The Bearing Characteristics of Sand Anchors under Vibrating Load

Abstract

In particular environments, such as the Gobi Desert, the problems encountered in a project are complex, resulting in reduced stability of the anchoring system and multiple forms of failure. This paper takes the factors influencing the stability of sand anchors under vibration loads as the research background. Theoretical analysis and indoor model tests were used to study the load-bearing performance of sand anchors under vibration loads; in addition, a comparative analysis of this performance along with failure forms of sand anchor systems, various sand soil moisture contents, and vibration parameters was performed. The results of the study showed that as the water content becomes higher, the cohesive force of the sand decreases and produces a higher displacement in the water content, with most of the anchor solids becoming prone to fatigue failure. When the water content and vibration frequency remain stable and the vibration amplitude increases, the anchor rod is disturbed after the ultimate pullout bearing capacity forms a decreasing trend, with a decline rate of approximately 40%. By keeping the water content and vibration amplitude stable and changing the vibration frequency, the ultimate pullout capacity of the anchor does not change significantly, and the frequency reaches a certain level when it attains a compacting effect on the surrounding soil and thus has less influence on the anchor. The anchor pullout resistance bearing is most sensitive to the change in sand moisture content, more sensitive to the vibration amplitude, and less sensitive to the vibration frequency, but its correlation is not significant.

1. Introduction

Anchor support is widely used in slope engineering, tunnel engineering, and underground foundation engineering and has become an important means of support for anchoring technology because of its reasonable force, adaptability, and ability to carry loads. During the use of the anchor support system, it is susceptible to dynamic loads such as vehicle, blasting, and impact. Under the action of a vibrating load, the strength and support structure of the geotechnical body are prone to damage and destruction, which seriously affects engineering safety [1]. Several authors have performed dynamic strain measurements with strain gauges mounted on the ends of anchor rods and performed velocity measurements with velocimeters mounted on anchor rods. The response of anchor rods under dynamic loading conditions was analyzed, and a numerical model was developed to explain the effects of dynamic loads caused by explosions on anchor rods [2,3,4]. Tutuncu et al. [5] analyzed sedimentary rocks under cyclic loading and showed that the characteristics of the stress–strain hysteresis curve are related to the frequency and amplitude of the cyclic loading. Zhu et al. [6], Yang et al. [7], and Jia et al. [8] established a dynamic three-dimensional numerical model to master the loss law of anchor cable prestress over time under the action of train vibration load; this formed theoretical guidance for the design and construction of anchor cables in deep and large foundation pits of adjacent railroads. Bao and Li [9] established the longitudinal one-dimensional anchor wave equation by the response law of stress waves in anchor rods and combined it with the theory of elastic dynamic principles to study the longitudinal vibration response under several boundary conditions. The main theory that the anchor rod vibration response is caused by dynamic transient vibration was deduced. Abbas and Mohamood [10] and Shrestha et al. [11] determined the optimal configuration of piles by developing a cyclic laboratory system that can test piles to comprehend the effect of axial load and pile shape on the performance of group piles under cyclic loading. Yao [12] used kinetic theory combined with numerical simulation software to show that the main influencing factors for the deformation of the roadway envelope are the length of the anchor and the distance anchor. Ivanović and Neilson [13] presented a continuous dynamic model for the axial vibration of rock anchor systems, examining the stiffness ratio of grout and anchor head relative to the fixed length anchor stiffness, and thus they provided a viable tool to help evaluate the condition of the bolts. Hagedorn [14] used a special dynamic test apparatus to calculate the maximum breaking load that could be transmitted by the grouting length of the anchors based on a large amount of measured data. Sun et al. [15] and Du et al. [16] used the properties of acoustic waves to perform nondestructive testing experiments on rock anchors and analyzed them based on the stress wave reflection method to create a solution for reducing the signal-to-noise ratio due to loading. Li et al. [17] customized a multifunctional experimental bench to filter and analyze stress wave signals using the VMD decomposition method and Hilbert-Huang signal processing method; the customization was used to verify the effectiveness of the stress-wave-based nondestructive testing method for anchor rods.

Many scholars have conducted studies on soil anchors. Kim et al. [18,19,20] effectively predicted the load–displacement curve of anchors by modeling the soil, grout, anchor rod, and anchor-soil interface and performing a finite element analysis of the anchor rod using the proposed model. To ensure the stability of deep foundation pits and slopes, the reinforcement effect of multirow piles as well as prestressed anchor cables on deep foundation pits and slopes was investigated thoroughly through engineering monitoring and other means. The timeliness of data during construction was improved to provide a reference for the construction information on related working conditions [21,22,23,24]. Joseph [25] used a total of four different types of reinforcement materials and four different internal diameter circular foundation models to investigate the effect of the foundation chronology ratio on the bearing capacity of sand layers under different reinforcement conditions. Hu and Hsu [26,27] found that frictional stresses in various anchor rods in sandy soils exhibit progressive yielding along the fixed ends of anchor rods with longer fixed lengths and can be eliminated by using composite anchor rods. To improve the bearing capacity of anchor rods in sandy soils, anchor plates in sandy soils were analyzed by theoretical calculation results and model tests, and the variation laws of vibration time, constant strain rate, axial plate diameter, plate thickness/plate diameter, and boundary distance with the load–displacement curve were investigated [28,29,30]. Ren et al. [31] established computational models with the help of field tests using ANSYS/LS-DYNA software. The axial force, interfacial shear force, and deformation distribution of anchorages at different deformation stages were deduced, thus improving the accuracy of geotechnical anchorage work. Other scholars analyzed the dynamic response characteristics in terms of slope displacement, horizontal and vertical velocity, acceleration, maximum principal stress, and anchor cable axial force using MIDAS/GTS numerical simulations and centrifuge model experimental studies; the analysis aimed to conduct an in-depth study of the anchorage mechanism of slope anchor cables under seismic action [32,33,34,35].

In view of the above background, this paper mainly studies the effect of a vibrating load on the bearing capacity of sandy soil anchors. Due to the special soil quality of sandy soil, it produces large deformation under the action of vibration loads, such as earthquakes and vehicle impacts, which seriously threatens engineering safety. Therefore, the effect of the vibration load on sandy soil anchor rods needs to be considered. The author focuses on the effects of sand soil moisture content, vibration amplitude, and vibration frequency on the bearing capacity of sand soil anchors while vibrating.

2. Test Details

2.1. Materials

The sandy soil in this test was taken from the typical sandy soil in the Inner Mongolia region; the soil has a depth of 0.5–1 m. The soil was air-dried, crushed, and stored in a cool, dry place. The basic physical and mechanical properties of the soil samples were tested according to the Standard for Geotechnical Test Methods (GB/T 50123-2019) [36]. The tests included a specific gravity test (GB/T 7.1–7.2), sieve test (GB/T 8.1–8.2), and straight shear test (GB/T 21.1–21.4). The basic physical properties of the soil are shown in the following charts (

Table 1. Overview of the physical and mechanical parameters of soils.

Name	Fineness Modulus	Porosity/%	Dry Density/g·cm−3	Wet Density/g·cm−3
Sandy soil	0.194	40.98	1.42	1.51

and Figure 1 and Figure 2). The sand soils were prepared with 10%, 12%, and 14% moisture content according to the test requirements, and their densities were 1.72 g/cm³, 1.75 g/cm^3, and 1.73 g/cm³, respectively. The anchor hole grouting material was standard sand, ordinary silicate cement, and water at a ratio of 1:1:0.43, and ordinary silicate cement with strength class 42.5 was used, the basic properties of which are shown in

Table 2. Basic performance parameters of cement.

Characteristics	Fineness (mm)	Compressive Strength (MPa)		Flexural Strength (MPa)		Setting Time (min)		Standard Consistency
		3 d	7 d	3 d	7 d	3 d	7 d
Value	0.03	28.4	84.3	4.9	7.8	180	370	30

3 d, 7 d: cement setting times of 3 days and 7 days.

. The anchors are made of common ribbed steel bars with a diameter of 14 mm.

2.2. Testing Instruments

To study the factors related to the influence of wind accumulation sand anchors under vibration load, an electrohydraulic servo fatigue test system is used in this paper. The system consists of a host, controller, servo-hydraulic source, microcomputer control system, movable counterforce frame, actuator, and model test box with other functional accessories and units. The test system is a single-axis axial loader, with a servo valve as the control core and controller to form an automatic control system, mainly used for fatigue testing of the specimen. The servo-hydraulic source is a device that converts electrical energy into hydraulic energy and provides hydraulic power to the actuating element; its rated pressure is 21 MPa. The actuator can provide a maximum force value of 50 kN, which can meet a variety of conditions. The model test chamber is made of a 5 cm steel plate welded together, which has the advantages of high load capacity and easy operation. The test system is shown in Figure 3.

2.3. Test Method

Given the purpose of this paper, the experimental design is divided into two main parts: static load test and dynamic load test. First, the ultimate pullout load capacity was obtained by static pullout tests on anchors of different diameters under different moisture content conditions, and the results were recorded. The center value, vibration frequency, and vibration amplitude of the vibration load are set with reference to the ultimate pullout load capacity of the static load test. Hence, the disturbance of anchor rods caused by earthquakes and blasting high-speed train loads is simulated and compared with the load-bearing characteristics of anchor rods under natural anchorage conditions. The main test conditions are shown in

Table 3. Experimental protocol.

Number	Anchor Solid Diameter/mm	Frequency/Hz	Average Load/kN	Amplitude/kN	Moisture Content/%
1	60	/	/	/	10, 12, 14
2	80
3	100
4	60	5		30% F1
5			50% F1	40% F1
6				50% F1
7	80	5		30% F1	10, 12, 14
8			50% F1	40% F1
9				50% F1
10	100	5		30% F1
11			50% F1	40% F1
12				50% F1
13	100	8		30% F1	10, 12, 14
14			50% F1	40% F1
15				50% F1
16	100	10		30% F1
17			50% F1	40% F1
18				50% F1

F1 is the ultimate pullout capacity of the anchor under static load.

.

(1)

Anchor preparation. The anchor rods used in this test are ordinary ribbed steel bars with a diameter of 14 mm, and the anchor solids are prepared with a length of 30 d and a length of approximately 400 mm with reference to literature. Three sizes are used for the diameter, 60 mm, 80 mm, and 100 mm. The rebar was first intercepted to a length of 1.25 m, and the section was smoothed with sandpaper to be set aside. The anchor solid was precast in a cylindrical acrylic mold with a thickness of 9 mm. The hollow cylindrical acrylic plate was cut from the middle, and the cut was smoothed with sandpaper. The inner wall and the lid were evenly coated with machine oil, which was brushed and then combined, while the bottom lid, which was lined with moistened filter paper, was covered and sealed with tape wrapped around the bottom. The reinforcement is inserted and fixed to the center by passing through the predrilled holes in the bottom cover. Water, cement, and standard sand are evenly poured for 3 min into the mixer according to the ratio and mix. The well-mixed cement mortar is introduced into the acrylic mold; to prevent air bubbles from affecting the strength of the anchor solids during the introduction process, the air bubbles are continuously vibrated and removed during the introduction process. The anchor solids were de-molded and placed in a dry and cool place for maintenance for 14 d. The anchor solids were sealed with tape wrapped around the top cover after the introduction. To simulate the process of cementing anchor solids with sandy soil during casting-in-place, the surface of anchor solids was poured roughly and polished with sandpaper. The cement mortar used for pouring the anchor solids was composed of standard sand, ordinary silicate cement, and water at 1:1:0.43.

(2)

Test piece production. The retrieved sand was placed in an oven to dry the moisture and sieved using a 2 mm sieve. The required moisture content is configured according to the test protocol, and the configured soil is mixed well and then placed in a sealed bag for 24 h to ensure that the moisture evenly diffuses. The model box for the test is cleaned, and after the sand reaches the maintenance time, the model box is filled by the layered filling method, leveled with a ruler every 15 cm during filling, and tamped with a concrete standard test block weighing approximately 3 kg, and the bottom of the model box is first filled with a layer and then tamped. In this process, the prefabricated and maintained anchor rods are placed in the model box, and the anchor rod aligner is placed above the model box and fixed in the middle of the box using the anchor rod aligner. The next step is to fill in the configured sandy soil in layers and tamp it with concrete standard test blocks until it reaches the specified filling height. Then, the anchor aligner is removed, and the soil is leveled. After the filling is completed, a layer of cling film is placed on the surface of the leveled sand, and a thermal insulation cover is placed to reduce moisture loss and is left for half a day. When the sand settles and stabilizes, the insulation board is opened, the cling film is removed, and the actuator is placed directly above the anchor with the movable reaction frame. The controller and the oil source are turned on to adjust the hydraulic clamp position so that it can clamp the anchor rod smoothly. The software parameters are set, a vibration load is applied to the anchor rod with a specific vibration wave type, and the changes in the anchor rod and sand under the vibration load are observed and recorded. The test is stopped after the change becomes stable or the anchor rod fails and the relevant data are recorded and saved. The experimental procedure is shown in Figure 4.

3. Results and Analysis

3.1. Anchor Ultimate Pullout Force Test under Static Load

The test was completed in the laboratory in the structural plant of the Hebei Institute of Construction Engineering, and the instrument used in the test was a PA-50J electrohydraulic servo fatigue test system manufactured by Jilin Guanteng Automation Technology Co., Jilin, China. This test system can complete a variety of tests: the tensile test, compression test, and low-temperature test. It can apply cyclic loads by selecting various forms of waveforms, mainly sine waves, triangle waves, and custom waves. The test system has a wide range of loading frequencies and can provide a variety of loading frequencies for cyclic loads. The instrumentation is shown in Figure 5.

Ultimate Pullout Force of the Anchor Rod under Static Load

To understand the effect of different water contents on the bearing performance of sand anchors and the form of failure and to provide reference data for the subsequent dynamic load test, the tests were carried out for different diameters of anchor solids with the same moisture content.

The loading test under static load is conducted using the displacement-controlled loading method. The test data are recorded in real time through the test software with built-in sensors. The displacement loading rate is 6 mm/min, and the end of the test is controlled by the displacement control method, setting the final displacement to 10 mm and determining the anchor failure according to the change in its anchor-bearing capacity. The data are organized, and the following graph is created.

Figure 6 shows the pullout bearing capacity–displacement relationship curves of sandy soil anchor rods with different anchor diameters under the same moisture content. From the above figure, it can be seen that the anchorage force of the anchor rod increases as the anchor solid diameter under the static load is increased with the same water content in the sandy soil.

Figure 7 shows the pullout bearing capacity–displacement relationship curves of sandy soil anchor rods with the same anchorage diameter under different water content conditions. From the above figure, it can be seen that the anchorage force of the anchor rod under static load with the same anchorage diameter is inversely proportional to the moisture content of sandy soil and it decreases with the increase in the moisture content of sandy soil.

Comprehensive Figure 6 and Figure 7 show that the change curve of the anchor pullout bearing capacity with displacement basically maintains a similar development law, and the anchor pullout bearing capacity–displacement curve under static load is divided into three stages. In the first stage, the static load is applied to the anchor rod at the beginning when the vertical displacement of the anchor rod is small. Under this action, the sandy soil suffers compression, and the anchor pullout bearing capacity grows linearly with the displacement. Therefore, the anchor solid does not provide pullout bearing capacity, and the main pullout force is provided by the frictional force at the anchor-soil interface. In the second stage, as the loading process proceeds, the vertical displacement of the anchor rod increases. The friction force at the anchor-soil interface reaches the maximum value, the anchor solid starts to provide the pullout resistance, and the relationship curve between the pullout resistance and displacement of the anchor rod becomes parabolic. This phase produces a clear turning point, and the slope continues to decrease after the turning point. In the third stage, the displacement continues to increase, the slope tends to zero, the pullout bearing capacity no longer grows, and the soil surface is destroyed, at which time the anchor fails. At the end of this process, it was found that the soil surface was mainly in the form of mesh damage (see Figure 8).

3.2. Study on the Bearing Characteristics of Anchor Rods under a Vibration Load

The vibration for this experiment was loaded using a sinusoidal wave. The main loading process is the following steps. First, the loading speed is increased to a certain load at 6 mm/min, and then the test is performed according to the sine wave vibration mode. The main loading characteristics of the sine wave are shown in Figure 9. T is the cycle period, and $F_{\max }$ is the maximum value of the vibration load. $F_{\min }$ is the minimum value of the vibration load. $F_a=(F_{\max }+F_{\min })/2$ is the average load, and $F=(F_{\max }-F_{\min })$ is the amplitude of the vibration load.

3.2.1. Effect of Water Content on Bearing Capacity of Anchor Rods under Vibrating Load

Figure 10 shows the anchor-bearing capacity–displacement curve under vibration loads with different sand moisture contents of the same diameter. The tests mainly used anchor solids with diameters of 60 mm, 80 mm, and 100 mm to vary the moisture content of sandy soil under the same vibration frequency vibration load, and three main sandy soil moisture contents of 10%, 12%, and 14% were set. To keep the vibration frequency consistent, the vibration frequency was set to 5 Hz when the vibration load was applied.

The diameter of the anchor solid is 60 mm, and the moisture content of the sand is 10%. First, the anchor was loaded at a rate of 6 mm/min to 65% of the ultimate pullout capacity (F1) under static anchor load, and this load value was approximately 0.85 kN, and it was the peak value of this vibration load. The valley value is 35% of the ultimate pullout bearing capacity under the static load of the anchor, and the value of this load is approximately 0.46 kN. The amplitude of the vibration load is 30% F1, and its value is approximately 0.39 kN. The average load is 50% F1, and the number of vibrations is 1000. As seen in Figure 10a, the anchor solid displacement has a large sudden change and rapid growth and has reached the fatigue failure state. Repeating the above steps, vibratory loads were applied to the sand specimens with 12% and 14% moisture content. The anchor solids have reached the fatigue failure state under this vibration load condition.

The diameter of the anchor solid is 80 mm, and the moisture content of the sand is 10%. First, the anchor was loaded at a rate of 6 mm/min to 65% of the ultimate pullout capacity (F1) under static anchor load, and the value of this load was approximately 1.03 kN, and it was the peak value of this vibration load. The valley value was 35% of the ultimate pullout capacity under static anchor load, and the value of this load was approximately 0.56 kN. The amplitude of the vibration load was 30% F1, and its value was approximately 0.48 kN. The average load was 50% F1, and the number of vibrations was 1000. As seen in Figure 10b, the anchor solid produced a displacement of 0.59 mm at the initial stage of loading, which is a small displacement. After the application of the vibration load, the anchor solid produced an upward displacement of approximately 2 mm, and it did not fail. At a later stage of destructive testing, the anchor solid produced a displacement of 2.8 mm, and its remaining bearing capacity was approximately 1.13 kN, which is a 28.9% reduction in bearing capacity. The above operation was repeated, and vibratory loads were applied to the sand specimens with 12% and 14% moisture content. The anchor solids reached the fatigue failure state under this vibration load condition.

The diameter of the anchor solid is 100 mm, and the moisture content of the sand is 10%. First, the anchor was loaded at a rate of 6 mm/min to 65% of the ultimate pullout resistance (F1) under static anchor load, and the value of this load was approximately 1.22 kN, which was the peak of this vibration load. The valley value was 35% of the ultimate pullout resistance under static anchor load, and the value of this load was approximately 0.66 kN. The amplitude of the vibration load was 30% Fmax, and its value was approximately 0.56 kN. The average load was 50% F1, and the number of vibrations was 1000. As seen in Figure 10c, the anchor solid produced a displacement of 0.75 mm at the initial stage of loading, which is a small displacement. After the application of the vibration load, the anchor solid produced an upward displacement of approximately 1.8 mm, and it did not fail. In the later destructive testing stage, the anchor solid produced a 3 mm displacement, and its remaining bearing capacity was approximately 1.41 kN, which was reduced by 24.6%. At 12% moisture content of sand, the displacement was approximately 0.57 mm at the initial stage of uniform loading to 1.11 kN, which was small; after the vibration load, the anchor solid produced approximately 1.7 mm of upward displacement, and it did not fail. In the later destructive testing stage, the anchor solid produced a 2.85 mm displacement, and its remaining bearing capacity was approximately 1.18 kN, which is a 30.9% reduction in bearing capacity. Repeating the above operation, the anchor solid reached the fatigue failure state when the moisture content of the sand was 14%.

It can be seen that the ultimate pullout resistance of the anchor solids under this vibration load varies greatly, and the load capacity decreases significantly after the vibration load disturbance, which is due to the water content becoming higher, the cohesiveness of the sand soil decreasing and producing larger displacement under the action of high-water content, causing fatigue failure of most of the anchor solids.

3.2.2. Effect of Vibration Frequency on the Bearing Capacity of Anchor Rods under Vibration Load

As shown in Figure 11, the bearing capacity–displacement curves of anchor rods with different vibration frequencies of the same diameter are shown. An anchor solid of 100 mm diameter was used for the test. The vibration frequency of the vibration load was changed under the same moisture content condition, and three vibration frequencies of 5 Hz, 8 Hz, and 10 Hz were set.

In the state of sand soil moisture content of 10%, the first loading takes place at the rate of 6 mm/min to 65% of the ultimate pullout resistance (F1) under the action of anchor static load. This load value is approximately 1.22 kN, which is the peak of this vibration load; the valley value is 35% of the ultimate pullout resistance under the action of anchor static load, which is a load value of approximately 0.66 kN; the amplitude of the vibration load is 30% F1; its value is approximately 0.56 kN; the average load is 50% F1; and the number of vibrations is 1000. As seen in Figure 11a, the vibration frequency was first set to 5 Hz when the vibration load was applied at the beginning, and the anchor solid produced a displacement of 0.75 mm at the initial stage of loading, which was small. After the application of the vibration load, the anchor solid produced an upward displacement of approximately 1.8 mm, and it did not fail. In the later destructive testing phase, the anchor solid produced a 3 mm displacement, and its remaining bearing capacity was approximately 1.41 kN, which is a 24.6% reduction in bearing capacity. Repeating the above steps and changing the vibration frequency to 8 Hz, the anchor solid produced a small displacement of 0.73 mm during the initial loading phase. After the application of the vibration load, the anchor solid produced an upward displacement of approximately 1.58 mm, and it did not fail. In the later destructive testing phase, the anchor solid produced a displacement of 2.1 mm, and its remaining bearing capacity was approximately 1.6 kN, which is a 14.4% reduction in bearing capacity. Repeating the above steps and changing the vibration frequency to 10 Hz, the anchor solid produced a displacement of 0.72 mm in the initial stage of loading, which was smaller. After the application of vibratory loads, the anchor solid produced an upward displacement of approximately 1.38 mm, and it did not fail. In the later destructive testing phase, the anchor solid produced a displacement of 1.76 mm, and its remaining bearing capacity was approximately 1.8 kN and had a 3.74% reduction in bearing capacity.

In the state of 12% moisture content of sand soil, first, loading took place at the rate of 6 mm/min to 65% of the ultimate pullout resistance (F1) under the action of anchor static load, and this load value is approximately 1.11 kN, which is the peak of this vibration load. The valley value is 35% of the ultimate pullout resistance under the action of anchor static load, and this load value is approximately 0.59 kN. The amplitude of the vibration load is 30% F1, and its value is approximately 0.52 kN. The average load is 50% F1, and the number of vibrations is 1000. As seen in Figure 11b, the vibration frequency was first set to 5 Hz when the vibration load was applied at the beginning, and the anchor solid produced a displacement of 0.57 mm at the initial stage of loading, which was small. After the application of the vibration load, the anchor solid produced an upward displacement of approximately 1.7 mm, and it did not fail. In the later destructive testing phase, the anchor solid produced a displacement of 2.85 mm, leaving a bearing capacity of approximately 1.18 kN, which is a 30.9% reduction in bearing capacity. Repeating the above steps and changing the vibration frequency to 8 Hz, the anchor solid produced a displacement of 0.6 mm in the initial stage of loading, which was smaller. After the application of vibratory loads, the anchor solid produced an upward displacement of approximately 1.25 mm, and it did not fail. In the later destructive testing phase, the anchor solid produced a displacement of 2.15 mm, and its remaining bearing capacity was approximately 1.36 kN, which is a 20.5% reduction in bearing capacity. Repeating the above steps and changing the vibration frequency to 10 Hz, the anchor solid produced a displacement of 0.58 mm at the initial stage of loading, which is a small displacement. After applying the vibration load, the anchor solid produced an upward displacement of approximately 1.6 mm, and it did not fail. At a later stage of destructive testing, the anchor solid produced a displacement of 1.96 mm, and its remaining bearing capacity was approximately 1.58 kN, with a 7.6% reduction in bearing capacity.

In the state of sand soil moisture content of 14%, first, the loading took place at the rate of 6 mm/min to 65% of the ultimate pullout resistance (F1) under the action of anchor static load, and this load value is approximately 0.87 kN, which is the peak of this vibration load. The valley value is 35% of the ultimate pullout resistance under the action of anchor static load, with a load value of approximately 0.47 kN. The amplitude of the vibration load is 30% F1, its value is approximately 0.4 kN, the average load is 50% F1, and the number of vibrations is 1000. From Figure 11c, it can be seen that the anchor solid with a diameter of 100 mm has a large sudden change in displacement at different vibration frequencies. The displacement growth is fast, and all of them have reached the fatigue failure state.

Under the same moisture content conditions, the ultimate pullout resistance of anchor solids under such a vibration load mainly decreases, and the load capacity decreases significantly when the vibration frequency is 5 Hz, while the ultimate pullout resistance does not change significantly when the vibration frequency is 8 Hz and 10 Hz. After the vibration load disturbance, the ultimate pullout resistance only decreases slightly and can withstand displacement under high vibration frequencies. The change in the anchor solid pullout bearing capacity after vibration load disturbance is mainly due to the small number of vibrations. Under the same number of vibrations, the high-frequency vibrations produce a compression-density effect on the soil around the anchor solid, and no fatigue failure occurs in the anchor solid during the whole vibration process, so the change in the anchor solid ultimate bearing capacity under the high-frequency vibration load is small.

3.2.3. Effect of Vibration Amplitude on the Bearing Capacity of Anchor Rods under Vibration Load

As shown in Figure 12, the bearing capacity–displacement curves of anchor rods under different amplitude vibration loads of the same diameter are shown. An anchor solid of 100 mm diameter was used for the test. The amplitude of the vibration load was changed under the same moisture content condition, and three amplitudes of 30% F1, 40% F1, and 50% F1 were set. To keep the vibration frequency consistent, the vibration frequency was set to 5 Hz when the vibration load was applied.

In the state of sand soil moisture content of 10%, first, loading took place at the rate of 6 mm/min to 65% of the ultimate pullout resistance (F1) under the action of anchor static load, and this load value is approximately 1.22 kN, which is the peak of this vibration load. The valley value is 35% of the ultimate pullout resistance under the action of anchor static load, with a load value of approximately 0.66 kN. The amplitude of the vibration load is 30% F1, its value is approximately 0.56 kN, the average load is 50% F1, and the number of vibrations is 1000. As seen in Figure 12a, the anchor solid produced a displacement of 0.75 mm at the initial stage of loading, which is a small displacement. After the application of the vibration load, the anchor solid produced an upward displacement of approximately 1.8 mm, and it did not fail. In the later destructive testing phase, the anchor solid produced a 3 mm displacement, and its remaining bearing capacity was approximately 1.41 kN, with a 24.6% reduction in bearing capacity. The above operation is repeated to change the amplitude of the vibration load. The amplitude of the vibration load is 40% of F1, and the load is 0.74 kN. The peak is 70% of the ultimate pullout resistance, and the load is 1.31 kN. The trough is 30% of the ultimate pullout resistance, and the load is 0.56 kN. The displacement of the anchor solid at the initial stage of loading is 0.79 mm, which is small. After the application of vibratory loads, the anchor solid produced an upward displacement of approximately 2.06 mm, and it did not fail. In the later destructive testing phase, the anchor solid produced a displacement of 3.47 mm, and its remaining bearing capacity was approximately 1.28 kN, with a 31.6% reduction in bearing capacity. The amplitude of the vibration load is 50% of F1, which is 0.93 kN. The peak of the load is 75% of the ultimate pullout capacity, which is 1.4 kN, and the trough is 25% of the ultimate pullout capacity, which is 0.47 kN. The displacement of the anchor solid at the initial stage of loading is 0.82 mm, which is small. After the application of the vibration load, the anchor solid produced an upward displacement of approximately 2.14 mm, and it did not fail. In the later destructive testing stage, the anchor solid produced a 2.6 mm displacement, and its remaining bearing capacity was approximately 1.1 kN, with a 41.2% reduction in bearing capacity.

In the state of 12% moisture content of sand soil, first, loading took place at the rate of 6 mm/min to 65% of the ultimate pullout resistance (F1) under the action of anchor static load, and this load value is approximately 1.11 kN, which is the peak of this vibration load; the valley value is 35% of the ultimate pullout resistance under the action of anchor static load, and this load value is approximately 0.59 kN; the amplitude of vibration load is 30% F1, and its value is approximately 0.52 kN, the average load is 50% F1, and the number of vibrations is 1000. The above Figure 12b shows that the anchor solid produces a displacement of 0.57 mm at the initial stage of loading, which is a small displacement. After applying the vibration load, the anchor solid produced an upward displacement of approximately 1.7 mm, and it did not fail. In the later destructive testing stage, the anchor solid produced a 2.85 mm displacement, and the remaining bearing capacity was approximately 1.18 kN, with a 30.9% reduction in bearing capacity. The above operation is repeated to change the amplitude of the vibration load. The amplitude of the vibrating load was 40% of F1, and the load was 0.69 kN. The peak was 70% of the ultimate pullout resistance, and the load was 1.2 kN; the trough was 30% of the ultimate pullout resistance, and the load was 0.51 kN. The displacement of the anchor solid at the initial stage of loading was 0.6 mm, which was small. After the application of the vibration load, the anchor solid produced an upward displacement of approximately 1.85 mm, and it did not fail. At a later stage of destructive testing, the anchor solid produced a 3.1 mm displacement, and its remaining bearing capacity was approximately 0.99 kN, with a 42.1% reduction in bearing capacity. The amplitude of the vibration load is 50% of F1, which is 0.85 kN. The peak of the load is 75% of the ultimate pullout resistance, which is 1.28 kN, and the trough is 25% of the ultimate pullout resistance, which is 0.43 kN. The displacement of the anchor solid at the initial stage of loading is 0.64 mm, which is small. After the application of the vibration load, the anchor solid produced an upward displacement of approximately 2.05 mm, and it did not fail. In the later destructive testing stage, the anchor solid produced a 3.1 mm displacement, and its remaining bearing capacity was approximately 0.95 kN, with a 44.1% reduction in bearing capacity.

In the state of sand soil moisture content of 14%, first, the loading took place at the rate of 6 mm/min to 65% of the ultimate pullout resistance (F1) under the action of anchor static load, and this load value is approximately 0.87 kN, which is the peak of this vibration load. The valley value is 35% of the ultimate pullout resistance under the action of the anchor static load, with a load value of approximately 0.47 kN. The amplitude of the vibration load is 30% F1, its value is approximately 0.4 kN, the average load is 50% F1, and the number of vibrations is 1000. The above operation was repeated to change the amplitude of the vibration load. The amplitudes are 40% F1 and 50% F1, and the average load is 50% F1. From Figure 12c, it can be seen that the anchor solid with a diameter of 100 mm has reached the fatigue failure state due to the large sudden change in displacement and fast growth of displacement at different amplitudes.

The ultimate pullout resistance of anchor solids under such a vibrating load change significantly under the same moisture content condition. After the vibration load is disturbed, the ultimate pullout resistance decreases significantly. The main reason for the decrease in the ultimate pullout resistance of the anchor solid under this vibration load is the increase in the vibration load amplitude. After the application of vibration load, the high amplitude vibration causes cracks and damage at the anchor-soil interface, thus causing the anchor solid to have a lower ultimate pullout capacity than the static load after the vibration load disturbance and even at the anchor fatigue failure state.

4. Discussion

Previous studies analyzed the anchor force of anchors under the vibration loads by considering the energy conversion method [6,7,8]. The anchors were subjected to the vibratory load, although no macroscopic features of damage were evident. However, the anchoring effect under the vibration load is weakened. Thus, this research mainly evaluates the residual anchorage force of anchor rods under the vibration load by destructive testing. When the water content increases, the shear strength and friction at the anchor-soil interface decrease, which is more evident when the vibratory load is applied to the anchors.

Factors such as different vibration amplitudes, vibration frequencies, and water contents of the sand have certain effects on the residual anchorage force. When the water content and vibration frequency are constant, the ultimate pullout bearing capacity presents a decreasing trend as the vibration amplitude increases, with a decline rate of approximately 40%. By keeping the water content and vibration amplitude constant, the ultimate pullout capacity does not change significantly as the vibration changes, with a decline rate of approximately 10%. Thus, compared with the vibration frequency, the vibration amplitude has a greater weakening effect on the anchor anchorage force. These research results are expected to provide a key reference for the design of sandy soil anchor rods under vibration loading, so as to improve the reinforcement effect of the sand anchors.

5. Conclusions

For the study of the bearing characteristics of sandy soil anchor rods under vibration loading, this paper uses the self-developed indoor anchor-pulling system to conduct anchor-pulling tests and investigate the effects of changes in sandy soil moisture content, vibration amplitude, and vibration frequency on the bearing characteristics of sandy soil anchor rods. Based on a basic theory, this paper uses an indoor model test to further analyze the damage mode during the specimen-pulling process. The main conclusions are as follows:

(1)

Under the condition that the vibration frequency, vibration amplitude, and vibration number are certain, the ultimate pullout capacity of anchor solids decreases with the change in moisture content of sand and soil, and the decrease is large. This is because as the water content becomes higher, the cohesive force of sand and soil decreases, the ultimate pullout resistance of anchor solids decreases rapidly after vibration load disturbance, and most anchor solids exhibit fatigue failure.

(2)

The ultimate pullout capacity of anchor solids did not change significantly under the condition that the vibration amplitude and the number of vibrations were constant when vibration loads were applied to anchor rods of the same diameter at different vibration frequencies. When the vibration frequency was 5 Hz, the anchor solid bearing capacity changed significantly after the vibration load disturbance and it decreased significantly; when the vibration frequency was increased to 8 Hz, the anchor solid bearing capacity changed less after the vibration load disturbance and decreased slightly; when the vibration frequency was increased to 10 Hz, the anchor solid ultimate bearing capacity remained the same compared with that under static load.

(3)

The ultimate pullout resistance of anchor solids changes significantly under the condition that the vibration frequency and the number of vibrations are certain when vibration loads are applied to anchor rods of the same diameter at different vibration amplitudes. With a vibration amplitude of 30% F1, the change in the ultimate pullout resistance of the anchor solid is small; with the increase in vibration amplitude to 40% F1 and 50% F1, the ultimate pullout resistance of the anchor solid decreases significantly after the vibration load disturbance, and the bearing capacity decreases rapidly.

(4)

In terms of ultimate pullout bearing capacity, anchor solids are sensitive to changes in the water content of sandy soil. By analyzing the anchor solid with a 100 mm diameter, it turned out to be sensitive to both vibration frequency and vibration amplitude after vibration load disturbance, but the correlation was not significant.

(5)

In this article, the model test limited by the model box lacks microscopic study. A dynamic strain collector should be added to collect the stress–strain at the anchor-soil interface. Add microscopic analysis of the anchor-soil damage interface.