Centrifugal Model Test of Multi-Level Slope under Combined Support of Pile-Anchor and Frame-Anchor

Abstract

The combination support structure of pile-anchor and frame-anchor is widely used in multi-level slope engineering, but the relevant theoretical research lags behind engineering practice. To make up for this deficiency, this paper takes the multi-level slope under combined support of pile-anchor and frame-anchor as the research object, conducts a model test using the geotechnical centrifuge, analyzes the most relevant structural force and slope deformation in engineering, and provides some reinforcement suggestions. The test results show that the combination support structure of pile-anchor and frame-anchor has a good reinforcement effect on multi-level soil slopes, but the deformation range of the slope is greatly affected by the anchoring structure and the anchor rods located within the deformation zone. The structural force condition is significantly different from traditional structures that place the anchor rod anchoring section in a stable soil layer. According to the structural force characteristics, it is recommended that the support design fully consider the positional relationship between the anchor rods and the sliding surface. The design of the frame-anchor support section should strictly control the anchoring depth, so that the potential sliding surface of the slope can be moved backward, thereby increasing the difficulty of sliding. The design of pile-anchor support should ensure that the anchor rods have sufficient length to provide greater anchoring force, thereby improving the bearing capacity of the pile. These research results can enrich and improve the support design theory of multi-level soil slopes, providing guidance for engineering practice.

1. Introduction

With the continuous advancement of infrastructure construction in mountainous areas, the number of high and steep slopes is increasing [1]. To ensure slope safety, engineers and technicians usually treat high and steep slopes into stepped multilevel slopes and reinforce them with support measures. The combination support structure of pile-anchor and frame-anchor has a good effect on anchoring deep soil and limiting slope displacement, and is widely used in multi-level slope reinforcement, especially along highways and railways [2]. However, the interaction between the composite structure and the soil is very complex. The design process is largely empirical, and slope instability accidents occur frequently. Therefore, conducting research on the problems related to multi-level slopes under the combined support of pile-anchor and frame-anchor is an urgent requirement for engineering construction.

At present, the research on pile-anchor structures and frame-anchor structures has covered multiple aspects, such as theoretical analysis, test research, and numerical simulation. Based on theoretical analysis, the structural calculation model can be established, and corresponding force calculation formulas can be derived [3,4]. Numerical simulation can effectively restore the complex relationship between structure and soil, and provide an in-depth analysis of slope deformation and structural force [5,6,7]. Conducting in situ tests on engineering sites can directly and genuinely reflect the actual stress on the support structure and slope, and detect abnormal situations such as deformation and damage to the slope structure in good time [8]. Scaling down the prototype slope in the laboratory and conducting scaled model tests can simulate the mechanical response, deformation characteristics, and failure process of the prototype slope [9,10,11,12,13,14]. These studies have greatly promoted the development of support structures, but the objects involved are mostly simple structures. Studies on complex structures are scarce, especially those related to multi-level slopes under the combined support of pile-anchor and frame-anchor. Meanwhile, in terms of test research on supported slopes, field tests, large-scale static model tests, and vibration table model tests are the main approaches. Although the centrifugal model test can restore the real stress state of the structure and soil, there are relatively few studies on pile-anchor structures and frame-anchor structures on this basis [15,16,17,18,19,20,21].

In response to the above deficiencies, this paper takes a multi-level slope under the combined support of pile-anchor and frame-anchor as the research object, conducts the centrifugal model test by using the geotechnical centrifuge, analyzes the structural force and slope deformation that are of great concern in engineering, and provides some targeted suggestions for the design of a pile-anchor and frame-anchor joint support structure. The obtained results can provide reference and inspiration for the stability study of multi-level slopes under the combined support of pile-anchor and frame-anchor, and for subsequent similar centrifugal model tests.

2. Centrifugal Model Design Fabrication

The centrifugal test can compensate for the loss of self-weight caused by model size reduction with the help of centrifugal acceleration. Taking a model scaled down by a factor of $n$ as an example, the vertical stress at a certain point when the model is placed in a 1 g gravity field is $1/n$ of the corresponding position of the prototype, and the vertical stress at that point is the same as that of the prototype when the model is placed in a $n$ g gravity field. Therefore, with the help of the centrifugal model test, the smaller size model can reach the same stress level as the prototype, realizing the real simulation of the prototype, reproducing the deformation and damage process of the prototype, and providing an intuitive basis for understanding the mechanical behavior of the actual engineering.

2.1. Overview of Prototype Slope

The prototype slope is a three-stage slope with each stage being 8 m, as shown in Figure 1. The reinforcement design adopts the combination support structure of a pile-anchor and a frame-anchor. The bottom level of the slope is reinforced with a pile-anchor structure. The spacing between piles is 2.5 m, and the pile length is 15 m. Two layers of anchor rods with a length of 12 m are installed on the pile. The upper two levels of the slope are reinforced with a frame-anchor structure. Each level has three layers of anchor rods, and the longitudinal and transverse spacing of the anchor rods are 2.5 m. The length of the anchor rods located in the middle level is 14 m. The length of the anchor rods located at the top is 16 m. The geological composition is loess and sandstone, with loess being in part of the slope, and sandstone being in the underlying strata. The specific geotechnical parameters are shown in

Table 1. Geotechnical parameters of the prototype slope.

Stratum	Density (kg/m3)	Cohesion (kPa)	Internal Friction Angle (°)
Loess	1650	15	25
Sandstone	2200	150	35

.

2.2. Test Equipment and Model Dimensions

The three-level support slope had a greater height and contained more structural components. The selection of scale ratio is crucial when making a model. If the scale ratio is small, the model size will be larger, but many existing geotechnical centrifuges are unable to meet the requirements for larger dimensions. If the scale ratio is large, the size of the support structure is very small, and the production difficulty is extremely high. Therefore, it is necessary to choose a large geotechnical centrifuge and control the model size.

(1)

Test equipment

After investigation and comparison, a TLJ-500 large geotechnical centrifuge of state key laboratory of geohazard prevention and geoenvironment protection was used for this test. The device is shown in Figure 2. Its main technical parameters include: a maximum capacity of 500 g·t, a maximum centrifugal acceleration of 250 g, and it can operate continuously for 12 h under full load conditions. The selected model box size for the test is 1.0 m × 0.6 m × 0.8 m.

(2)

Similarity relationship

In order for the model in a high centrifugal force field to accurately simulate and reflect the mechanical behavior and deformation process of the prototype, the various metrics in the scaled model need to present a certain deterministic correspondence with the prototype. This relationship is called the similarity ratio. When the geometric similarity ratio is $n$, the other similarity ratios are as follows (

Table 2. Similarity ratios for centrifugal model tests (model/prototype).

Physical Quantity	Prototype	Model	Physical Quantity	Prototype	Model
acceleration	1	$n$	angle	1	1
length	1	$1/n$	density	1	1
area	1	$1/n^2$	moisture content	1	1
volume	1	$1/n^3$	cohesion	1	1
displacement	1	$1/n$	internal friction angle	1	1
stress	1	1	particle size	1	1
bending moment	1	$1/n^3$	inertia time	1	$1/n$

).

(3)

Centrifugal model dimensions

After considering the scale of the prototype slope, the size of the model box, and the difficulty of making structural components, the similarity ratio for this test was determined to be n = 50. According to this similarity ratio, the height of the scaled slope obtained was 480 mm. Other dimensions are shown in Figure 3.

2.3. Model Material Selection and Preparation

(1)

Model Soil Preparation

The reshaped soil mechanical properties have a large influence on the test results [22,23,24]. So how to restore the physical and mechanical parameters of the original soil is key to determining the success of the test. In order to meet the similarity of geotechnical materials, the in situ soil taken from the site was reshaped. By comparing the cohesion and internal friction angle of the remolded soil at different moisture contents and different fill densities, the final fill parameters could be determined. The remodeled sandstone was formed by mixing loess and cement with water, where the mass ratio of loess and cement was 5:1 and the water content was 8.0%. The density was controlled to be 1835 kg/m³ during filling. The water content of the reshaped loess was 9.5%, and its density was 1750 kg/m³ during filling. The model soil created on the basis of these control parameters was closest to the in situ soil in terms of cohesion and internal friction angle, as shown in

Table 3. Geotechnical parameters of the scaled slope.

Stratum	Density (kg/m3)	Cohesion (kPa)	Internal Friction Angle (°)
Loess	1750	15.5	24.6
Sandstone	1835	161	35.2

.

(2)

Support Structure Fabrication

In order to make the structural materials of the model and prototype as similar as possible, cement and wire were chosen as the scaled structural materials. Support piles and pile-top connecting beams are bending components in actual work, and the structural bending moment should meet the requirement of similarity ratio. The cross-sectional size of the scaled pile was considered to be 24 mm × 24 mm, and the reinforcement was 4 iron wires with a radius of 0.8 mm. The cross-sectional size of the scaled connecting beam was considered to be 24 mm × 20 mm, and the reinforcement was 4 galvanized iron wires with a diameter of 1.2 mm. The crossbeams and columns of the frame structure are also bending components in actual work. The reduced cross-sectional size was considered to be 8 mm × 10 mm, and the reinforcement was 2 iron wires with a radius of 0.36 mm. When making scaled anchor rods, the diameter of the scaled anchor rods was considered to be 8 mm, the wrapping material of the anchoring section was cement slurry, and the core material of the rod was 1 iron wire with a radius of 0.5 mm. In practical engineering, anchor rods and slope support structures are connected at the anchor head through specially designed anchors. Therefore, the connection quality between the iron wire and the scaled structure should be ensured to avoid damage to the connection under high centrifugal acceleration. After comparing multiple options, it was decided to use two different small wire clamps as connecting components. In the model, the wire clamp and the scaled structure were cast together, which effectively fixed the galvanized iron wire. The specific scaled structures and structural connectors are shown in Figure 4.

2.4. Sensor Arrangement on the Support Structure

This test mainly monitors the structure force and slope deformation. To avoid model boundaries adversely affecting the test results, the sensors should be located away from the sidewalls of the model box. Considering the size effect of sensors and the intersection of circuits, it was ultimately decided to arrange two monitoring profiles. Profile 1 was located at the 6th column structure and was mainly used for arranging strain gauges, as shown in Figure 5a. The frame–anchor support section included two test anchor rods, and the pile-anchor support section included one test anchor rod. The anchoring section of each anchor rod was uniformly and symmetrically pasted with 5 pairs of strain gauges. The support pile had eight pairs of strain gauges symmetrically pasted on it. According to the data measured by strain gauges, the distribution and variation of anchor rod axial force and support pile bending moment during centrifugal loading could be obtained. Profile 2 was located at the 7th column support structure and was mainly used for arranging soil pressure boxes, as shown in Figure 5b. Micro-soil pressure boxes were installed around the support pile and on the inner side of the frame beams, numbered T1–T9 from top to bottom. T1–T2 were located in the upper frame–anchor support section, T3–T4 were located in the middle level frame–anchor support section, and T5–T9 were located in the lowest level pile–anchor support section. According to the measured data of the soil pressure box, the distribution and variation rule of soil pressure acting on the frame and pile during centrifugal loading could be obtained. In addition to the arrangement of strain gauges and soil pressure boxes, displacement monitoring points were also set on the slope. Based on the data obtained from displacement monitoring points, the deformation and failure of the slope during centrifugal loading could be obtained.

2.5. Model Making Process

The main steps in making a scaled model are as follows: (1) Draw reference points inside the model box based on the size of the model slope, providing a benchmark for model filling. (2) Apply silicone oil inside the model box to reduce the influence of boundary effects. (3) Fill the geotechnical materials, layer by layer, according to the slope shape and anchor rod position. The depths of filling were 100 mm, 100 mm, 80 mm, 60 mm, 50 mm, 50 mm, 50 mm, 60 mm, 50 mm, 50 mm, 50 mm, and 30 mm in sequence. The density was strictly controlled during model soil filling. During the sandstone fill stage, position and secure the scaled piles. During the loess-filling stage, when the soil is filled to the corresponding height of each layer of anchor rods, the soil within the designated area for anchor placement is excavated. After placing the anchor rods, the excavated soil is re-compacted, and then the soil surface is loosened to facilitate the subsequent filling of the next layer of soil. This process is repeated until the design elevation is reached. (4) Excavate the soil according to the designed slope ratio, and position the scaled frame structure simultaneously. (5) Set small markers with a spacing of 50 mm × 50 mm on the top surface and cross-section of the slope to observe slope deformation. The centrifugal model production process and final model are shown in Figure 6.

2.6. Test Loading Process

When the centrifugal acceleration is within 50 g, the load increases by 10 g each time and the stabilization time is 2 min. When the centrifugal acceleration exceeds 50 g, the load increases by 5 g each time and the stabilization time is 5 min. During the loading process, the loading stops immediately if the slope is damaged, and continues until the centrifugal acceleration reaches 80 g if there is no obvious damage to the slope.

3. Centrifugal Model Test Results

3.1. Structural Force Analysis of Pile-Anchor Support Section

(1)

Distribution of bending moments on piles

The strain values on the pile can be obtained from strain gauges affixed to the piles, and the corresponding bending moments are calculated as follows:

$$M=EI{\displaystyle \frac{\left({\epsilon }_{i1}-{\epsilon }_{i2}\right)}{B}}$$

(1)

where: $M$ is the bending moment value of each measuring point on the pile; $E$ is the elastic modulus of the pile material; $I$ is the sectional moment of inertia of the pile; ${\epsilon }_{i1}$ is the micro-strain measured by the strain gage on the left side of the pile at measurement point $i$ in Figure 5; ${\epsilon }_{i2}$ is the micro-strain measured by the strain gage on the right side of the pile at measurement point $i$ in Figure 5; $B$ is the distance between the strain gauges on both sides of the pile at the same measuring point.

Since the bending moment at the measurement point is proportional to the corresponding strain difference, the distribution of bending moment on the pile can be analyzed by the strain difference. After calculation, the distribution of strain difference on the pile is shown in Figure 7.

In the above figure, the bending moment on the upper part of the pile is different from that at other positions. The bending moment always follows an S-shaped distribution from top to bottom, and the zero point of the bending moment is located within about 20% to 30% of the pile length from the top of the pile. The free side of the pile above the zero point is under tension, and the strain difference is negative. The soil side of the pile below the zero point is under tension, and the strain difference is positive. The maximum bending moment occurs at approximately 57% of the pile length from the top of the pile.

Compared with ordinary anti-skid piles without anchor rods, the anchoring force effectively improved the pile force in this test [25]. Compared with anchor piles with very good anchoring effects, the improvement of the pile bending moment in this test appears to be relatively small [13]. Analysis suggests that the distribution of pile bending moments in the pile-anchor structure is greatly influenced by the anchoring effect of anchor rods. When the anchoring effect is good, the anchor rods can effectively control the displacement of the pile top, so that the free side of the pile above the sliding surface position is under tension. The damage of the pile is mainly caused by the plastic hinge failure in the middle of the support section. When the anchoring effect is poor, the sliding force of the slope will cause the pile to deform outward, and then pull the anchor rod to slide out together. The force condition of the piles in the test belongs to the latter, mainly due to the fact that the multistage-supported slopes have a large deformation range. The anchor rods are located within the deformation zone and will move along with the soil, making it unable to exert a good anchoring effect.

(2)

Distribution of soil pressure behind piles

The distribution of soil pressure behind the pile is shown in Figure 8. As the acceleration increases, the soil pressure gradually increases and exhibits a parabolic distribution, and the maximum value is always located at 30% of the pile length from the top of the pile. According to the soil pressure behind the pile at 45%, the pile length from the top of the pile is greater than that at 15% pile length from the top of the pile, and it was found that the combined force of slope downturn was located in the middle and lower parts of the pile-support section, which is consistent with the usual assumption that the combined force of the support piles is located at 1/3~1/2 height of the pile-support section.

The soil pressure on the pile at the foot of the slope is shown in Figure 9. With the increase of centrifugal acceleration, the soil pressure in front of the pile increases very quickly, which indicates that the pile has tilted forward, while the soil pressure behind the pile at the foot of the slope under the influence of the pile deformation increases to a lesser extent.

(3)

The strain value on the tested anchor rods

For anchor rods, the axial force at the measuring point is proportional to the axial strain, so the distribution of axial force can be analyzed through axial strain. The specific axial strain value can be calculated according to Equation (2). The calculated axial strain and its variation with acceleration are shown in Figure 10.

$$\epsilon ={\displaystyle \frac{\left({\epsilon }_1+{\epsilon }_2\right)}{2}}$$

(2)

where: $\epsilon$ is the axial strain value; ${\epsilon }_1$ and ${\epsilon }_2$ are the strain values above and below the measurement point, respectively.

In the above figure, the axial strain at each measuring point increases gradually from deep to outward, with the maximum value being located at the end of the tested anchor rod. This phenomenon is consistent with the results of the support pile force analysis. The pile top anchor rod has an outward displacement trend under the influence of pile deformation, and the lateral friction resistance around the anchoring section gradually generates from the outside to the inside, so the end axial force is the highest.

3.2. Structural Force Analysis of the Frame-Anchor Support Section

(1)

Distribution of soil pressure on the frames

The distribution of soil pressure on the frames and its variation with acceleration are shown in Figure 11. Measurement points 1 and 2 are located on the soil side of the upper level frame column, while measurement points 3 and 4 are located on the soil side of the middle level frame column. The distribution law of soil pressure can indirectly reflect the displacement of the slope and the force on the anchor rod. Usually, the greater the soil pressure, the more obvious the displacement trend at that position, and the corresponding force on the anchor rod is also greater. Therefore, the foot of the middle level of the slope is where the frame-anchor support section is displaced the most, as well as where the entire supported slope is displaced the most.

(2)

The strain value on the tested anchor rods

The strain values were distributed in an upward convex shape along the axial direction of the anchor rods, as shown in Figure 12. At the same acceleration, the strain of the tested anchor rod #2 was greater than that of the tested anchor rod #1. This indicates that the soil pressure in the middle of the slope was greater than that in the upper part of the slope, and this conclusion is consistent with the results of the soil pressure analysis. At different loading stages, the maximum axial strain was located at different monitoring points. When the acceleration was small, the maximum strain was located at the second monitoring point. When the acceleration reached 80 g, the maximum strain was located at the fourth monitoring point. This indicates that the lateral frictional resistance at the end of the anchor rods occurred first and then gradually extended outward. Slope displacement can be revealed by analyzing the lateral friction resistance of the anchoring section. Within the range of the left and middle ends of the anchoring section (between measurement points 1 and 4 in the Figure), the strain value gradually increased. This indicates that the anchor rods within this range were moving outward relative to the soil. Within the range of the right end of the anchoring section (between measurement point 4 and measurement point 5 in the Figure), the strain value gradually decreased. This indicates that the soil within this range was moving outward relative to the anchor rods. At the same time, the growth rate of axial strain from measurement point 1 to measurement point 4 gradually decreased, which is different from the force characteristics of anchor rods anchored in rock layers or absolutely stable soil layers. This indicates that the support structure affected the deformation range of the slope, and the anchor rod was not located in a stable soil layer.

Further comparison of the axial strain at the end of the three tested anchor rods yields Figure 13. The force on the anchor rod in the pile-anchor support section was the highest, while the force on the upper anchor rods in the frame-anchor support section was the lowest. The force on the lower anchor rod in the frame-anchor support section was between the above two. Analysis suggests that the force on anchor rods is related to the soil pressure on the structure and the deformation of the piles. The upper part of the slope was mainly a vertical settlement, and the soil pressure was relatively small, so the corresponding anchor rod force was also relatively small. The lateral displacement and soil pressure in the middle of the slope were greater than those in the upper part of the slope, so the corresponding anchor rod force was relatively large. The anchor rods in the pile-anchor support section were connected to the piles, and the deformation of the piles pulled the anchor rods outward. So the lateral friction resistance around the anchor rods connected to the pile was more fully utilized, and the force of the anchor rods was the highest.

3.3. Slope Deformation Characteristics

The high-definition camera of the centrifuge is shown in Figure 14a, and the deformation of the slope is shown in Figure 14b. The combination support structure of pile-anchor and frame-anchor had a significant reinforcement effect on multi-level soil slopes during centrifugal loading. The slope did not experience instability with increasing loading, and the deformation remained relatively slow. When the acceleration value reached 80 g, the vertical settlement at the top of the slope was about 2 mm, and the soil between the piles partially fell off. The frame-anchor support section experienced displacement, but the displacement was relatively small. The displacement of the pile-anchor support section was the smallest. Although there was no obvious sliding deformation zone, the potential deformation range of the slope can be analyzed by the force situation of the anchor rod. Combined with the results of force analysis of the tested anchors in Section 3.1 and Section 3.2, it can be seen that the anchor rods were located within the displacement zone, and the actual displacement zone of the slope was relatively large.

In order to verify the test results and clarify the deformation range of the slope, finite element software PLAXIS 3D was used to simulate the test slope. In the finite element model, the soil material was simulated by the Mohr–Coulomb model, the frame beam was simulated by conventional beam unit, the pile was simulated by plate unit, and the anchored section and free section of the anchor were simulated by embedded pile and point-to-point anchor, respectively. The incremental displacement obtained from the simulation reflected the deformation of the slope, so the slope incremental displacement was used to analyze the position of the slope sliding surface and the relative displacement in the sliding area. Figure 15a shows the incremental displacement shaded diagram, and Figure 15b shows the incremental displacement isosurface diagram. The Figure shows that the slope deformation range is large, and all the reinforced areas are within the deformation zone. The displacement of the intermediate level of the slope is obviously larger than that of the other two levels, and the largest displacement occurs at the foot of the intermediate level. When slope instability occurs, the slope may slide as a whole along the end of the anchored section and at the toe of the slope. It can be seen that the numerical simulation results are consistent with the conclusion that the anchor rods are all located within the deformation zone obtained from the tests.

4. Suggestions for the Design of Combined Support of a Pile-Anchor and Frame-Anchor for Multi-Level Soil Slopes

The potential deformation range of the multi-level slope under combined support of a pile-anchor and frame-anchor in the test is relatively large, and the anchor rods were located within the displacement zone. The force condition of the tested anchor rods was different from that of the anchor rods completely located in a stable soil layer. The anchoring force of the tested anchor rods was not fully utilized. The analysis suggests that this is mainly due to the lack of structural planes in multi-level soil slopes and the influence of support structures on the deformation range of slopes. The interaction between anchor rods and soil will induce a concerted deformation of the soil over a larger area. This makes it difficult to form a failure surface that passes through the anchor rods, and the sliding surface shifts towards the depth of the slope. Therefore, in order to further improve the performance of the support structure, the following suggestions are proposed for the design of combined pile-anchor and frame-anchor support for multi-stage soil slopes:

(1)

The potential deformation range of the frame-anchor support section is greatly influenced by the anchoring depth of the anchor rods. The design should strictly control the anchoring depth of the anchor rods, so that the potential sliding surface can move backwards, thereby increasing the sliding path;

(2)

In the pile-anchor support section, the improvement effect of anchor rods on the pile bending moment depends on whether the anchoring force can be effectively exerted. The support design should ensure that the anchor rods have sufficient length to anchor with deep soil, providing greater anchoring force and effectively improving the bearing capacity of the pile.

5. Conclusions

This paper took a multi-level slope under the combined support of a pile-anchor and frame-anchor as the research object, and conducted model experiments using a geotechnical centrifuge. The following conclusions were drawn:

(1)

The combined support structure of pile-anchors and frame-anchors had a good reinforcing effect on the multi-layer soil slope, but the deformation range of the slope was greatly influenced by the support structure, and the anchor rods were not in the absolutely stable soil layer.

(2)

In the pile-anchor support section, the anchoring force of the anchor rods was the highest, and the anchoring force effectively improved the bearing capacity of the pile. The bending moment followed an S-shaped distribution from top to bottom, with the maximum bending moment located at the foot of the slope. The soil pressure behind the pile was parabolic in distribution from top to bottom, and the resultant force point was between 1/3~1/2 of the height of the pile support section.

(3)

In the frame-anchor support section, the anchoring structure had a significant impact on the deformation range of the slope, and the anchor rods were not anchored in a stable soil layer. The strain values were distributed in an upward convex shape along the axial direction of the anchor rods. At different loading stages, the maximum axial strain was located at different monitoring points. The lateral frictional resistance at the end of the anchor rods occurred first and then gradually extended outward. The soil pressure on the frame gradually increased from top to bottom. The displacement trend of the slope was more obvious at the position where the soil pressure was higher, and the corresponding anchoring force of the anchor rods was also greater.

(4)

The deformation range of multi-level soil slopes was greatly influenced by the support structure. The design of the frame-anchor support section should strictly control the anchoring depth of the anchor rods, so as to make the potential sliding face move backward and increase the difficulty of sliding. The design of the pile-anchor support section should ensure that the anchor rods have sufficient length to provide greater anchoring force, thereby improving the bearing capacity of the pile.