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Article

Experimental Investigation on Unloading-Induced Sliding Behavior of Dry Sands Subjected to Constant Shear Force

by
Wengang Dang
1,2,3,
Kang Tao
4,
Jinyang Fu
3,5,* and
Bangbiao Wu
1
1
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China
2
State Key Laboratory for Tunnel Engineering, School of Civil Engineering, Sun Yat-sen University, Zhuhai 519086, China
3
National Engineering Research Center of High-Speed Railway Construction Technology, Changsha 410075, China
4
Institut für Geotechnik, TU Bergakademie Freiberg, 09599 Freiberg, Germany
5
School of Civil Engineering, Central South University, Changsha 410075, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2025, 15(1), 401; https://doi.org/10.3390/app15010401
Submission received: 4 December 2024 / Revised: 26 December 2024 / Accepted: 2 January 2025 / Published: 3 January 2025
(This article belongs to the Topic Geotechnics for Hazard Mitigation)
Browse Figures
Figure 1
<p>Testing apparatus and experimental materials: (<b>a</b>) the DJZ-500 shear box device; (<b>b</b>) dry sands used in tests; and (<b>c</b>) grain grading curve of the sand samples.</p> "> Figure 2
<p>Experimental configuration: (<b>a</b>) setup of direct shear test under unloading normal force and constant shear force; (<b>b</b>) normal and shear force application scheme during three-stage loading process.</p> "> Figure 3
<p>Normal force variation as function of elapsed time and experimental results of normal and sliding displacement versus time for each test. (<b>a</b>) Normal force, normal displacement, and sliding displacement versus time for different unloading rates (Group A). (<b>b</b>) Normal force, normal displacement, and sliding displacement versus time for different shear force (Group B).</p> "> Figure 4
<p>Sliding velocity versus time for each test since the beginning moment of normal unloading. (<b>a</b>) Sliding velocity versus time for different unloading rates. (<b>b</b>) Sliding velocity versus time for different shear force.</p> "> Figure 5
<p>(<b>a</b>) Relationship between shear displacement and shear force under <span class="html-italic">F</span><sub>N</sub> = 30 kN in a conventional direct shear test. Within the displacement range, the shear strength of the granular material keeps increasing with larger shear displacement. (<b>b</b>) The peak shear force (shear strength) for different normal force in 0.0833 mm/s shear-displacement-controlled conventional direct shear test. (<b>c</b>) Shear displacement (solid lines) and normal displacement (dash lines) versus time for low (0.08 kN/s) and high (0.8 kN/s) unloading rates extracted from <a href="#applsci-15-00401-f003" class="html-fig">Figure 3</a>a and illustration to explain sliding deceleration/intermission.</p> "> Figure 6
<p>Variation in normal force at different sliding velocities. (<b>a</b>) For different unloading rate (Group A) and (<b>b</b>) for different shear force (Group B).</p> "> Figure 7
<p>Normal force versus unloading rate and shear force at sliding velocity of (<b>a</b>) 3.7 mm/s, (<b>b</b>) 2.5 mm/s, and (<b>c</b>) 1.5 mm/s.</p> "> Figure 8
<p>(<b>a</b>) Apparent friction coefficient when the sliding velocity reaches 3.7 mm/s (i.e., ultimate value in the test) for different unloading rates and different shear force. (<b>b</b>) Apparent friction coefficient versus unloading rate and shear force at sliding velocity of 3.7 mm/s. (<b>c</b>) The variation in friction coefficient versus normal unloading time for different shear force (the recorded data in Group B). The different colors represent different single tests.</p> ">
Versions Notes

Abstract

:
Infilled joints or faults are often subjected to long-term stable shear forces, and nature surface processes of normal unloading can change the frictional balance. Therefore, it is essential to study the sliding behavior of such granular materials under such unloading conditions, since they are usually the filling matter. We conducted two groups of normal unloading direct shear tests considering two variables: unloading rate and the magnitude of constant shear force. Dry sands may slide discontinuously during normal unloading, and the slip velocity does not increase uniformly with unloading time. Due to horizontal particle interlacing and normal relaxation, there will be sliding velocity fluctuations and even temporary intermissions. At the stage of sliding acceleration, the normal force decreases with a higher unloading rate and increases with a larger shear force at the same sliding velocity. The normal forces obtained from the tests are less than those calculated by Coulomb’s theory in the conventional constant-rate shear test. Under the same unloading rate, the range of apparent friction coefficient variation is narrower under larger shear forces. This study has revealed the movement patterns of natural granular layers and is of enlightening significance in the prevention of corresponding geohazards.

1. Introduction

Granular matter is widely distributed in the earth’s lithosphere and surface. Under long-term complex geological action, faults and joints on the earth are usually filled by grained gouges (quartz, clay, and phyllosilicates, etc.). The convex bodies on the ordinary fault surfaces will break under shear and compression. This can cause the fracture zone of the fault to be filled by small-sized grains, forming a fault gouge with a thickness of several meters [1,2,3]. When the gouge reaches a certain thickness, the shear strength of the structural surface will depend entirely on the characteristics of the filler [2,3], making the particle-filled structure more prone to damage under critical loading conditions.
The granular materials acting as gouges in joints or faults are often subjected to long-term stable shear forces. Human activities (e.g., reservoir drainage or excavation works), earth’s surface processes (river cutting or glacial ablation, etc.) or tectonic movements [4,5,6,7] can change the stress state of these earth masses in the disturbed areas. Mostly, a pre-existing fault zone subjected to normal and shear stresses was initially in a frictional equilibrium state. The normal stress was larger than the shear stress. The reduced normal stress applied to the fault zone causes the deformation of the fault gouges in the fault segment. Specifically, if excavating a tunnel near a fault zone, the normal stress on the fault will be reduced [5]. Also, for example, when an earthquake wave from a distance is transmitted to a sheared fault, the normal stress applied will also drop sharply. Consequently, intensive unloading and stress redistributions can lead to the fast sliding of earth, causing landslides, ground surface cracking, and earthquakes [4,6,7]. Many former studies have focused on baldly contacted rock joints [8,9,10] or a small block sample with a thin layer of gouge [11,12,13,14,15,16] under the conditions of normal turbulence [8,9,10,11,12,13,14,15,16]. The effects of the characteristics of fault gouge, including humidity, mineral compositions, particle radii, and shapes, on the slip patterns have been studied mechanically and microscopically [17,18,19,20]. In particular, tests involving velocity stepping and slide-hold-slide have shown that the frictional weakening phenomenon is strongly related to instability. However, the mechanical behavior of granular layers in the thick-filled faults in nature have not attracted enough academic attention.
The shear strength of dry granular matters mainly depends on the normal force, shear rate, and the physical properties of the grains [21,22,23]. Wu et al. [24] investigated the particle crushing of isotropically consolidated silica sand specimens. Jiang et al. [25] studied the fundamental role of particle size and shear speed in the frictional instabilities of locally sheared granular materials. Wu and Zhao [26] investigated the dynamic triggering of frictional slip on simulated granular gouges. Shear experiments of geomaterials with complex stress routines were widely performed, and some of them also considered hydraulic effects [27,28,29,30,31,32].
Because of the un-prescribed sliding velocity, the shear properties of granular materials under normal unloading conditions can be quite different from the conventional experiments. However, related topics have not been explored before. Therefore, in this study, we intend to reveal the mechanical patterns of dry sands under invariable shear forces during the normal unloading process. This work is useful for better comprehending the movement patterns of natural granular layers and the prevention of corresponding geohazards.

2. Experimental Setup

2.1. Apparatus and Sample Preparation

We use the DJZ-500 shear box device (Figure 1a) to perform the unloading shear tests under constant shear forces. The shear displacement is measured by a horizontal LVDT, which is attached to the upper part of the shear box. Normal and shear loads are measured by the load cells with a sampling rate of 50 times per second. The granular material used in the experiments is directly placed into the shear box with a length × width × height = 400 mm × 200 mm × 100 mm (Figure 1a). Steel balls are placed between the upper and lower shear boxes to avoid frictional contact. At the same time, PVC film is laid on the inner wall of the shear box to prevent sand leakage.
The gouge layers are sometimes considered to have no cohesion [20]. Therefore, it is reasonable to use dry sands to study the behavior of gouge layers. We use natural sand collected from the coastal areas of southeast China as the experimental granular material, as shown in Figure 1b. The gradation diagram of the sand is shown in Figure 1c, which indicates that it is poorly graded. For each test, we layer 23.0 kg of sand into the shear box and fully compact it to reduce the porosity as much as possible. Since the height of the specimen is kept at 100 mm, the initial density of sand in the shear box is 2875 kg/m3, i.e., the initial porosity of the granular sample is a constant, and the porosity distribution in the experimental samples is uniform. Typical particle sizes and other detailed properties of the sand are reported in Table 1. The relevant literature [33] confirms that under the authorized pressure in this study, no obvious particle breakage occurs. Therefore, we hold the precondition that the properties of particulate matter remain unchanged during the experiment.

2.2. Experimental Scheme

As illustrated in Figure 2a, the granular matter in the shear box is subjected to both vertical force (normal force FN) and horizontal force (shear force FS). Consequently, the shear plane in the middle of the granular specimen is subjected to a normal stress σ and a stable shear stress τ. In the experiment, the sliding accelerations are minimal, so the inertia force on the shear box and specimen can be ignored, i.e., the force on the horizontal loading cell is equal to the shear force. During the unloading process, the shear force is kept constant by the horizontal servo system, and the applied normal force FN decreases linearly with a constant rate a:
F N = F N 0 − a t
According to the loading scheme illustrated in Figure 2b, the test procedure includes three stages:
  • Stage I: Load the vertical force to 20 kN at a loading rate of 40 kN/min. Then, maintain this normal force for 30 s. After that, load the shear force to the predetermined value within 20 s by activating the horizontal piston.
  • Stage II: Maintain the shear force and the normal force at their respective values for 60 s, where the stress state of the whole system remains unchanged.
  • Stage III: Unload the normal force linearly at a predetermined rate. The gradient of the descent line in Figure 2b equals the unloading rate. When the normal force descends to a certain level, the shear box begins to slide.
We conducted two groups of unloading direct shear tests (Group A and Group B) at room temperature, considering two variables: unloading rate and magnitude of shear force. The parameters used in the tests are shown in Table 2. Referring to a similar experiment studying rock specimens [30], the constant shear forces used in the tests are less than the ultimate shear strength under the given normal force and greater than the shear strength under zero normal force.

3. Results and Analysis

3.1. Displacement and Velocity During Sliding Process

Unlike unloading slip behavior of rock joints [28,30], the mechanical behavior of the tested dry sands during the normal unloading process is more complex. The displacement of the shear box does not change for one minute during Stage II, where the normal and shear forces remain constant. When the unloading begins, the corresponding frictional sliding does not start immediately. We define the corresponding moment when the shear box begins to move as ‘start time’, ti, and the corresponding moment when the shear box reaches the maximum velocity as the ‘end time’, tj. The values of ti and tj recorded in the tests are shown in Table 3.
The variation curves of normal displacement and sliding displacement versus experimental time are drawn in Figure 3, based on the original data recorded by the shear device for each test (Group A and Group B). Figure 4 illustrates the results of sliding velocity as a function of elapsed time for each test, from the beginning moment of normal unloading (i.e., the slopes of sliding displacement vs. time curve). As can be seen from the lower part of Figure 3, the sliding displacement does not increase uniformly over time. More related details can be seen in Figure 4. During the early seconds of normal unloading, the sliding velocity fluctuates (except for test B5), and in some tests the velocity value drops to zero, i.e., the sliding deceleration or intermission occur absolutely in the experiment, but the shear box accelerates persistently in the last seconds of normal unloading. Also, the slope change in sliding displacement has a strong correlation with the normal displacement.
For our test apparatus, the maximum moving velocity of the horizontal piston is around 3.7 mm/s. Therefore, when the sliding velocity reaches 3.7 mm/s, the test will automatically be stopped, so the final vertical ordinate values of the curves in Figure 4 are the same. Note that even at the fastest sliding rate, the acceleration of the shear box is still minimal, and the unbalanced force of the shear test system (acceleration times total mass) is negligible. This is consistent with the anticipation in Section 2.2 that the shear force of the granular matter is the force on the horizontal loading cell, i.e., the constant value that we set.

3.2. Shear Strength and Sliding Deceleration/Intermission

The conventional direct shear tests (direct shear at a constant shear displacement rate with a constant normal force) are widely used to measure the frictional criteria of granular matters. In Coulomb’s theory, as the peak shear strength increases linearly with larger normal stress, there are two frictional criteria: frictional angle (φ) and cohesion. Since the cohesion of the granular matter equals zero, the relationship between the ultimate shear stress and normal stress can be described as Equation (2). In Equation (2), τm reflects the maximum shear capacity of the granular material, and the ratio of shear force to normal force (Fs/FN) is friction coefficient (μ), which equals the tangent of friction angle when the cohesion is zero (Equation (3)).
τ m = σ tan φ
μ = tan φ = 0 . 6897
To study the frictional criterion (friction angle) of the granular matter used in this study, we additionally perform a series of conventional direct shear tests (selected constant shear rate = 0.0833 mm/s) (Figure 5a,b). The obtained friction coefficient and friction angle are 0.6897 and 34.6°, respectively, as shown in Figure 5b. As illustrated in Figure 5a, at the normal force of 30 kN, the shear resistance of the experimental granular material keeps increasing with a wide shear displacement range (from 0 to 25 mm), before reaching the potential peak strength τm in Equation (2).
The experimental results (Figure 5a) show that the shear resistance of the sands increases with higher normal load and larger shear displacement in a wide range. As the horizontal loading is being applied, the system is in a delicate state of equilibrium, which has a strong relationship with the accumulated sliding displacement. When the normal unloading begins, the upper restraint on the material is gradually relaxed and the balance tends to be broken, so the shear box moves forward in an attempt to find a new balance.
From a mesoscopic point of view (Figure 5c), there are two kinds of effects in the sliding process: particle interlacing and normal relaxation. If the unloading effect is not taken into consideration (when the unloading rate is low) after horizontal displacement (Δd), the sheared particles are embedded. Then, the system coordination number (average contact number for a single particle) increases. This leads to shear shrinkage and enhances shear strength. On the other hand, normal unloading makes the compressed particles bounce up and reduces the contact force (the darker balls in Figure 5c) between the particles, and the shear resistance may disappear. Within a certain unloading range, the effect of particle slip embedding may be greater than that of unloading, resulting in sliding velocity fluctuation and even sliding pause. Nevertheless, if the unloading rate or shear force is relatively high, the unloading effect will play a dominant role. In this case, there will be no obvious sliding deceleration/intermission phenomenon. The corresponding change in the normal displacement confirms our conjecture. Meanwhile, at the accelerating stage of sliding, the granular matter needs to slide rapidly to achieve the required shear force.

3.3. Effects on the Normal Force of Unloading

Values of instantaneous normal forces corresponding to the slip velocity of 3.7 mm/s, 2.5 mm/s, and 1.5 mm/s during the final fast sliding stage in test Group A and Group B are shown in Figure 6. As can be seen, the corresponding normal force has a strong relationship with both normal unloading rate and shear force with different sliding velocities. With a higher normal unloading rate, the corresponding normal force during fast sliding decreases. The change in corresponding normal force is more drastic when the unloading rate is too low or too high. When the unloading rate is 0.3~0.7 mm/s, the normal force is less sensitive to the change in the unloading rate. For the first several tests of Group A, due to the low normal unloading rates, the decrease in the corresponding normal force is insignificant. So, the three curves in Figure 6a are very close at the beginning. Thanks to the effects of a high unloading rate, the interval between these three curves enlarges gradually. In Figure 6b, the corresponding normal force during fast sliding increases with larger shear force. To better demonstrate the influence of normal unloading rates and constant shear forces on the corresponding normal force at different velocities, we fit the results above to synthesize 3D surfaces in Figure 7. When both shear force and unloading rate are in their respective middle ranges, the variation in normal force is not very conspicuous.
In the process of normal unloading, the sheared sand is in an unstable and fast motion state, where the normal constraint is constantly relaxed. Therefore, its shear strength characteristics cannot be explained by the Coulomb theory obtained from conventional low-rate direct shear tests. In Figure 6a, the normal forces are much lower than the theoretical value calculated by the Coulomb theory (10/0.6897 kN ≈ 14.50 kN). In addition, as shown in Figure 6b, the curves are not straight lines, and the corresponding normal force is always less than the theoretical value given by Equation (2).

3.4. Variation in Apparent Friction Coefficient

The ratio of shear force to normal force is defined as the apparent friction coefficient in the unloading period. Different from conventional direct shear tests, the temporal variation in the apparent friction coefficient in unloading shear tests is artificially designed. According to Equation (4), since Fs is a constant and FN linearly decreases with unloading time, the friction coefficient will increase inversely and reach the maximum value when the normal unloading stops. As illustrated in Figure 8a,b, at the maximum sliding velocity of 3.7 mm/s, the corresponding friction coefficient increased with the increase in unloading rate, and decreased with a larger applied shear force.
In test Group B (with no intermission during the sliding), since the unloading rate is a constant (=0.24 kN/s), the apparent friction coefficient is a function of time and shear force, as formulated in Equation (5). Its corresponding surface in the space is an inclined concave surface. Obviously, after the same normal unloading time, the smaller the shear force, the smaller the friction coefficient. Because the sliding friction coefficient exists only during the stage of continuous slip, the range of friction coefficient variation is limited. This is reflected by the inverse proportional function curves from ti to tj in Figure 8c. The points beyond these lines are the values that the coefficient of friction has not reached in our tests. It can be seen that the greater the shear force, the narrower the range of the friction coefficient will be. The initial value of the friction coefficient is lower than that of the conventional direct shear test, and it changes according to the inverse proportional function. Also, the ultimate value of the friction coefficient is significantly greater than the tan φ value in Equation (3), which matches the result in Figure 6b when the normal force is fairly low.
μ = F S F N = F s F N 0 − a t
μ = μ ( F S , t ) = F s 20 − 0.24 t , t ∈ ( t i , t j )

4. Conclusions

We performed sliding tests on dry sands which were subjected to constant shear loads, and the normal loads were linearly unloaded. Normal force, shear force, and shear displacement were recorded during the unloading process. The main conclusions drawn were as follows:
The granular sample discontinuously slides during the unloading of normal force, and the slip velocity does not increase uniformly with the elapsed time. Due to the increase in inner material friction strength caused by the accumulated shear displacement, the sliding velocity of dry sands fluctuates, and temporary sliding intermission occurs. With different normal unloading rates and different constant shear forces applied, the dry sands begin to slide under almost the same corresponding normal force. The corresponding normal force decreases with larger unloading rates and increases with larger shear force at different sliding velocities in the final fast sliding stage. These normal force values are less than the values given by Coulomb’s theory based on conventional displacement-controlled shear tests. The temporal variation in the apparent friction coefficient under the same normal unloading rate satisfies the inverse proportional function relation during the sliding, and the greater the constant shear force, the variation range of friction coefficient is narrower. Under a specified sliding velocity (the maximum experimental velocity), the apparent friction coefficient (i.e., the maximum friction coefficient) decreases with a higher normal unloading rate, and increases with larger shear force.
Regarding the limitations of this study, the sliding intermission phenomenon is not analyzed quantitatively, and the hypothesis in this paper can be verified by FEM and DEM numerical simulations in the future. Further investigations considering more environmental factors (e.g., temperatures and fluids [28,34]) are expected to better reflect the conditions in situ.

Author Contributions

Conceptualization, W.D., K.T., J.F. and B.W.; methodology, K.T.; software, K.T.; data curation, W.D.; writing—original draft preparation, K.T.; writing—review and editing, W.D. and J.F.; visualization, K.T.; supervision, W.D.; project administration, J.F. and B.W.; funding acquisition, J.F. and B.W. All authors have read and agreed to the published version of the manuscript.

Funding

This research is financially supported by the National Natural Science Foundation of China (No. 52474122), the Open Foundation of National Engineering Laboratory for High-Speed Railway Construction (HSR202105), the open research fund of the State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University (No. HESS-2317), and the Natural Science Foundation of Guangdong Province of China (2022A1515240009).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Testing apparatus and experimental materials: (a) the DJZ-500 shear box device; (b) dry sands used in tests; and (c) grain grading curve of the sand samples.
Figure 1. Testing apparatus and experimental materials: (a) the DJZ-500 shear box device; (b) dry sands used in tests; and (c) grain grading curve of the sand samples.
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Figure 2. Experimental configuration: (a) setup of direct shear test under unloading normal force and constant shear force; (b) normal and shear force application scheme during three-stage loading process.
Figure 2. Experimental configuration: (a) setup of direct shear test under unloading normal force and constant shear force; (b) normal and shear force application scheme during three-stage loading process.
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Figure 3. Normal force variation as function of elapsed time and experimental results of normal and sliding displacement versus time for each test. (a) Normal force, normal displacement, and sliding displacement versus time for different unloading rates (Group A). (b) Normal force, normal displacement, and sliding displacement versus time for different shear force (Group B).
Figure 3. Normal force variation as function of elapsed time and experimental results of normal and sliding displacement versus time for each test. (a) Normal force, normal displacement, and sliding displacement versus time for different unloading rates (Group A). (b) Normal force, normal displacement, and sliding displacement versus time for different shear force (Group B).
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Figure 4. Sliding velocity versus time for each test since the beginning moment of normal unloading. (a) Sliding velocity versus time for different unloading rates. (b) Sliding velocity versus time for different shear force.
Figure 4. Sliding velocity versus time for each test since the beginning moment of normal unloading. (a) Sliding velocity versus time for different unloading rates. (b) Sliding velocity versus time for different shear force.
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Figure 5. (a) Relationship between shear displacement and shear force under FN = 30 kN in a conventional direct shear test. Within the displacement range, the shear strength of the granular material keeps increasing with larger shear displacement. (b) The peak shear force (shear strength) for different normal force in 0.0833 mm/s shear-displacement-controlled conventional direct shear test. (c) Shear displacement (solid lines) and normal displacement (dash lines) versus time for low (0.08 kN/s) and high (0.8 kN/s) unloading rates extracted from Figure 3a and illustration to explain sliding deceleration/intermission.
Figure 5. (a) Relationship between shear displacement and shear force under FN = 30 kN in a conventional direct shear test. Within the displacement range, the shear strength of the granular material keeps increasing with larger shear displacement. (b) The peak shear force (shear strength) for different normal force in 0.0833 mm/s shear-displacement-controlled conventional direct shear test. (c) Shear displacement (solid lines) and normal displacement (dash lines) versus time for low (0.08 kN/s) and high (0.8 kN/s) unloading rates extracted from Figure 3a and illustration to explain sliding deceleration/intermission.
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Figure 6. Variation in normal force at different sliding velocities. (a) For different unloading rate (Group A) and (b) for different shear force (Group B).
Figure 6. Variation in normal force at different sliding velocities. (a) For different unloading rate (Group A) and (b) for different shear force (Group B).
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Figure 7. Normal force versus unloading rate and shear force at sliding velocity of (a) 3.7 mm/s, (b) 2.5 mm/s, and (c) 1.5 mm/s.
Figure 7. Normal force versus unloading rate and shear force at sliding velocity of (a) 3.7 mm/s, (b) 2.5 mm/s, and (c) 1.5 mm/s.
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Figure 8. (a) Apparent friction coefficient when the sliding velocity reaches 3.7 mm/s (i.e., ultimate value in the test) for different unloading rates and different shear force. (b) Apparent friction coefficient versus unloading rate and shear force at sliding velocity of 3.7 mm/s. (c) The variation in friction coefficient versus normal unloading time for different shear force (the recorded data in Group B). The different colors represent different single tests.
Figure 8. (a) Apparent friction coefficient when the sliding velocity reaches 3.7 mm/s (i.e., ultimate value in the test) for different unloading rates and different shear force. (b) Apparent friction coefficient versus unloading rate and shear force at sliding velocity of 3.7 mm/s. (c) The variation in friction coefficient versus normal unloading time for different shear force (the recorded data in Group B). The different colors represent different single tests.
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Table 1. Grain properties of granular matter used in experiments.
Table 1. Grain properties of granular matter used in experiments.
d10 (mm)d10 (mm)d10 (mm)Uniformity Coefficient (Cu)Coefficient of Curvature (Cc)
0.110.220.847.640.524
Table 2. Experimental scheme under a series of unloading rate and shear force conditions. Group A: varying unloading rate, keeping constant shear force of 10 kN. Group B: varying shear force, keeping a constant unloading rate of 0.24 kN/s.
Table 2. Experimental scheme under a series of unloading rate and shear force conditions. Group A: varying unloading rate, keeping constant shear force of 10 kN. Group B: varying shear force, keeping a constant unloading rate of 0.24 kN/s.
TestsNo.Unloading Rate (kN/s)Shear Force (kN)Initial Shear Force (kN)Maximum Sliding Velocity (mm/s)
Group AA10.0810203.7
A20.161020
A30.321020
A40.41020
A50.481020
A60.561020
A70.721020
A80.81020
Group BB10.248203.7
B20.24920
B30.241120
B40.241220
B50.241420
Table 3. The timing that sliding begins (‘start time’) and ends (‘end time’).
Table 3. The timing that sliding begins (‘start time’) and ends (‘end time’).
TestsNo.Start Time (s)End Time (s)
Group AA1152.2221.2
A2137.4194.6
A3127.5160.3
A4125.6151.8
A5125.1147.4
A6125.1143.3
A7123.1139.0
A8123.3139.6
Group BB1134.0191.1
B2134.9183.5
B3132.9172.0
B4131.2168.2
B5127.6136.4
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Dang, W.; Tao, K.; Fu, J.; Wu, B. Experimental Investigation on Unloading-Induced Sliding Behavior of Dry Sands Subjected to Constant Shear Force. Appl. Sci. 2025, 15, 401. https://doi.org/10.3390/app15010401

AMA Style

Dang W, Tao K, Fu J, Wu B. Experimental Investigation on Unloading-Induced Sliding Behavior of Dry Sands Subjected to Constant Shear Force. Applied Sciences. 2025; 15(1):401. https://doi.org/10.3390/app15010401

Chicago/Turabian Style

Dang, Wengang, Kang Tao, Jinyang Fu, and Bangbiao Wu. 2025. "Experimental Investigation on Unloading-Induced Sliding Behavior of Dry Sands Subjected to Constant Shear Force" Applied Sciences 15, no. 1: 401. https://doi.org/10.3390/app15010401

APA Style

Dang, W., Tao, K., Fu, J., & Wu, B. (2025). Experimental Investigation on Unloading-Induced Sliding Behavior of Dry Sands Subjected to Constant Shear Force. Applied Sciences, 15(1), 401. https://doi.org/10.3390/app15010401

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