Laboratory Model Test Study on Bearing Characteristics of Super-Long and Large-Diameter Post-Grouting Piles in Clay Stratum

Abstract

In this study, the impacts of various grouting methods and volumes on the vertical bearing characteristics of model piles in clay strata were investigated through indoor static load tests on one ungrouted model pile and two model piles with grouting at the pile tip, as well as two model piles with distributed grouting at the pile tip and along the pile side. These tests were performed in conjunction with data obtained from optical fiber sensors that monitored changes in the internal forces of the pile body. The results indicate that, compared to the ungrouted model pile Z1, the ultimate bearing capacities of the grouted model piles Z2 to Z5 were increased by 83.9%, 175.0%, 125.0%, and 253.6%, respectively. Additionally, the displacements at the pile tops after failure reached 57.6%, 62.3%, 69.5%, and 73.5% that of the ungrouted model pile Z1. These results demonstrate that post-grouting can significantly enhance the ultimate bearing capacity of model piles and reduce settlement at the pile top. Under various loads, the axial force of the pile body decreases gradually with the increasing depth of the pile foundation and increases with the increasing load at the pile top. The increase in the ultimate average side friction resistance and ultimate tip resistance of the grouted model piles (i.e., Z2 to Z5), in comparison to the ungrouted pile, was positively correlated with the grouting volume at the pile tip and along the pile side. All five model piles displayed the characteristics of friction piles.

1. Introduction

Both traditional and new infrastructure construction in China have shown accelerated upgrading, integration of development strategies, continuous innovation, and optimization of construction processes. The construction of a modern comprehensive three-dimensional transportation network has been accelerated, and the overall level of infrastructure has achieved leapfrog development. As the primary foundation form for building structures, bored piles are widely utilized in various civil engineering fields due to their advantages of high bearing capacity, strong geological adaptability, excellent seismic performance, convenient construction, and low noise. However, the inherent defects of bored piles, such as pile tip sedimentation, pile side mud sloughing, and stress relaxation of the soil around the pile, significantly affect their bearing capacity. To address these issues, post-grouting technology for pile foundations is widely used due to its favorable engineering benefits [1,2,3].

Gabaix [4] first proposed a pile side grouting device in research on post-grouting devices for pile foundations. During single-hole grouting, other grouting hole positions are sealed through the water-filled expansion system of double isolation plates to support layered grouting construction on the pile side. Fleming [5] mentioned a new type of U-shaped grouting pipe that works in a similar form to open grouting. Pooranampillai et al. [6] developed a low-fluidity grouting device, which mainly includes an internal pipe with an inner diameter of 2 inches and a start-up hole under the pile to promote the transportation of low-flow slurry through the pile tip. Sze et al. [7] studied a pile side grouting device for welding grouting tubes on the outside of steel cages and applied it to square piles and underground continuous walls during a project in Hong Kong. Thiyyakkandi et al. [8] developed a modular precast pile side grouting device, which was shown to effectively control the slurry path, prevent diffusion along the weak zone, and improve the grouting accuracy and reinforcement effect. Nguyen et al. [9] developed a pile side grouting device that consists of a grouting core tube and two upper and lower sealed rubber balloons. The grouting pipe at the grouting front reduces the device to the position of the grouting hole on the side of the pile, the upper and lower rubber balloons are swelled via water injection to form a closed space, and the slurry is injected into the soil around the pile under pressure. Zhang et al. [10] developed a pile side grouting device that binds a fixed grouting ring pipe on a steel cage, in which each grouting ring pipe is connected by a vertical grouting steel pipe and multiple one-way grouting devices are distributed on the grouting ring pipe. Dai et al. [11] developed a distributed post-grouting device for the pile side that has a controllable grouting position and uniform distribution of slurry along the soil layer around the pile.

In laboratory test research on a post-grouting pile, Osamu Kusakabe et al. [12] revealed the failure mechanism of grouted solid by conducting a model test of grouting at the end of prefabricated piles in sandy soil. Lai et al. [13] innovatively applied the load transfer method to the study of post-grouting piles and proposed an exponential load transfer model. Hu et al. [14] proposed a new method for testing the post-grouting effect of super-long pile tips based on distributed optical fiber sensing technology and verified the feasibility and effectiveness of the method through model tests. Dai et al. [11] carried out laboratory model tests to compare and analyze the bearing characteristics of a single pile under a vertical load in a clay layer using three reinforcement methods: annular point grouting, distributed grouting, and high-pressure jet grouting. They revealed the mechanism of different grouting processes. Zhang et al. [15] studied the influence of different grouting methods and grouting amounts on the bearing characteristics of pile foundations through laboratory model tests. Wu et al. [16] carried out a series of cast-in-place pile model tests to analyze the bearing characteristics of a post-grouting pile and the mechanism of slurry diffusion along the pile tip under different grouting and pile tip soil unloading conditions. Asgari et al. [17] (2024) found that in dense sandy soil, grouting around the pile side contributes more to improving the pile foundation bearing capacity than grouting at the pile tip, suggesting that a strategy focusing on the pile side should be adopted in grouting design. This study further confirms the broad application value of post-grouting technology in enhancing the pile foundation bearing capacity under different soil conditions.

In field test research on post-grouting piles, Kister et al. [18] innovatively applied distributed optical fiber sensing technology to monitor the process of field pile foundation using 16 fiber grating sensors, which promoted the development of structural health monitoring technology. Dapp et al. [19] compared and analyzed the bearing characteristics of ungrouted piles and post-grouting piles in sand using field tests and found significant differences between them. Miao et al. [20] proposed an intelligent processing scheme for distributed optical fiber detection pile foundation data based on machine learning and conducted practical engineering applications. Xing et al. [21] studied the influence of the pile top load, pile length, pile diameter, and soil moisture content on the negative friction resistance of pile foundations in collapsible loess areas through field tests. In order to evaluate the improvement effect of post-grouting technology on the bearing capacity of bored piles, Zheng et al. [22] conducted static load tests on post-grouting bored piles at Beijing Capital International Airport. Wan et al. [23] conducted field post-grouting tests on pile foundations in ultra-thick fine sand layers and systematically studied six pile tip + pile side composite grouting piles and two pile side grouting piles. The effect of post-grouting reinforcement was comprehensively evaluated using electromagnetic wave CT technology and a standard penetration test (SPT). Using a field static load test of four full-scale post-grouting piles, Wan et al. [24] systematically studied the reinforcement mechanism of pile tip + pile side combined grouting in ultra-thick fine sand soil layers. Sun et al. [25] studied the application of distributed optical fiber sensing technology in an axial load test of prefabricated piles through field tests and proposed corresponding data processing methods. Thiyyakkandi et al. [26] studied the construction technology and bearing capacity of a new jet-grouting precast pile in cohesionless soil through field static load tests and verified the strong performance of the pile foundation in cohesionless soil. Wang et al. [27] studied the influence of pile tip sediment and pile side mud on the axial bearing capacity of super-long and large-diameter bored piles through field-distributed post-grouting tests. Beddelee et al. [28] proposed a pile foundation bearing capacity detection method based on distributed optical fiber sensing (DFOS) and applied it to a field pile foundation static load test. This method can be used to monitor the strain distribution of the pile body in real-time and calculate the bearing capacity of the pile foundation based on strain data.

Gao et al. [29] studied the deformation law of cast-in-place large-diameter piles under different load conditions using model tests and numerical simulation, and further analyzed the application of FBG sensors in pile foundation deformation monitoring. Zhou et al. [30] proposed a pile tip composite post-grouting technology and studied its influence on the bearing characteristics of cast-in-place pile foundations through field tests and numerical simulation. Huang et al. [31] studied the application of elastic wave CT technology in the detection of the post-grouting effect of pile foundations and verified the feasibility and effectiveness of the technology through model tests and field tests. Zhan et al. [32] studied the influence of pile tip + pile side post-grouting on the bearing characteristics of super-long bored piles through field tests and numerical simulations. Using laboratory tests and numerical simulation, Zang et al. [33] studied the mechanical properties of the post-grouting pile–soil interface under different grouting materials (such as cement slurry, chemical slurry, bentonite slurry, etc.). Through laboratory tests and numerical simulation, Shi et al. [34] studied the influence of grouting pressure, grouting volume, grouting slurry viscosity, and other parameters on grouting pile–soil interaction. Li et al. [35] proposed pile side distributed geopolymer post-grouting technology and studied its influence on the vertical bearing capacity of pile foundations through model tests and numerical simulation. Mohsen Bagheri et al. [36] used the concrete damage plasticity (CDP) model in Abaqus software to perform numerical simulations of the mechanical behavior of concrete in pile foundation structures.

In summary, domestic and international researchers have conducted extensive studies on post-grouting of pile foundations, delving into multi-factor coupling, novel monitoring technologies, grouting equipment, materials, and techniques. These investigations have been conducted through field tests, laboratory model tests, theoretical analyses, and numerical simulations, with a focus on enhancing the theory and technology of post-grouting to improve the bearing capacity of pile foundations. Nevertheless, few laboratory model tests have been conducted on distributed super-long and super-diameter post-grouting model piles at the pile tip and pile side. Previous scholars have predominantly utilized prefabricated components, such as concrete piles, steel pipe piles, and organic glass pipe piles, for simulation purposes. The test models were constructed by embedding sensors within the pile body and grouting pipes and artificially increasing the roughness. However, this simplified approach fails to accurately replicate the pile-forming process and on-site maintenance environment of cast-in-place piles. Additionally, it is challenging to achieve multi-layer distributed grouting on the pile side, and the roughness in the artificial simulation significantly deviates from that of the actual pile-forming surface.

To study the influence of post-grouting on the bearing characteristics of bridge cast-in-place pile foundations, a new model pile-formation process and a pile side distributed grouting process were employed. Laboratory static load tests were conducted using one ungrouted model pile, two pile tip grouting model piles, and two pile tip plus pile side distributed grouting model piles. A soil pressure box was utilized to detect changes in soil pressure around the piles during the grouting process, and distributed sensing fibers were used to monitor changes in pile internal force during the static load tests. Through comparing and analyzing the load–settlement relationship of each model pile under different grouting methods and grouting amounts, the transfer law of the axial force of the pile body, the performance characteristics of pile side friction resistance, and pile tip resistance were examined.

2. Model Test Design and Preparation

2.1. Model Pile Design Principles

The model test primarily ensures similarity between the model and prototype through geometric and mechanical similarities. Geometric similarity pertains to the proportional relationship between the geometric size of the model test and the prototype structure. Mechanical similarity encompasses elastic similarity, strength similarity, stress similarity, and the mechanical properties of the foundation soil. Depending on the conditions of model fabrication and loading equipment, the geometric model similarity constant is chosen as the first fundamental quantity, while the elastic modulus similarity constant is selected as the second fundamental quantity. Based on the specific conditions of the test, the geometric model similarity constant $C_L$ is calculated using Formula (1), and the elastic modulus similarity constant $C_E$ is calculated using Formula (2) [37].

$$C_L={\displaystyle \frac{L_P}{L_m}}$$

(1)

$$C_E={\displaystyle \frac{E_P}{E_m}}$$

(2)

In the formulas, $L_P$ and $L_m$ are the dimensions of the prototype pile and the model pile, respectively; $E_P$ and $E_m$ are the elastic modulus of the prototype pile and the model pile, respectively.

Combined with the application of a post-grouting bored pile in practical engineering, the geometric model similarity constant of this model test was set as 40:1. Given the limitations of laboratory equipment, mechanical similarity was not fully implemented; this limitation is acknowledged, and its potential impact on interpretation of the test results is discussed in Section 3.

2.2. Preparation of Laboratory Model Test

2.2.1. Model Box

The model test employed a square steel box measuring 2.0 m in length, 2.0 m in width, and 3.0 m in height, as depicted in Figure 1 and Figure 2. The box was positioned within the model test pit, where it descends by 1.0 m. The southeastern face of the model box features high-transparency tempered glass, allowing for clear observation of the foundation soil-filling process. On the northeast side, the model box was equipped with a layered, detachable, movable door secured by bolts, which enabled layer-by-layer filling and excavation of the model test’s foundation soil.

2.2.2. Model Pile Design and Layout

Most existing laboratory model post-grouting test piles are constructed from steel pipe, aluminum alloy pipe, concrete prefabricated piles, and so on. After the model pile is built, it is installed in the foundation soil within the model box using pre-burial or static pressure. However, this method does not accurately reproduce the actual pile formation process, curing conditions, or the realistic sidewall roughness of cast-in-place piles in field conditions. To address this, while filling the foundation soil in this model test, PVC pipes similar in size to the model pile were placed at the predetermined pile positions beforehand to simulate pore formation. Once the filling work was completed, the grouting pipe was inserted into the PVC pipe, after which the PVC pipe was removed, and high-strength fiber mortar was re-infused to form the pile body. This process simulates the pile-forming and curing process in the stratum and ensures that the roughness of the pile body meets the test requirements.

Five test piles were designed for this test. Among them, model pile Z1 did not undergo grouting, while model piles Z2 and Z4 were subjected to pile tip grouting only. Model piles Z3 and Z5 received both pile tip and pile side distributed grouting. The model piles were scaled down from the field prototype test piles at a ratio of 40:1. The scaled pile length was 2.5 m, and the pile diameter was 63 mm. A U-shaped distributed sensing fiber was embedded within each of the five model piles to detect internal forces under various loading conditions. The grouting pipe within the pile body was made of PVC with an inner diameter of 14 mm. The grouting pipe at the pile tip was situated in the center of the pile body. The grouting pipes on the pile side were evenly distributed with three pipes around the pile’s circumference. Each pile side grouting pipe was drilled at positions −0.5 m, −1.0 m, −1.5 m, and −2.0 m from the pile body’s center, and the grouting hole positions were sealed with electrical tape. The schematic diagram of the distributed grouting pile at the pile tip and pile side is illustrated in Figure 3. Model pile Z1 was situated in the center of the model box, whereas model piles Z2 through Z5 were positioned at the four corners of the model box, 50 cm from the inner wall. The plane layout of the model piles is depicted in Figure 4.

2.2.3. Foundation Soil Filling and Soil Pressure Box Burying

Restricted by factors such as equipment conditions, the test environment, and time, laboratory model pile tests often have difficulties in fully reproducing the complex geological conditions faced in actual projects. Based on this, to ensure the feasibility of the test, the test conditions were appropriately simplified and only a single stratum condition was simulated, thus ensuring the controllability of the test process. The test soil was taken from the field test pile area. Through field investigation and sampling analysis, silty clay was selected as the soil for the test of the model. The basic physical and mechanical parameters of the soil used in the model test are shown in

Table 1. Basic physical and mechanical parameters of soil for model test.

Soil Sample Name	Liquid Limit (%)	Plastic Limit (%)	Maximum Dry Density (g/cm3)	Optimum Moisture Content (%)	Cohesion (kPa)	Internal Friction Angle (°)
Silty Clay	29.9	17.7	1.86	18.26	27.01	21.3

.

The test soil was evenly wetted and mixed in batches, adhering to the optimal moisture content. During the pre-compaction experiment, it was determined that a method involving the control of the thickness of the compacted soil layers should be implemented to ensure uniform density of the soil in each layer, closely resembling the wet density of the soil sample at the optimal moisture content. Specifically, the procedure entails laying down 10 cm of loose soil per layer and compacting it to a thickness of 7 cm. The foundation soil filling process is depicted in Figure 5. Considering the impact of pile tip grouting and pile tip sedimentation during actual construction, 5 cm of fine sand was embedded at the bottom of the PVC pipe to mimic pile tip sedimentation, as illustrated in Figure 6.

To measure the change in soil pressure near the pile tip and along the pile side of each model pile before and after grouting, a miniature soil pressure box was embedded 10 cm below the slurry hole of each model pile. The model used was BW-28, with a line length of 5 m, a diameter of 28 mm, and a measurement range of 0–200 kPa. The installation of the miniature soil pressure box is depicted in Figure 7 and Figure 8.

2.2.4. Model Pile Forming and Grouting

Before the model pile is constructed, it is essential to extract the PVC pipe embedded in the test soil to simulate the hole. Once the PVC pipe was removed from the foundation soil and the hole was formed, the pile tip and pile side grouting pipes within the pile hole were realigned. Subsequently, fiber-reinforced high-strength mortar, mixed with water, was poured into the pile from the top of the pile hole. Upon completion of the pile, the excess grouting pipe at the pile tip was trimmed and the pile tip was smoothed and leveled using a grinding machine. The process of forming the model pile is illustrated in Figure 9 and Figure 10.

In this model pile grouting test, ordinary Portland cement with stable strength, good fluidity, and strong cohesion with soil was selected as the grouting material, and the water to cement ratio was 0.7. According to the “Technical Code for Building Foundation” (JGJ 94-2008) [38], the termination pressure for grouting at the bottom of piles should be determined based on the nature of the soil layer and the depth of the grouting point. For weathered rock, unsaturated clay and silt, the grouting pressure is preferably 3 to 10 MPa; for saturated soil layers, the grouting pressure is preferably 1.2 to 4 MPa, with a lower value for soft soil and a higher value for dense clay. Additionally, the grouting flow rate should not exceed 75 L/min. The grouting volume of post-grouting piles should comprehensively consider the influence of multiple factors. However, the amount of grouting of laboratory model piles calculated based on the standard formula is generally too large, indicating that the current standard formula has applicability limitations in the laboratory model pile grouting test. Before the formal grouting test, it is necessary to determine the grouting amount at the pile tip and the amount of grouting at the pile side of different grouting model piles using the pre-grouting test. There is no uniform method to determine the grouting pressure, and the influence of grouting pressure on the grouting effect is not considered in this model test. The grouting test parameters are shown in

Table 2. Grouting test parameters.

Pile No.	Pile Side Grouting Amount (L)		Pile Tip Grouting Amount (L)	Single Pile Grouting Amount (L)	Water to Cement Ratio	Grouting Method
	Single-Layer Grouting Amount (L)	Number of Layers
Z1	-	-	-	-	-	Ungrouted
Z2	-	-	2.0	2.0	0.7	Pile Tip Grouting
Z3	1.5	4	2.0	8.0	0.7	Pile Tip + Pile Side Distributed Grouting
Z4	-	-	3.0	3.0	0.7	Pile Tip Grouting
Z5	2.5	4	2.0	12.0	0.7	Pile Tip + Pile Side Distributed Grouting

. The grouting test is illustrated in Figure 11 and Figure 12.

2.2.5. Test Loading Scheme and System

This laboratory model test employed the rapid maintenance load method, in which the load at the pile top is progressively increased using the point control mode of the control box. Following each load application, readings from the electronic displacement meter were recorded every 5 min. When the settlement of the pile top measures less than 0.1 mm/h over two consecutive observations, it can be concluded that the settlement of the model pile is approaching stability, and the next load can then be applied. The loading was terminated upon reaching one of the following conditions, indicating that the model pile has reached its limit state:

When the settlement of the pile top under a certain load exceeds five times that of the preceding load level, the loading should be halted immediately. Should the total settlement of the pile top be greater than or equal to 40 mm, or if the settlement rate continues to increase without demonstrating a stable pattern, the loading must be ceased immediately.

Upon termination of the loading process, the initial load that failed the test pile is considered the ultimate bearing capacity of the pile, and it should then be unloaded incrementally back to zero.

Based on the indoor static load test scheme for pile foundations, a vertical static load test system was self-assembled. The primary components of this system are the portal reaction frame, hydraulic jack, electric hydraulic oil pump, and the static load test equipment. Throughout the loading test, the electric hydraulic oil pump was operated via the manual control button on the control box of the static load test equipment, facilitating the loading and unloading processes. The test loading system is depicted in Figure 13 and Figure 14.

2.2.6. Data Acquisition System

The vertical static load test data acquisition system is a comprehensive monitoring system designed to collect and record the mechanical response data of the model pile during static load tests in real-time. This system primarily comprises a pressure transducer, a displacement meter, a Donghua acquisition instrument, an Omnisens distributed optical fiber demodulator, and additional equipment. Through enabling these devices to work in unison, it was possible to fully monitor critical parameters such as the pile top load, pile top displacement, and pile strain. The data acquisition system is depicted in Figure 15 and Figure 16.

3. Test Results and Analysis

3.1. Soil Pressure

During the model pile grouting process, the dynamic changes in soil pressure near the pile tip and the grouting hole at the pile side serve as a crucial indicator for evaluating the grouting effect. To investigate the impacts of varying grouting quantities on the soil pressure at the tip of the pile tip grouting model piles, the soil pressures at the pile tips of model piles Z2 and Z4 as the grouting amount changes were compiled into a chart, as depicted in Figure 17.

Figure 17 shows that the soil pressure at the pile tip is positively correlated with the grouting volume at the pile tip. As the grouting volume at the pile tip increases, the solidification effect of the cement slurry on the sediment at the pile tip, the penetration and cementation of the soil layer at the pile tip, the splitting reinforcement, and the bottom expansion effect enhance the density of the soil layer near the pile tip. This, in turn, improves its bearing stiffness and the stress transfer path of the soil layer at the pile tip.

In terms of the soil pressure response on the pile side, both model piles Z2 and Z4 showed a trend of gradually increasing soil pressure with an increase in grouting volume, but there were clear differences in the response characteristics. The larger increase in soil pressure of model pile Z2 indicates that the soil at the pile side is more sensitive to grouting reinforcement, which is presumed to be closely related to the upward return of the slurry, pile-end spreading, and soil splitting and encryption during the grouting process, which significantly improves the densification and structural stiffness of the soil layer on the pile side within the depth of 2.4 m. In contrast, model pile Z4 shows the same trend of increase in soil pressure with the grouting volume, but there are significant differences in the response characteristics. In contrast, the increase in soil pressure on the pile side of model pile Z4 was relatively small, which may be due to its high in situ soil compactness, restricted slurry diffusion path, or weak construction disturbance, thus limiting the grouting effect.

In summary, model pile Z2 showed more significant structural optimization and bearing capacity enhancement effects during grouting reinforcement, while model pile Z4 showed a weaker response to grouting.

To investigate the impacts of varying grouting quantities at the pile tip and pile side on the soil pressure around the pile, soil pressure data were collected at a depth of 1.1 m near the slurry outlet of model piles Z3 and Z5, as depicted in Figure 18.

Figure 18 shows that the soil pressure on the pile side positively correlates with the grouting volume at the pile side. As the grouting volume at the 1.0 m grouting hole position of the model pile increases, the penetration, cementation, splitting reinforcement, and diameter expansion effects of the cement slurry on the soil layer near the pile side enhance the density of the soil layer and improve the stress transfer path of the soil layer near the pile side grouting hole. When the total grouting volume at the 1.0 m grouting hole position of the model pile Z3 is 1.5 L, the soil pressures in the three soil pressure boxes along the horizontal direction are 18.12 kPa, 17.36 kPa, and 15.98 kPa, respectively. For model pile Z5, with a total grouting volume of 2.5 L at the 1.0 m grouting hole position, the soil pressures along the horizontal direction of the three soil pressure boxes are 25.19 kPa, 24.15 kPa, and 22.92 kPa, respectively. This indicates that after pile side grouting is completed, the impact of the cement slurry’s penetration and compaction on the soil pressure at the pile side along the horizontal direction gradually diminishes.

Further analysis reveals that the earth pressure at model pile Z3 is the greatest near the slurry outlet hole, which gradually decreases with the increase in distance, indicating that the influence range of grouting is relatively concentrated. In contrast, the difference in earth pressure shrinks at each measurement point of model pile Z5, and the distribution of stress becomes more uniform, indicating that the high grouting volume effectively enhances the spreading range of slurry and strengthens the overall reinforcing effect on the soil body. In comparison, the maximum earth pressure of model pile Z5 was increased by about 38.99% and the minimum earth pressure was increased by about 43.43%, which shows that it has a more significant effect in increasing earth pressure and improving stress transfer.

In conclusion, the grouting volume is a key parameter affecting the soil pressure distribution and reinforcement effect on the pile side, and an appropriate increase in the grouting volume can effectively improve the bearing performance of the soil around the pile. Simultaneously, however, it should be noted that there is a special attenuation law of the slurry in the horizontal diffusion process, and the reinforcement effect may be slowed down by the marginal effect under a high grouting volume. Therefore, reasonable control of the grouting volume is of great engineering significance for the realization of pile–soil cooperative work and optimization of the reinforcement effect.

3.2. Pile Top Load–Settlement

The load–settlement curve (Q–s) at the pile top is an important indicator for characterizing the bearing capacity of pile foundations. Analyzing the corresponding relationship between load and settlement on the curve, the vertical compressive ultimate bearing capacity of the model pile can be accurately determined. The load–settlement curves for the five model piles are depicted in Figure 19. The loading values and pile top displacements are presented in

Table 3. Model pile loading value and pile top displacement.

Pile No.	Grouting Method	Limit Load Value (kN)	Destroy Load Value (kN)	Pile Top Displacement after Destroy (mm)
Z1	Ungrouted	5.6	6.1	45.3
Z2	Pile Tip Grouting	10.3	11.5	26.1
Z3	Pile Tip + Pile Side Distributed Grouting	15.4	16.9	28.2
Z4	Pile Tip Grouting	12.6	14.2	31.5
Z5	Pile Tip + Pile Side Distributed Grouting	19.8	20.6	33.3

.

As depicted in Figure 19, the Q–s curves of the four grouted model piles exhibit a gradual change prior to reaching the failure load. Table 3 reveals that the ultimate bearing capacities of the five model piles are 5.6 kN, 10.3 kN, 15.4 kN, 12.6 kN, and 19.8 kN, respectively. Compared with the ungrouted model pile Z1, the grouted model piles Z2 through Z5 demonstrate a significant enhancement in ultimate bearing capacity, with increases of 83.9%, 175%, 125%, and 253.6%, respectively. When comparing the pile tip grouted model piles Z2 and Z4, it is evident that the ultimate bearing capacity rises by 22.3% when the pile tip grouting volume is augmented by 1 L. Similarly, a comparison of the pile tip and pile side grouted model piles Z3 and Z5 shows that the ultimate bearing capacity increases by 28.6% when the grouting amount at the pile tip remains constant and the grouting amount at each layer of the pile side is increased by 1 L. The displacement of the pile top after failure for the four grouted model piles is notably less than that of the ungrouted model pile, with the displacements being 57.6%, 62.3%, 69.5%, and 73.5% of the ungrouted model pile Z1, respectively. To assess the reliability of the reported displacement ratios, an uncertainty analysis of the measurement system was conducted. The pile head settlements were measured using electronic displacement meters with a resolution of ±0.05 mm. Considering potential fluctuations during manual loading, the total displacement measurement error was estimated to be within ±0.15 mm. Given that the failure stage displacements of the grouted piles ranged from 26 mm to 33 mm, the relative measurement error was approximately ±0.5%. When calculating the displacement ratios (relative to the ungrouted pile Z1), propagation of error leads to an estimated uncertainty of ±3.2%. These results indicate that the reported ratios are valid within acceptable experimental uncertainty bounds. The test results indicate that post-grouting slurry can enhance the structural stiffness of the soil surrounding the pile, increase both the pile tip resistance and pile side friction resistance, effectively reduce the settlement of the pile top, and improve the ultimate bearing capacity of the model pile. The impact of post-grouting slurry on the solidification, cementation, and compaction of pile tip sediment and pile side mud skin further enhances the structural stiffness of the soil around the pile, thereby increasing the pile tip resistance and pile side friction resistance, effectively reducing the settlement of the pile top, and improving the ultimate bearing capacity of the model pile. The ultimate bearing capacity of the model pile, when employing the same grouting method but varying grouting amounts, increases in correlation with the grouting volume.

3.3. Pile Axial Force

The axial force distribution of the five model piles under various loads can be indirectly calculated using the strain data collected by the U-shaped distributed sensing fiber embedded within the pile, with a spatial sampling interval of 0.25 m. The average strain value ${\epsilon }_i$ for $i$a section of the pile body can be determined using the following Formula (3):

$${\epsilon }_i={\displaystyle \frac{\left({\epsilon }_{i1}+{\epsilon }_{i2}\right)}{2}}$$

(3)

In the formula, ${\epsilon }_{i1}$ and ${\epsilon }_{i2}$ are the two strain values collected by the U-shaped distributed sensing fiber at the $i$ section position inside the pile body.

The axial force value $Q_i$ of the $i$ section of the pile body can be calculated according to the following Formula (4):

$$Q_i=EA{\epsilon }_i$$

(4)

In the formula, $E$ is the elastic modulus of the model pile; A is the cross-sectional area of the model pile.

The distribution curve of the axial force along the pile body for each model, with respect to the pile foundation depth, is depicted in Figure 20.

As shown in Figure 20, the axial force distribution of the ungrouted pile Z1 is linear under all levels of loads, with no obvious inflection points. This indicates that the axial force difference between two adjacent measuring points is similar, and the distribution of the pile side friction along the pile body is more uniform. When the pile top load is large, the pile axial force distributions of the pile tip grouting piles Z2 and Z4, as well as the pile tip and pile side distributed grouting piles Z3 and Z5, exhibit inflection points at the pile foundation depths of 1.75 m, 1.5 m, 2.0 m, and 1.75 m, respectively. The slope of the curve below these inflection points is significantly reduced, and the axial force of the pile body attenuates rapidly.

The overall variation trend in the axial force distribution of the five model piles is similar. Under various loading conditions, the axial force in the pile body decreases gradually as the depth of the pile foundation increases, and increases with the rise in the load applied at the pile top. In the initial stage of loading, as the axial force at the pile top is small, the axial force transmitted from the pile top to the lower sections is minimal due to the frictional resistance of the pile side. As the load on the pile top increases, the slope of the axial force curve gradually decreases and the axial force at the pile top dissipates more rapidly down the pile body, with a greater proportion transferring to the lower sections of the pile. The frictional resistance along the pile side and the resistance at the pile tip also gradually become fully effective.

3.4. Pile Side Friction

The lateral friction resistance value between two adjacent measuring points on the pile body, under various loads, is determined by the axial force difference between these points and the cross-sectional area of the pile. The calculation is performed using the formula provided in Equation (5).

$$q_{si}={\displaystyle \frac{∆P}{\pi DL}}$$

(5)

In the formula, $\Delta P$ is the axial force difference between the adjacent test sections of the pile body; D is the diameter of the pile; L is the vertical distance between the adjacent test sections of the pile.

The distribution curve of the frictional resistance of each model pile side, along with the burial depth of the pile foundation, is shown in Figure 21.

As shown in Figure 21, the distribution of side friction resistance for the five model piles exhibits similar regularity characteristics: during the low-load phase, the side friction resistance at the upper portion of the pile body predominates, increasing initially and then decreasing with depth. As the load on the pile top increases, the lateral friction resistance of the lower portion of the pile becomes significant, with its growth rate surpassing that of the upper part of the pile. This phenomenon demonstrates the evolution process of the pile foundation’s bearing mechanism: at the onset of loading, the load is primarily sustained by the side friction resistance of the pile’s upper section. As the load on the pile top intensifies, the side friction resistance of the lower part of the pile body and the tip resistance gradually grow, cooperatively increasing the bearing capacity and ultimately establishing a composite bearing system.

The side friction resistance distribution of the five model piles under the ultimate load is shown in Figure 22.

In Figure 22, under the ultimate load, the side friction resistance of the upper portion of the pile body for the four grouted model piles differs significantly from that of the lower portion, with a considerable variation in the side friction resistance of the pile. Under the ultimate load, the average pile side friction resistance for model piles Z1 through Z5 is 6.61 kPa, 13.08 kPa, 19.11 kPa, 15.33 kPa, and 26.14 kPa, respectively. The side friction resistance of the pile tip grouting piles Z2 and Z4 increased by 97.9% and 131.9%, respectively, compared to the ungrouted pile Z1, with the increase being positively correlated with the amount of pile tip grouting. The side friction resistance of the pile tip and pile side grouting piles Z3 and Z5 increased by 189.1% and 295.5%, respectively, compared to the ungrouted pile Z1. When the amount of pile tip grouting is constant, the increase is positively correlated with the amount of pile side grouting.

3.5. Pile Tip Resistance

The pile tip resistance of the model pile was approximately determined by the axial force value calculated from the strain data of the distributed sensing fiber at the pile tip position, which was collected by the optical fiber demodulator under various loads. The distribution of pile tip resistance for the five model piles under these loads is depicted in Figure 23.

In Figure 23, the overall trend of the end resistance for the five model piles is similar. Under all loading levels, the end resistance of each pile increases incrementally with the progressive increase in the pile top load. However, the behavior of the pile end resistance varies. During the initial loading phase, the pile end resistances of the five model piles gradually become effective. As the pile top load increases, the lateral resistance and end resistance of the ungrouted pile Z1 are fully utilized, reaching their maximum bearing capacity. In contrast, at this stage, the lateral resistance and end resistance of the grouted piles have not yet reached their full potential.

Under the ultimate load, the pile tip resistance of model piles Z1 through Z5 is 2.43 kN, 3.83 kN, 5.90 kN, 5.02 kN, and 6.87 kN, respectively, accounting for 43.4%, 37.2%, 38.6%, 39.8%, and 34.7% of their ultimate load, respectively. All five model piles exhibit characteristics of friction piles. The ultimate pile tip resistance of pile tip grouting piles Z2 and Z4 increased by 57.6% and 106.6%, respectively, compared to that of the ungrouted pile Z1, and this increase is positively correlated with the pile tip grouting amount. The ultimate pile tip resistance of pile tip and pile side grouting piles Z3 and Z5 increased by 144.9% and 182.7%, respectively, compared to that of the ungrouted pile Z1. When the pile tip grouting amount was the same, the range of increase was positively correlated with the pile side grouting amount. The test results indicate that grouting piles Z2 through Z5 support solidification, cementation, and reinforcement on the pile side mud skin caused by the simulated pile tip sediment and water plug opening due to the upward and downward seepage of the grouting slurry. Additionally, the expansion head formed by the slurry hardening at the pile tip and the compaction effect of the cement stone body formed on the pile side enhanced the structural stiffness of the soil around the pile, thereby increasing the pile side friction resistance and the pile tip resistance.

3.6. Comparative Analysis of Pile Side Roughness of Model Pile and Actual Bored Pile

To ensure that the model test results have good engineering adaptability, this study quantitatively compared the pile side roughness of the model pile with that of the actual bored pile. Considering that pile side mechanical resistance is one of the key indices reflecting the roughness of the pile–soil interface, this study used the average pile side mechanical resistance under the limit state for comparison.

The test results show that the average pile side mechanical resistance of the ungrouted model pile (Z1) was 6.61 kPa, while according to the Technical Specification for Pile Foundation of Construction (JGJ 94-2008) and the relevant engineering measurement data, the typical side mechanical resistance of actual bored piles in pulverized clay layer is in the range of 15–30 kPa. According to this, the pile side roughness of the model piles is about 1/2 to 1/4 of that of the actual bored piles, indicating that the modeled piles were formed with the roughness of the pile–soil interface. This indicates a gap in roughness recovery in the model pile formation process. The main reason for this difference is that the model piles were filled with mortar by pulling out the pipe, which partially simulates the filling process but cannot completely restore the complex process of on-site piling disturbance, mud skin removal, and natural hardening interface.

It is worth noting that the pile side resistances of the model piles (e.g., Z3 and Z5) with distributed post-grouting technology increased to 19.11 kPa and 26.14 kPa, which were close to (or even exceeded) the performances of some actual piles. This shows that the post-grouting slurry formed a consolidated body and expanded head structure in the model, which effectively enhanced the strength of the pile–soil interface and compensated for the insufficient roughness of the model pile side.

In summary, the post-grouting measures can compensate for the difference in the interface conditions between the model pile and the prototype pile side, to a certain extent, and improve the representativeness and application value of the model test results.

4. Conclusions

In this study, a laboratory model pile test was conducted to perform static load tests on the ungrouted model pile (Z1), pile tip grouting model piles (Z2 and Z4), and pile tip plus pile side distributed grouting model piles (Z3 and Z5), all buried in a silty clay stratum within a model box. This study investigated the effects of various grouting methods and quantities on the bearing characteristics of the pile foundation. The primary conclusions are as follows:

(1)

The soil pressure near the grouting hole around the pile is positively correlated with the amount of grouting. After pile side grouting, the impact of the cement slurry’s penetration and compaction on the soil pressure along the horizontal direction of the pile side diminishes gradually.

(2)

The effect of post-grouting slurry on the solidification, cementation, and compaction of pile tip sediment and pile side mud skin enhances the structural stiffness of the soil around the pile. Consequently, it increases the pile tip resistance and pile side friction resistance, effectively reducing the settlement of the pile top and improving the ultimate bearing capacity of the model pile.

(3)

The ultimate bearing capacity of the model pile, with the same grouting method and varying grouting amounts, increases with the grouting amount.

(4)

The overall variation trend of the axial force distribution curves for the five model piles is similar. Under various loads, the axial force in the pile body gradually decreases with the increasing burial depth of the pile foundation and gradually increases with the increasing load at the pile top.

(5)

At the initial stage of loading, the load is primarily supported by the side friction resistance of the pile’s upper section. As the load on the pile’s top increases, the side friction resistance and the end resistance of the pile’s lower section gradually contribute, collectively providing the bearing capacity and ultimately forming a composite bearing system.

(6)

The pile tip resistance of model piles Z1 through Z5 constituted 43.4%, 37.2%, 38.6%, 39.8%, and 34.7% of their respective ultimate loads. All five model piles exhibited load-transfer mechanisms dominated by side friction, consistent with the behaviors of friction piles defined in other studies.

In summary, this study provides the engineering community with systematic experimental evidence and quantitative relationships regarding the enhancement of bearing capacity, reduction of settlement, and optimization of load transfer mechanisms in drilled cast-in-place piles in clay through post-grouting of pile foundations (particularly distributed grouting along the pile side). The findings can be directly applied to guide engineering design (optimizing pile foundation dimensions, selecting grouting schemes and parameters), enhancing engineering safety and economic efficiency, and promoting the application of advanced technologies such as pile-side distributed grouting.