$ is the side resistance of pile, kN; $Q_e$ is the end resistance of pile, kN.

4.1. Calculated of $Q_s$

In this paper, $Q_s$ is calculated by the Mohr–Coulomb criterion(M-CC) and Duncan–Chang hyperbolic model (D-CHM), respectively.

(1)

Mohr–Coulomb Criterion

As reference [23], the side resistance of the pile in the soil layer is calculated as follows:

$$Q_s={\displaystyle \sum _i^{n}u{l}_i{q}_{si}}$$

(2)

where, $u$ is the perimeter of the pile; $l_i$ is the thickness of each soil layer; $q_{si}$ is the value of side resistance.

In this paper, the side resistance of the test pile is generated by the relative shear between the soil layer and the pile body, so the value of the ultimate friction resistance of the soil around the pile is considered to be calculated by Mohr–Coulomb Criterion:

$$q_{si}=c+\sigma \tan \phi$$

(3)

where, $c$ is the cohesion of the soil; $\sigma$ is the effective earth pressure; $\phi$ is the internal friction angle of the soil.

The pressure on the pile side is provided by the soil layer, so the average soil pressure of the test pile in the soil layer can be used:

$$\sigma =K_0\gamma h$$

(4)

$$K_0=1-\sin \phi$$

(5)

$$\gamma ={\rho }_{s}g$$

(6)

where, $K_0$ is the coefficient of earth pressure at rest; $\gamma$ is the weight of the soil; $g$ is gravity acceleration (10 m/s²); ${\rho }_s$ is the density of the soil.

(2)

Duncan–Chang Hyperbolic Model

According to Duncan–Chang’s hyperbolic model [24], the nonlinear transfer of pile side load in the soil layer is analyzed. The relationship between pile side resistance ${\tau }_s$ and pile–soil relative displacement $s$ is expressed as follows:

$${\displaystyle \frac{{\tau }_s}{s}}={\displaystyle \frac{1}{a+bs}}$$

(7)

Integral:

$${\displaystyle \frac{d{\tau }_s}{ds}}={\displaystyle \frac{a}{{\left(a+bs\right)}^2}}$$

(8)

The initial conditions of the hyperbolic model: $s=0$, ${\displaystyle \frac{d{\tau }_s}{ds}}=0$.

Substitute into Formula (7):

$${\tau }_s={\displaystyle \frac{s}{\frac{1}{E_s}+\frac{s}{q_{si}}}}$$

(9)

where, $E_s$ is the initial stiffness coefficient; $q_{si}$ is the ultimate side resistance, $q_{si}=K_0{\sigma }_s\tan \beta$, ${\sigma }_s$ is the vertical stress; $K_0$ is the coefficient of earth pressure at rest; $\beta$ is the friction angle of the pile–soil interface.

4.2. Calculated of $Q_e$

As reference [23], the end resistance of the pile in the soil layer is calculated as follows:

$$Q_e=A{q}_{se}$$

(10)

$$q_{se}=c{N}_c+\sigma N_q$$

(11)

$$N_q={\displaystyle \frac{\left(\cot \phi +\phi +\pi /2\right)}{\left(\cot \phi +\phi -\pi /2\right)}}$$

(12)

$$N_c={\displaystyle \frac{\pi \cot \phi }{\left(\cot \phi +\phi -\pi /2\right)}}$$

(13)

where, $A$ is the cross-sectional area of the pile; $q_{se}$ is the end resistance; $N_c$ and $N_q$ are bearing capacity coefficients, which are related to $\phi$.

4.3. Calculated of $Q$

$c$ and φ are measured by shear test. ${\rho }_s$ is converted by the maximum dry density. The parameters are brought into the above formula to obtain the calculation results. The calculated values are compared with the test value. The results are shown in

Table 5. Comparison of results under different compaction degrees of soil.

Pile No.	CDTP1	CDTP2	CDTP3	CTDP4
Test value (N)	648	733	757	856
M-CC value (N)	599	816	876	979
Error (%)	−7.6	11.4	15.7	14.4
D-CHM value (N)	526	658	726	783
Error (%)	18.8	10.2	4.1	8.5

and

Table 6. Comparison of results under different moisture content of soil.

Pile No.	MCTP1	MCTP2	MCTP3	MCTP4
Test value (N)	1172	733	691	557
M-CC value (N)	1047	816	658	562
Error (%)	−10.6	11.4	−4.7	0.8
D-CHM value (N)	793	658	622	568
Error (%)	32.4	10.2	10.1	−1.9

, and Figure 13.

It can be seen from Table 5 and Figure 13 that the error between the test value and the M-CC value is from −7.6% to 15.7%, and the average error is 8.5%. The error between the test value and the D-CHM value is from 4.1% to 18.8%, and the average error is 10.4%.

It can be seen from Table 6 and Figure 14 that the error between the test value and the M-CC value is from −10.6% to 11.4%, and the average error is −0.8%. The error between the test value and the D-CHM value is from −1.9% to 32.4%, and the average error is 12.7%.

The results indicated that M-CC and D-CHM methods can calculate the bearing capacity of the pile foundation in red clay under different compaction degrees and moisture content.

5. Conclusions

With the compaction degree of the red clay increases from 86% to 92%, the ultimate bearing capacity of the test pile increases progressively, with an average growth rate of 4.91%, indicating that enhancing the compaction degree of the red clay subsoil effectively improves the bearing capacity of the pile foundation. However, with the increase in compaction degree, the ratio of the pile end bearing to the pile side bearing decreases from 0.825 to 0.476, suggesting that the increase in compaction degree, clay cohesion and internal friction angle significantly increases the pile side resistance.

With the moisture content of the red clay increases from 17% to 26%, the ultimate bearing capacity of the pile foundation gradually decreases, with an average decreased rate of 10.43%, indicating that reducing the moisture content of the red clay subsoil effectively enhances the bearing capacity of the pile foundation. With the increase in moisture content, the ratio of the pile end bearing to the pile side bearing increases from 0.439 to 0.927, indicating that the increase in moisture content significantly reduces the pile side resistance.

The ultimate bearing capacity of test piles is calculated by the Mohr–Coulomb criterion and Duncan–Chang hyperbolic model, respectively. The average error ranges from −0.8% to 12.7%, indicating that M-CC and D-CHM methods can accurately calculate the bearing capacity of the pile foundation in red clay.

This paper is to investigate the effect of compaction degree and moisture content of red clay on the bearing characteristics of pile foundations, with emphasis on regularity. However, the shortcoming of this study is that the coefficient of friction on the side surface of the pile between ABS plastic and soil is 40% to 60% lower than between concrete and soil. And the size effect of the model test compared with the field test makes it difficult to apply the conclusions directly and accurately to engineering practice, but the regularity results can be used as a guide and reference for engineering practice.