Investigation of the fabric effect on the arching effect in granular materials

A series of trapdoor experiments and DEM simulations were carried out in this study to examine the arching effect in granular materials, with the focus being on the influence of the direction for particle deposition. In the tests, particles (e.g. rice grains, PVC particles and nylon particles) were dropped as if they were raining at different directions to construct granular material layers with various fabric orientations. It is shown that the mobilization of arching effect depends on the direction of particle deposition, with the arching ratio ρ increasing at first and then decreasing. The arching effect is the weakest at a deposition angle of θ = 30° in obliquely deposited granular masses. It is also found that the vertical displacement of particles in the ultimate phase increases initially; it then decreases with the variation in the orientation of particle deposition, and the largest displacement occurs at θ = 30°.


Introduction
Soil arching which is caused by the non-uniform displacement of soil medium, is a common phenomenon in nature [1].Extensive studies have been conducted to explore this interesting phenomenon.Early studies primarily used macroscopic experiments, such as the trapdoor test, to examine the impact of particle material, particle size, soil height, and trapdoor shape on the soil arching [1,2,3,4,5].The load pattern is also a key factor affecting soil arching.It has been observed that soil arching deteriorates under a local surface load [6,7]; meanwhile, the dynamic load exerts a greater influence on soil arching than the static load [8,9].It is found that the extent of degradation owing to soil arching increases with the load amplitude and frequency [10].
The arching effect in some practical situations such as tunnels and pile foundations, have also been brought into focus and modeled in the physical experiments [11,12,13,14,15].Besides model experiments, advanced numerical simulation methods such as discrete element modeling are also used to examine the effect of soil arching under various conditions, including the trapdoor experiment, soilpile interaction, and tunnel settlement [16].Rui et al. [17] conducted a DEM simulation analysis of the trapdoor tests by considering different soil heights and trapdoor widths, and observed three patterns in the evolution of soil arches namely the triangular expansion pattern, evolution and equal settlement patterns.In addition, the digital image correlation technique and the visualization of force chains are used to probe the mechanism of the soil arching [18] [19].
It is seen that previous studies focused on the investigation of soil arching by considering the factors such as the particle properties, width of trapdoor and cover height; however, the fabric effect on soil arching has not been systematically investigated.In this study, the trapdoor experiments and DEM 1330 (2024) 012052 IOP Publishing doi:10.1088/1755-1315/1330/1/012052 2 simulations are conducted to examine arching in granular materials, with the focus being on the influence of grain-scale fabric which is created by depositing particles in different directions.The development of soil arching is closely scrutinized at both the macro and micro levels.The mechanism of soil arching is also discussed schematically.

Experimental device
In this study, an apparatus was designed for investigating the fabric effect on soil arching, as shown in figure 1.This apparatus consists of a container cell, lifting jack, rotatable shaft, displacement controller and load cells.The dimensions of the container cell, are as seen in figure 1 Three trapdoors are provided at the bottom of the container cell, the size of which is 40 × 40 mm.The trapdoor can be controlled to move downwards, causing load transfers in the granular layers above it.The vertical stress (p) on the trapdoor, and at the bottom of container cell were measured using a load cell.A displacement controller was used to control the displacement of the trapdoor.The container cell could be rotated around the fixed rotatable shaft, creating a deposition plane of varying orientations.

Test material
Three granular materials are used in this study, including rice grains, PVC particles and nylon particles (see figures 2(a), 2(b) and 2(c)), with the densities of the particles being 0.582 g/cm 3 , 0.593 g/cm 3 and 0.507 g/cm 3 , respectively, and particle aspect ratios (AR), which are defined to be the ratio of the particle minor-axis length over the particle major-axis length; AR = 0.425, 0.5 and 0.5, respectively, for the three granular particles.The detailed material information is given in table 1

Test procedure
The experimental procedure is described in figure 3. A steel structure with a slot at the top serves as a line source to release particles, and the container cell is placed below the steel structure, as shown in figure 3(a), with the region A enlarged and described in figure 3(b).The height of the granular heaps is set to be four to five times that of the trapdoor width, which makes it possible to visually observe the impact of the particle deposition angle on the arching effect in granular materials.As shown in figure 3(c), the container cell is initially set to be at an inclined position with an angle θ (deposition angle) relative to the horizontal direction, and then particles are released in a layered sequence [20].The thickness of the layer is approximately equal to one trapdoor width.To gain a better comprehension of the impact of the deposition angle, five deposition angles were considered (i.e., θ = 0°, 10°, 20°, 30°, and 45°) for the construction of a granular heap.Upon the completion of particle deposition, the container cell was meticulously restored to its original horizontal position for the performance of tests (see figure 3(d)).Lastly, the trapdoor was moved down at a rate of 1 mm/5 s, simulating a quasi-static loading process, and the experimental data were collected using a TDS-630 and input to a computer for further analysis.

Numerical setup
The experimental process is simulated by PFC3D, as clarified in figure 4. The density of the particles is 2.65 g/cm 3 .A "clump" is used to simulate irregular-shaped particles, and an aspect ratio of 0.5 is adopted (see figure 4(a)).The linear elastic model is utilized to characterize the contact behavior between particles.The sliding friction coefficient is set to be 0.5, and rolling friction is ignored.The container cell has dimensions of 375 × 325 × 40 mm.The movable part in the center of the bottom plate was used to simulate the trapdoor.In this study, the wall stiffness was set to be ten times the particle stiffness, and the relative micromechanical parameters of particles based on those given in [21][22] [23].
The particle deposition angle θ, namely the direction angle of the gravity field relative to the vertical direction includes θ = 0°, 10°, 20°, 30°, 45°, 60°, 75°, and 90° in this numerical study.gravitational acceleration is 10 m/s 2 .Taking θ = 30° as an example, a layer-by-layer deposition method was employed to deposit particles, and the thickness of each layer was controlled to be equal one trapdoor width ( figure 4(b)).After depositing the particles, the trapdoor was moved downwards at a speed of 0.2 mm/s, and the mechanical responses of the granular masses were recorded (see figure 4(c)).In the numerical simulation, a state with the "mratio" less than 1.0 × 10 -4 can be treated as an equilibrium state, at which the ratio ( mratio) of the unbalanced force against the average contact force is not greater than 1.0 × 10 -

Load-displacement curve
A generalized description of the load-displacement curve is shown in figure 5.The arching ratio ρ is the ratio of the real-time vertical stress acting on the trapdoor (p) over the initial vertical stress, Δ is the trapdoor displacement, and B is the trapdoor width.As indicated in figure 5, the load-displacement curve can generally be divided into three phases: the initial, transition, and ultimate phases.

The arching ratio in the initial and ultimate phases at different deposition angles
Figure 7 describes the relationship between the arching ratio (ρmin, ρmax) and the deposition angle (θ) in both the initial and ultimate phases.θ ranges from 0° to 45° in the tests and from 0° to 90° in the DEM simulation.
The experiments reveal that the initial arching ratio increases with the deposition angle (θ) until θ = 30°, which is followed by a slight decline.Ultimately the arching ratio increases with the deposition angle (θ), with the peak occurring at θ in the range of 30° to 45°.In the DEM simulation results, the arching ratios of the initial and ultimate phases both exhibit a trend of "first increasing and then decreasing" with increase in the deposition angle (θ), with the maximum value being at θ = 30°.
A relatively small arching ratio (ρ) indicates that the pressure from the granular masses are mostly transmitted to the bottom parts beside the trapdoor; this also suggests a relatively strong arching effect.Therefore, it can be concluded that the arching effect is weakest at θ = 30°, with the maximum arching ratio on the trapdoor occurring at a deposition angle of θ = 30°.This phenomenon may be associated with the shear strength of the granular assemblies deposited in an inclined direction, because the weakest shear strength is mobilized around θ = 30° (i.e., when the angle formed between the direction of maximum principal stress and the normal of the deposition plane is about 60°) for granular materials as reported in the literature [24,25,26], and the weakest shear strength is responsible for the weakest arching effect.

Displacement under the different deposition angle
Figure 8 illustrates the vertical displacement contours of particles in the ultimate phase for various deposition angles.At θ = 0°, the vertical displacement exhibits the "tower-shaped" pattern described by Rui et al. [17], and it is almost symmetrical about the central axis.The vertical displacements at other deposition angles are at a relatively high level, given that a particular part is taken for reference.To quantitatively analyze the variations in the vertical displacements of particles at different deposition angles in the final phase, the vertical displacements at x = -3/8B at the locations I, II, III, and IV are brought into focus, as depicted in figure 9.It is evident that the vertical displacements at a given location differ distinctly for different deposition angles.The difference is comparably pronounced at relatively high positions.Note that the Position IV is higher than Position I.The maximum vertical displacement occurs at θ = 30°, indicating that the granular heap is less stable at θ = 30°.This is associated with having a more compressible particle skeleton for this case.In this connection, the pressure on the trapdoor is expected to be higher than that for the other cases of particle deposition

Conclusion
In this study, the influence of particle deposition direction on the arching in granular materials was investigated, through the physical experiments and DEM simulations.The following conclusions were drawn： The arching ratios at the initial and ultimate phases both increase first and then decrease with the increase of particle deposition angle θ, with the maximum value occurring at θ=30°, indicating that the arching effect is weakest at θ = 30°.
2. The vertical displacements of particles differ at different particle deposition angles.The largest vertical displacement takes place at θ = 30°, which indicates that the granular masses are the least stable at θ = 30°.

3.
With the increase of deposition angle, the arching effect increases first and then weakens.The vertical displacements of the particles correspondingly increase initially and then decrease.This is assumed to be associated with the particle deposition direction dependency for the shear strength of granular materials.

Figure 2 .
Figure 2. Photos of test materials.

Figure 3 .
Figure 3. (a) the structure serving as a line source and the container cell; (b) focus area A; (c) particle deposition at a tilting angle  ; (d) the performance of the trapdoor tests at a normal horizontal position.

Figure 6 Figure 6 .
Figure6presents the load-displacement curves for the trapdoor for different deposition angles.The vertical axis is the arching ratio ρ, with the horizontal axis being the normalized displacement (Δ/B).The load-displacement curves of the experiment and the DEM simulation match well.As the vertical displacement increases, the stress on the trapdoor rapidly decreases to a minimum value, and then increases slightly until it enters a final stable stage.

Figure 7 .
Figure 7.The relationship between the arching ratio ρ on the trapdoor and the deposition angle θ: (a) initial phase; (b) ultimate phase.

Figure 8 .
Figure 8.Comparison of vertical displacement contour at different deposition angles.

Figure 9 .Figure 10 .
Figure 9.The vertical displacement values of x = -3/8B at the positions I, II, III and IV at different deposition angles: (a) location illustration; (b) vertical displacement values.