Investigation on the Bearing Characteristics and Bearing Capacity Calculation Method of the Interface of Reinforced Soil with Waste Tire Grid

Abstract

Geogrids are frequently utilized in engineering for reinforcement; yet, they are vulnerable to construction damage when employed on coarse-grained soil subgrades. In contrast, waste tire grids are more appropriate for subgrade reinforcement owing to their rough surfaces, integrated steel meshes, robust transverse ribs, extended degradation cycles, and superior durability. Based on the limit equilibrium theory, this study developed formulae for calculating the internal and external frictional resistance, as well as the end resistance of waste tires, to ascertain the interface bearing properties and calculation techniques of waste tire grids. Based on this, a mechanical model for the ultimate pull-out resistance of waste-tire-reinforced soil was developed, and its validity was confirmed through a series of pull-out tests on single-sided strips, double-sided strips, and tire grids. The results indicated that the tensile strength of one side of the strip was approximately 43% of that of both sides, and the rough outer surface of the tire significantly enhanced the tensile performance of the strip; under identical normal stress, the tensile strength of the single-sided tire grid was roughly nine times and four times greater than that of the single-sided and double-sided strips, respectively, and the grid structure exhibited superior anti-deformation capabilities compared to the strip structure. The average discrepancy between the calculated values of the established model and the theoretical values was merely 2.38% (maximum error < 5%). Overall, this research offers technical assistance for ensuring the safety of subgrade design and promoting environmental sustainability in engineering, enabling the effective utilization of waste tire grids in sustainable reinforcement applications.

1. Introduction

Highway engineering features long mileage and wide coverage. With significant variations in hydrogeological conditions along the route, the operational state of the subgrade is significantly affected by the surrounding environment. Among them, for the subgrade located in soft soil areas and hilly and mountainous areas, due to the poor foundation conditions or by the influence of hydrogeological conditions, highway subgrades often experience uneven settlement, subgrade slippage, cracking, and other engineering disasters, leading to transverse and longitudinal pavement cracks, which seriously affect the safety of traffic operation. In order to avoid the problem, the engineering often adopts different treatments, such as supporting structures, composite foundations, lightweight subgrades, and geogrid reinforcement [1,2,3,4]. Among them, geogrid technology has been widely used in engineering due to its features of high strength, flexible setting, and convenient construction.

In order to verify the application effect of geogrid reinforcement technology, Liu et al. [5] carried out a static load test based on an indoor geogrid reinforced waterlogged sand embankment, and the results showed that the reinforcement effect was enhanced with the increase in the number of reinforcement layers and the reduction in reinforcement depth; the geogrid-reinforced embankment effectively improved the ultimate bearing capacity of the embankment and reduced the settlement of the embankment. Du et al. [6] conducted an in-depth study on the static performance of geogrid-reinforced embankments through field tests and discrete element simulations, and the results showed that the ultimate bearing capacity of the embankment was gradually enhanced with the increase in the number of geogrid layers and the width of geogrids. However, geogrids are limited by the material type, and when applied to subgrades such as weathered materials, they are very susceptible to damage caused by construction crushing, which seriously affects their service life. In order to study the effect of construction damage on the long-term strength of geogrids during construction and their use, Yang et al. [7] calculated the construction damage discount factor of geogrids up to 1.13 by rolling the reinforced soil on site as well as by tensile tests. For comparison, waste tires have good interfacial friction characteristics, tensile strength, and deformation resistance due to their rough outer surface pattern and the inclusion of steel wire mesh, which makes them less prone to construction damage. Meanwhile, rubber is a difficult material to degrade, and the degradation cycle is up to 100 years. From a cost perspective, although the price of a single waste tire grid is about 30% higher than that of an ordinary geogrid, considering its service life of more than 50 years, which is much longer than the conventional service life of 10–15 years of geogrids, calculated from the whole life cycle cost, the waste tire grid does not need to be replaced frequently, which can significantly reduce the additional costs caused by multiple constructions. If properly utilized as subgrade reinforcement material, waste tires can meet both the mechanical property requirements of reinforced subgrades and durability standards, making them a promising application option. Currently, there are three main categories relating to the use of waste tires for reinforcement in subgrades, namely, strip, grid, and granular.

In order to reveal the mechanical properties of waste tire strip reinforced soils, Sun [8] studied the interfacial friction characteristics of tire strip reinforced sandy soils by direct shear test, and found that tire strips significantly increase the equivalent internal friction angle of sandy soils, while the effect on apparent cohesion is small. Ma et al. [9] conducted direct shear tests on waste tire strips reinforced brick powder and showed that the addition of waste tire strips to the brick powder increased the angle of internal friction and cohesion, and the optimum volume percentage of waste tire strips was determined to be 6%. Du et al. [10] explored the shear properties of tire strip–loam mixtures during direct shear, and similar conclusions were obtained. The use of waste tire particles has also been investigated since the 1990s, revealing that they can improve the shear strength and reduce the self-weight of the soil. Li et al. [11] carried out a triaxial compression test and resonant column test; with the increase in rubber content, the damage morphology of cement rubber sand composite (RCS) soil samples was changed from strain softening to strain hardening. Meanwhile, the increase in rubber content can effectively slow down the modulus decay of RCS soil. He [12] conducted indoor tests on shear strength and bearing ratio of rubber–sand composite soils, and the results showed that an increase in rubber particle dosage within a certain range could improve the shear strength of the composite soils. Yuan [13] and Wang [14] used the integrated reinforcement of tire strip and tire particles (TDA) materials to investigate the pull-out behavior in sandy and chalky soils, respectively, and verified the application of integrated reinforcement.

Further analysis of the tire specifications showed that the thickness of the tire was about 1.5 cm, which also increased the end resistance and interfacial friction resistance to a certain extent if it was used as a cross rib and fixed to the strip to form a grid structure. Therefore, in order to verify its reinforcing effect, Tajabadipour et al. [15] made scrap truck tires into grid shapes (various grids with sizes of 21 × 7, 11.5 × 7 and 7 × 7 cm) as reinforcing materials and conducted a series of ballast box tests, and the grid with a size of 11.5 × 7 cm performed the best. Gholamhosein et al. [16] investigated the reinforcing effect of the proposed tire grid under various working conditions, such as different burial depths and loading plate diameters, by carrying out large-scale repetitive flat plate loading tests, and the results showed that the tire grid contributed significantly to the improvement of the performance of sandy slopes, with a two-fold increase in the load carrying capacity as compared to the un-reinforced condition. Zhang et al. [17] analyzed the bearing characteristics and reinforcement mechanism of soil slopes reinforced with used tire strips by using a combination of model test (combined with particle image velocimetry, PIV) and numerical simulation, and the results showed that used tire strips can effectively improve the bearing capacity of slopes and cut off the potential damage surface. However, current relevant research results mainly focus on carrying out tests on the bearing characteristics of tire grids under different working conditions and analyzing the reinforcement effect, lacking a calculation model for the pull-out load of reinforced soil that considers multiple factors such as the double-sided friction mechanism of tires. Therefore, it is of great significance to study the method for accurately calculating the ultimate pull-out force of tire grids based on theoretical models and experimental verification methods.

The purpose of this study was to establish a calculation formula for the ultimate pull-out force of waste tire grid reinforced soil that comprehensively considered interface frictional resistance and end resistance based on the limit equilibrium theory. Next, pull-out tests on single strips, double strips, and tire grids were carried out to explore the interface bearing characteristics and the variation law of the ultimate pull-out force of waste-tire-reinforced soil. Finally, the parameters to be determined in the theoretical model were derived according to the test results, and the reliability of the theoretical model was verified. The conclusions of this study can provide meaningful reference values for the structural design of waste tire grids used in reinforced subgrade engineering.

2. Mechanical Modelling of Ultimate Pull-Out Forces in Waste-Tire-Reinforced Soils

2.1. Waste Tire Grid Structure Type

The strips are the basic building blocks of the grid and are cut from scrap tires. The waste tire grid is formed by interlocking the cut strips and tying them together to form a grid structure in the shape of a tic-tac-toe. Its basic structure consists of transverse ribs and longitudinal ribs, and the joints are wire-tied. As shown in Figure 1, the transverse ribs are ribbed structures arranged along the transverse direction of the waste tire grid. When buried in soil, the scrap tire grid utilizes its structural characteristics to create lateral constraints on soil particles during shear deformation. The transverse ribs provide horizontal resistance while the longitudinal ribs offer vertical resistance, collectively enhancing the interface bearing capacity.

2.2. Interfacial Moisture Resistance

Interfacial frictional resistance is generated by the contact between the surface of the waste tire grid and the soil. As shown in Figure 2, there is a significant difference in flatness due to the inconsistent structural form of the inner and outer surfaces of the tire. For ease of differentiation, the frictional resistance on the outer surface of the tire is defined as ${\tau }_1$ and on the inner surface as ${\tau }_2$. The geometric feature of the outer surface is that uneven patterns are distributed in a certain proportion, and the rest of the surface is flat. This structure can provide more contact points and embedding space for soil particles, while ensuring the basic contact area with soil particles. When the tire interacts with the soil, the soil particles will naturally fill the depressions on the pattern surface and fit closely with the outer surface of the tire, thus forming an effective interlocking effect. The outer surface friction force ${\tau }_1$ consists of two components: the contact friction between the soil particles and the strip; the embedding action between the soil particles and the patterned part of the outer surface of the waste tire, which produces sliding friction as well as occlusal friction between the two. The internal surface frictional resistance ${\tau }_2$ is mainly a pure contact friction effect between the soil particles and the strip. This multifactorial composition of the composite friction mechanism jointly affects the total interfacial frictional resistance $F_u^{\prime }$ in the pull-out test.

2.3. Load-Bearing Characteristics of Transverse Rib Structure

During the pulling process of the waste tire grid, the transverse ribs exert end resistance because they are embedded in the dense filler. As shown in Figure 3, when the tire grid is relatively displaced by the pulling action, the transverse ribs subsequently compress the soil in front of the ribs, which in turn produces the end resistance σ. The magnitude and characteristics of this end resistance can vary under different soil conditions. In particular, in cohesive soils, the end resistance comprises not only the passive compression resistance of the soil, but is also affected by the adhesion between the soil particles and the cross ribs. In sandy soils, the end resistance is mainly due to mutual extrusion and friction between soil particles.

2.4. Basic Equation for Load Bearing Capacity of Waste Tire Grid

2.4.1. Waste Tire Grid Load Bearing Capacity Composition

According to Moraci [18], assuming that the frictional resistance on the surface of the geogrid reinforcement and the end resistance on the transverse ribs reached the maximum value at the same time and did not affect each other in the horizontal pull-out test, the formulae for calculating the ultimate pull-out force were derived as shown in Equation (1).

$$P_R=P_{\mathrm{RS}}+P_{\mathrm{RB}}$$

(1)

where $P_R$ is the total bearing capacity. $P_{RS}$ is the total friction resistance at the surface of the reinforcement. $P_{RB}$ is the end resistance of the transverse rib.

$$P_{RS}={2\alpha }_S{W}_r{L}_r{\sigma }_n\mathit{tan}\delta$$

(2)

where ${\sigma }_n$ is the effective principal stress. $\delta$ is the angle of external friction between the contact surface of the grid and the soil. $L_r$ is the length of the grid. ${\alpha }_s$ is the effective contact surface coefficient of the grid. $W_r$ is the width of the grid.

Based on the above equations and the tire grid force mechanism, the following load bearing capacity composition was proposed, as shown in Figure 4, where each dimensional parameter was first defined.

(1)

Equation for frictional resistance on the inner surface of waste tire strip.

$$P_{RI}=P_{\mathrm{RSI}}$$

(3)

(2)

Equation for the frictional resistance of the outer surface of waste tire strip.

$$P_{RII}=P_{RSE}$$

(4)

(3)

Equation for resistance at transverse rib end of waste tire grid.

$$P_{RIII}=P_{RB}$$

(5)

Equation for total load bearing capacity of waste tire grid.

$$P_R=P_{\mathrm{RSI}}+P_{\mathrm{RSE}}+P_{\mathrm{RB}}$$

(6)

2.4.2. Equation for Interfacial Frictional Resistance at the Inner Surface of a Waste Tire Grid

For the longitudinal ribs of the tire grid, the friction force on the inner surface of the tire is shown in the following equation.

$$P_{\mathrm{RSI}}={\alpha }_S{W}_r{L}_r{\sigma }_n\mathit{tan}{\delta }_1$$

(7)

where ${\sigma }_n$ is the effective principal stress. ${\delta }_1$ is the angle of external friction of the contact surface between the reinforcement and the soil. $L_r$ is the length of the reinforcement. ${\alpha }_s$ is the effective contact surface coefficient of the grid. $W_r$ is the width of the reinforcement.

2.4.3. Equation for Interfacial Frictional Resistance on the Outer Surface of a Waste Tire Grid

In order to take into account the different contributions of the different areas of the surface of the tire strip (with and without tread) to the friction resistance, the friction resistance of the outer surface of the tire was given in the following equation.

$$P_{\mathrm{RSE}}={\alpha }_S\xi W_r{L}_r{\sigma }_n\mathit{tan}{\delta }_2+\left(1-\xi \right)W_r{L}_r\left(c+{\sigma }_n\mathit{tan}\phi \right)$$

(8)

where ${\sigma }_n$ is the effective principal stress. ${\delta }_2$ is the external friction angle of the contact surface between the strips and the soil. $L_r$ is the length of the strips. ${\alpha }_s$ is the effective contact surface coefficient of the grid. $W_r$ is the width of the strips. c is the soil cohesion. $\phi$ is the soil internal friction angle. $\xi$ is the ratio of the area of the patternless part to the total area of the strip.

2.4.4. Equation for Resistance at the End of Waste Tire Grid

As mentioned earlier, waste tires had a certain thickness, and their transverse ribs were embedded in the dense fill as if they were anchor plate structures. Therefore, in order to construct the transverse rib end resistance calculation formula, the calculation method of anchor plate end resistance in the soil layer was referred to. Commonly used methods included the integral shear damage model (MD-1) proposed by Perterson and Anderson [19], the punching shear damage model (MD-2) proposed by Jewell et al. [20] and the modified shear damage model (MD-3) proposed by Bergado et al. [21]. These three computational models are shown in Figure 5.

The specific formula for end resistance is shown in Equation (9).

$$P_{RB}=n{W}_{r}B{\alpha }_B{\sigma }_b$$

(9)

where B is the thickness of the transverse rib unit. n is the number of transverse rib units. $L_r$ is the length of the strip. s is the spacing between the strips. ${\alpha }_B$ is the correction factor. ${\sigma }_b$ is the bearing stress on the transverse rib unit, which was determined as shown in Equation (10).

$${\sigma }_{bmax}=c{N}_c+{\sigma }_n{N}_q$$

(10)

where ${\sigma }_n$ is the vertical stress. c is the filler cohesion. N_c and N_q are the bearing capacity parameters. The above parameters are shown in

Table 1. Calculation table of load bearing parameters N_c, N_q.

Modelling	Nq	Nc
MD-1	$N_q=e^{\pi \mathit{tan}\phi }{\mathit{tan}}^2\left({\displaystyle \frac{\pi }{4}}+{\displaystyle \frac{\phi }{2}}\right)$	$N_c=\left(N_q-1\right)\mathit{cot}\phi$
MD-2	$N_q=e^{({\displaystyle \frac{\pi }{2}}+\phi )tan\phi }{tan}^2({\displaystyle \frac{\pi }{4}}+{\displaystyle \frac{\phi }{2}})$	$N_c=\left(N_q-1\right)\mathit{cot}\phi$
MD-3	$N_q=\left[{\displaystyle \frac{1+k}{2}}+{\displaystyle \frac{1-k}{2}}\mathit{sin}(2\beta -\phi )\right]{\displaystyle \frac{1}{\mathit{cos}\phi }}{e}^{2\beta \mathit{tan}\phi }\mathit{tan}\left({\displaystyle \frac{\pi }{4}}+{\displaystyle \frac{\phi }{2}}\right)$	$N_c={\displaystyle \frac{1}{\mathit{sin}\phi }}{e}^{2\beta \mathit{tan}\phi }\mathit{tan}\left({\displaystyle \frac{\pi }{4}}+{\displaystyle \frac{\phi }{2}}\right)-\mathit{cot}\phi$

Note: φ is the packing internal friction angle.

.

According to Zhang et al. [22], the modified punching shear model could more accurately simulate the damage pattern of waste tire grids in tests such as pull-out. Therefore, the MD-3 model was adopted in this paper to calculate the ultimate bearing stress on the transverse rib unit.

3. Waste-Tire-Reinforced Weathered Sand Interface Pull-Out Test

Based on the calculation model for the ultimate pull-out force of waste-tire-reinforced soil, a mathematical description of the pull-out behavior of tire reinforcements has been established, with each parameter in the calculation model clearly defined. To explore the adaptability and preliminary accuracy of this model in practical engineering, the objective of this section is to simulate the mechanical response of tire-reinforced structures in horizontal pull-out tests under different vertical stresses. Therefore, weathered sand was used as the test fill in this test, and the interfacial pull-out test of waste tire strip-type and grid-type reinforced soil was carried out to study the interfacial characteristics of waste tire strip-type and grid-type reinforced soil under different vertical loading conditions.

3.1. Experimental Materials

3.1.1. Weathered Sand

(1)

Particle Gradation

Weathered sand is characterized by widespread presence, good mechanical properties, etc. It usually has a distinctive angular surface and different particle sizes, and is often used as roadbed fill in engineering practice, as shown in Figure 6a. In order to facilitate the provision of basic parameters for later calculations, based on the ‘Highway Geotechnical Test Procedures’ (JTG 3430-2020) [23], the sieve test was carried out on the filler used after drying, and the particle grading curve shown in Figure 6b was obtained. Meanwhile, its physical parameters were calculated and shown in

Table 2. Physical parameters of filler.

Parameter	Value
Effective particle size, d10/(mm)	0.361
Median particle size, d50/(mm)	1.671
Unevenness coefficient, Cu	6.6
Curvature factor, Cc	0.73
Specific gravity of soil, Gs	2.65

. As can be seen from Table 2, it can be determined that this type of sand belongs to poorly graded coarse sand.

(2)

Relative compactness

According to the Geotechnical Test Procedure for Highways (JTG 3430-2020) [23], the maximum and minimum dry densities of the test sand were measured by the vibrating sieve method and the measuring cylinder method, which were ρdmax = 1.805 g/cm³ and ρdmin = 1.522 g/cm³, respectively.

(3)

Shear strength

In order to determine the shear strength of weathered sand, a dry sand soil sample with a relative compactness of Dr = 0.7 was used to carry out a direct shear test, and the measured shear strength indexes were angle of internal friction φ = 29°, and class cohesion c = 3.44 kPa.

3.1.2. Waste Tire Strips

(1)

Scrap Tire Tensile Properties

In line with the principle of controlling a single variable, to reduce the impact of the surface wear degree and pattern type of waste tires on the interface bearing characteristics, this test needed to select waste tire materials with similar wear degrees and identical pattern types. Through preliminary research, it was considered that the Triangle brand tires with the specification of 175/70R14 had a relatively high market share, so the Triangle brand tires of 175/70R14 were selected as the research object of this study. After dividing the tire tread and sidewall, the tire was cut into 5 tire strip samples with a width of 8 cm, a length of 20 cm, and a thickness of 2 cm for the tensile test, and the results are shown in Figure 7. As can be seen from Figure 7, the strain of the tire strip varied linearly with increasing load until it reached the ultimate load and broke in brittle fracture. The main tensile property parameters of waste tires were obtained by taking the average of the tests of five specimens and were listed in

Table 3. Tensile properties of tire strips.

Parameter	Value
Ultimate tensile force (kN)	21.2
Ultimate tensile strength (MPa)	23.5
Ultimate tensile ratio (%)	18.9

. As can be seen from Table 3, the ultimate pull-out force of the tire strip was 21.2 kN, and it had excellent deformation resistance. Processing it into a waste tire grid can significantly improve the deformation resistance from the structural aspect.

3.2. Horizontal Pull-Out Test Device for Reinforced Weathering Material for Tire Grids

To reveal the interface bearing characteristics and stress-deformation laws of waste tire grid reinforced soil, this study adopts a horizontal pull-out test device independently developed by the research group. This device can comprehensively consider the factors affecting the pull-out force, obtain the pull-out force–displacement curve relationship, and then analyze the strength of the reinforcement-soil interface of the reinforced soil. Figure 8 shows the pull-out test setup with loading mode, which consists of four parts: test box, horizontal loading system, vertical loading system, and data acquisition system. Loading was performed by applying loads in both vertical and horizontal directions. The specific parameters of each part of the components are as follows.

(1)

Test box size: the internal dimensions of the box are 800 mm (length) × 800 mm (width) × 500 mm (height). The front wall of the test box is equipped with a narrow horizontal slit with a width of 600 mm and a height of 20 mm, which is convenient for leading out the bar specimen connected to the external pulling device.

(2)

Horizontal pulling device: the horizontal loading system consists of a gearbox, a frequency converter, a fixture, and a telescopic rod and uses the displacement control loading mode.

(3)

Counterforce loading device: the vertical loading system consists of a counterforce beam, a pressure sensor, a jack, and a load plate. The maximum applied load is 200 kN, and the load is uniformly distributed on the load plate.

(4)

Data acquisition system: the data acquisition system is composed of a tension sensor and a displacement sensor; the tension sensor and displacement sensor are placed in the loading end of the strip or grid for real-time measurement of the pulling force and moving distance in the pulling process.

3.3. Experimental Protocols

For the pulling test, each specific test parameter is shown in

Table 4. Pulling test conditions.

Vertical Load (kPa)	Relative Density Dr	Reinforcement Type	Geometric Size (mm)
40/60/80/100	0.7	Single-side strip type	Length 650 × width 60
		Double-side strip type
		Grid type	Length 650 × width 60, net horizontal spacing between strips 120, net vertical spacing 150

, and the dimensions of the individual tire strips and grids are shown in Figure 9. To prevent boundary effects and size effects from affecting the results of the pull-out test, the placement position of the reinforcement material is shown in Figure 10. It could be seen from the figure that the end resistance generated by the transverse ribs had a certain influence range. Therefore, the embedding position was reasonably arranged to prevent the end resistance from extending to the side wall and affecting the overall pull-out behavior.

In this experiment, the single-sided friction meant that the outer side of the tire was coated with epoxy resin all over and with a certain thickness, so that the coefficient of friction was extremely low.

3.4. Test Procedure

The test adopted the method of layered filling, with filler compactness control at 0.7 ± 0.02 and each layer with a filling height of 10 cm for a total height of 40 cm. The specific test steps were as follows:

(1)

Collect the sufficient amount of weathered sand filler in the suitable site, transport it to the pre-treatment area after sieving to remove the impurities, test the particle gradation, relative compactness and water content of the original filler, and, according to the results of the water content test, adjust it to the optimal state through drying or adding water to mix, so as to ensure that the filler complies with the requirements of the test.

(2)

Calculate the mass of filler for each layer according to the specified degree of compaction. Pour the filler into the test box, and adopt the static compaction control method. Gradually increase the static pressure to allow soil particles to adjust and arrange slowly, avoiding local voids. Compact the filler to the predetermined height to achieve the corresponding degree of compaction (Dr = 0.7 ± 0.02), and use the ring knife method to detect the degree of compaction of the filler.

(3)

After the height of sand filling reaches the set position of the reinforcement, the tire strips or grids will be laid flat and fixed by using clamps.

(4)

After compaction of the overlying fill is completed, place a rigid cover plate and I-beam so that the vertical load can be uniformly transferred to the fill. Connect the jack and pressure transducer, and apply the vertical load step by step until the predetermined load is reached and maintained.

(5)

Perform horizontal pulling on the reinforcement material, set the horizontal pulling rate at 1 mm/min, record the pulling load–displacement data, and carry out a summary analysis of the results.

4. Results and Analysis

In this section, statistical analysis was conducted on the horizontal pull-out test data of single-sided tire strips, double-sided tire strips, and tire grids, and the variation law of the pull-out load–displacement curves was analyzed. Subsequently, the test results were substituted into the theoretical model for calculation, and the model parameters were revised. Through theoretical calculations, the theoretical error range of the model was analyzed, and its application effect in actual engineering was evaluated.

4.1. Load–Displacement Curves for Single-Sided Friction Pull-Out of Tire Strips

As shown in Figure 11, the results of the single-sided friction pull-out test of the waste tire strip under different vertical pressure conditions are presented. With the gradual increase in displacement, the tensile force of the strip increased approximately linearly until it reached the ultimate pull-out force. Under the same pull-out displacement, the tensile force of the strip increased with the increase in vertical pressure. Specifically, at a pull-out displacement of 5 mm, the ultimate pull-out forces corresponding to the four pressure levels were 1.07 kN, 1.22 kN, 1.45 kN, and 1.59 kN, respectively. Furthermore, as the pressure increased, both the ultimate pull-out displacement and pull-out force increased, and the values and the magnitude of the increase are shown in

Table 5. Summary of one-sided friction limit pull-out parameters for tire strips.

Number	Vertical Load (kPa)	Ultimate Pull-Out Force		Ultimate Pull-Out Displacement (mm)	Rigidity (kN/m)
		Value (kN)	Magnitude of Increase (%)
1	40	1.176	/	7.5	156.8
2	60	1.753	49.1	10.7	163.8
3	80	2.325	32.6	13.7	169.7
4	100	2.909	25.1	17.3	168.2

. As shown in Table 5, with the increase in normal stress, the improvement ranges of the ultimate pull-out force of the single-sided tire strips were 49.1%, 32.6% and 25.1%, respectively, and the improvement ranges gradually decreased. This indicated that the tensile performance of the single-sided tire strips changed more significantly under low stress. The average stiffness of the single-sided tire strips was 164.6 kN/m.

Each particle in the soil was in a state of equilibrium under the combined action of internal and external forces. To maintain this state of equilibrium, when the vertical pressure was increased as an external force, the contact force on the surface of the soil particles was correspondingly increased as an internal force, which led to an increase in the frictional interlocking between the particles, thereby limiting the misalignment and slippage between the soil particles. The composite of soil and reinforcement was further compacted and the tightness was increased. Therefore, as the vertical pressure increased, a greater pull-out force was required to achieve the same displacement.

4.2. Load–Displacement Curves for Double-Sided Friction Pull-Out of Tire Strips

Figure 12 shows the results of the double-sided friction pulling test of waste tire strip under different vertical pressure conditions. The pull-out displacement of waste tire double-sided strip increased with the increase in pull-out force. Under the same pull-out displacement, the strip pull-out force increased with the increase in vertical pressure. For example, at a pulling displacement of 10 mm, four pressures corresponded to the ultimate pulling forces of 2.86 kN, 3.88 kN, 4.53 kN, and 5.15 kN, respectively. Meanwhile, as the pressure increased, the ultimate pull-out displacement and pull-out force increased, and the values and the magnitude of the increase are shown in

Table 6. Summary of tire strip double-sided friction limit drawing parameters.

Number	Vertical Load (kPa)	Ultimate Pull-Out Force		Ultimate Pull-Out Displacement (mm)	Rigidity (kN/m)
		Value (kN)	Magnitude of Increase (%)
1	40	2.86	/	11.1	257.65
2	60	4.11	43.6	16.5	248.84
3	80	5.29	28.8	20.3	260.49
4	100	6.51	23.0	22.5	289.15

. As shown in Table 6, with the increase in normal stress, the improvement ranges of the ultimate pull-out force of the double-sided strips were 43.6%, 28.8% and 23.0%, respectively. Compared with single-sided strips, the improvement range decreased slightly under the same stress. The average stiffness of the tire double-sided strips was 264.0 kN/m, which was 60.39% higher than that of the single-sided strips.

The waste tire double-sided strip exhibited non-linearity in the pull-out force–displacement curve: Phase 1 was the elastic–plastic phase before the pull-out force reached the peak, the pull-out force in this phase gradually increased with the increase in pull-out displacement, and the two were approximately linear. Phase 2 was the softening phase after the peak pull-out force, in which the pull-out force decreased at a slower rate with increasing pull-out displacement. Since the waste tire itself exhibits elasticity and plasticity, the strip followed Hooke’s law in the elastic deformation stage, where the load and displacement varied linearly. Because both the inner and outer sides of the strip experienced frictional contact with soil particles, the friction on the smooth inner side decreased significantly after reaching the peak pull-out force. As the strip continued to displace relative to the soil, the friction on the smooth inner side declined further. However, the rough outer surface compensated for this loss of friction, maintaining the overall tensile properties of the strip in a relatively balanced state and preventing rapid degradation.

4.3. Tire Grid Pull-Out Load–Displacement Curve

Figure 13 shows the results of the pull-out test of waste tire grid under different vertical pressure conditions. The pull-out curve of waste tire grid in weathered sand exhibited a distinct peak value. Under the same pulling displacement, the strip pulling force increased with the increase in vertical pressure. For instance, at a pull-out displacement of 15 mm, the four pressures yielded ultimate pull-out forces of 10.39 kN, 12.11 kN, 13.47 kN, and 17.23 kN, respectively. Moreover, as the pressure increased, both the ultimate pull-out displacement and pull-out force increased, and the values and the magnitude of the increase are shown in

Table 7. Summary of tire grid friction limit pull-out parameters.

Number	Vertical Load (kPa)	Ultimate Pull-Out Force		Ultimate Pull-Out Displacement (mm)	Rigidity (kN/m)
		Value (kN)	Magnitude of Increase (%)
1	40	11.91	/	22.2	556.4
2	60	16.93	42.1	30.5	555.0
3	80	21.85	29.1	39.5	547.6
4	100	26.58	21.7	48.9	543.5

. As shown in Table 7, with the increase in normal stress, the improvement ranges of the ultimate pull-out force of the tire double-sided strips were 42.1%, 29.1%, and 21.7%, respectively, which were similar to those of the strip double-sided structure. The average stiffness of the tire double-sided strips was 550.6 kN/m, which was about 2.09 times that of the double-sided strips. This indicated that the deformation resistance of the grid structure was significantly better than that of the strip structure, and it had excellent stability.

Under vertical pressure of 40 kPa, 60 kPa, and 80 kPa, the pull-out force and displacement of the waste tire grid maintained a more stable linear change before reaching the peak value. After reaching the peak value, the pull-out force decreased at a faster rate as the pull-out displacement increased. Waste tire grid had a more stable linear change at the beginning of the pull-out due to its transverse rib structure and greater overall stability. As the pulling force reached its peak, the relative displacement of the grid and soil particles still continued to increase. This led to an expansion of pore spaces between soil particles, triggering particle rearrangement: the originally dense and stable particle arrangement gradually transformed into a loose and unstable structure. Consequently, the lateral confinement capacity of the soil on the grid was reduced, further causing a rapid decline in pull-out force.

4.4. Comparison of Ultimate Pull-Out Forces of Three Types of Reinforced Bodies

Figure 14 shows the results of the ultimate tensile force under different vertical pressure conditions for the three types of reinforcing bodies. Under the same normal stress, the tensile strength of the tire grid was significantly greater than that of the tire single-sided strip and the tire double-sided strip. This indicates that processing waste tire strips into a grid could effectively improve the performance of the reinforcement material to resist deformation, and the tensile performance enhancement of the tire grid was more obvious under higher vertical pressure conditions. Further calculations of the ultimate bearing capacity and proportionality of the waste-tire-reinforcing body for different interface conditions are provided in

Table 8. Ultimate bearing capacity of waste-tire-reinforced body with different interface conditions and scaling relationship.

Number	Type	Pulling Force	Vertical Load
			40		60		80		100
			PR	R	PR	R	PR	R	PR	R
1	Single-sided friction	PRSI	1.176	0.411	1.763	0.429	2.325	0.439	2.909	0.447
2	Double-sided friction	PRSI + PRSE	2.860	/	4.106	/	5.288	/	6.506	/
3	Tire grid	${\alpha }_C$ (PRSI + PRSE) + PRB	11.908	/	16.926	/	21.848	/	26.579	/
4	End resistance	PRB	4.615	0.388	6.456	0.381	8.363	0.383	9.989	0.376

Note: R1 = P_S/P_D; R2 = P_RB/P_R; P_RB = P_R − ${\alpha }_C$P_D, ${\alpha }_C$ is the correction factor, ${\alpha }_C$ = Strip area/Grid area = 2.55.

. As shown in Table 8, under different vertical loads, the average ratio of single-sided friction to double-sided friction was 0.432, indicating that in double-sided friction, the external friction resistance of the tire accounted for 0.568 of the total friction resistance, and the patterned part bore a larger proportion of the interface load during the pull-out process. In addition, the average ratio of end resistance to the pull-out value of the tire grid was 0.382, which showed that the transverse rib structure played a significant role in resisting deformation during the pull-out of the grid, bearing more than 1/3 of the load.

With the increase in normal stress, the ultimate pull-out force of the three types of reinforced bodies shows a linear increase. The trend of the ultimate pull-out force with the normal stress could be obtained from the fitting formulas: tire strip single-sided friction: $F_{u1}$ = 0.2698 + 0.02881${\sigma }_n$; tire strip double-sided friction: $F_{u2}$ = 0.4332 + 0.06079${\sigma }_n$; tire grid: $F_{u3}$ = 2.1233 + 0.24589${\sigma }_n$. The initial interfacial friction between the tire grids and the soil body was significantly greater than that of the tire strips due to the embedding effect of the material and the presence of initial interfacial friction when the normal stress was not applied, and therefore, the intercept of the fitted equations was not zero. When neglecting the effect of initial interfacial friction, the ultimate pull-out force of the three types of reinforcement varied linearly with the normal stress when other factors were constant.

4.5. Reinforced Soil Interface Strength Parameters

To delve deeper into the mechanical behavior of waste-tire-reinforced soil systems, a series of pull-out tests were previously conducted to systematically analyze the interfacial bearing characteristics. Key data under various working conditions (such as ultimate pull-out force and displacement variation patterns) were obtained, providing a solid data foundation for determining the parameters of the calculation model. Building upon these experimental results and the established basic equations for bearing capacity, this section focuses on developing the calculation method for bearing capacity and validating the theoretical model against the experimental data to ensure its accuracy in reflecting real-world pull-out test results. As shown in Figure 15, based on the results of the pulling test and the characteristics of the test material, the known parameters of the tire inner and outer lateral friction resistance and end resistance bearing capacity formula were obtained. According to Equations (7)–(10), the external friction angle ${\delta }_1$, ${\delta }_2$ and lateral earth pressure coefficient k of the contact surface between the reinforcement material and the soil were calculated, respectively. Finally, the parameters were substituted into the mechanical model of ultimate pull-out force of waste tire grid, and the theoretically calculated values were compared with the measured values of the test to verify whether the established mechanical model could reflect the real results of the pull-out test.

4.5.1. Resistance to Friction on the Inner Side of the Tire

In the single-sided pull-out test of tire strips, since the strips are only subject to the frictional effect of the smooth surface, the calculation can be performed using the formula for the internal friction resistance of the tire. Given parameters such as the width of the strip reinforcement, the length of the reinforcement, and the effective contact surface coefficient, the external friction angle δ₁ between the inner side of the tire strip and the filler in the internal friction resistance Formula (7) of the tire is solved.

According to the results of the single-sided friction pulling test of waste tire strip in working condition I and the material properties of waste tire single-sided strip, the calculation parameters of Equation (7) could be determined step by step as follows.

(1)

Width of bars

From Figure 9, the width of the reinforcement was calculated as the width of the strip.

$$W_r=0.06 \mathrm{m}$$

(11)

(2)

Bar length

From Figure 9, the length of the bar buried in the tensile test box was calculated as the length of the bar.

$$L_r=0.65 \mathrm{m}$$

(12)

(3)

Effective contact surface coefficient

The effective contact surface coefficient was defined as the ratio of the effective contact area of the interface to the total area of the reinforcement, and since the filler was sufficiently compacted, it was considered ideal to achieve complete contact between the waste tire strip and the filler.

$${\alpha }_S=1.0$$

(13)

(4)

Effective principal stresses

In the single-sided friction pull-out test of waste tire strips, the applied vertical stresses were four fixed values, and the effective principal stresses in the middle range and representative were selected as the reference values for calculation.

$${\sigma }_n=80 \mathrm{kPa}$$

(14)

(5)

Tire inner side friction

When the effective principal stress was 80 kPa, it could be obtained from Table 8 as follows.

$$P_{\mathrm{RI}}=2.325\mathrm{kN}$$

(15)

(6)

Interfacial friction coefficient

The integrated interfacial friction coefficient was a comprehensive parameter used to reflect the friction characteristics between the reinforcement material and the filler. According to Equation (7), under the condition of known parameters, the interfacial friction coefficient could be calculated as follows.

$$f_1={\displaystyle \frac{P_{\mathrm{RI}}}{{\alpha }_S{W}_r{L}_r{\sigma }_n}}=0.745$$

(16)

(7)

Angle of external friction at the contact surface between reinforcement and soil

The relationship between the coefficient of interfacial friction and the angle of external friction at the contact surface is shown in Equations (17) and (18).

$$f_1=\mathit{tan}{\delta }_1$$

(17)

$${\delta }_1={\mathit{tan}}^{-1}{f}_1=36.7°$$

(18)

Based on the specific calculation process described above, the benchmark table for the parameters of the formula for calculating the friction resistance of the inner face of the tire was given as follows. Through further calculations, the external friction angles (δ₁) between the reinforcement material and soil under 20 kPa, 40 kPa, and 100 kPa were obtained as 36.5°, 36.4°, and 36.2°, respectively. The error between these values and the calculated values in

Table 9. Benchmark parameters of formula for calculating the friction resistance of tire inner face.

Calculation Parameters	${\mathit{W}}_{\mathit{r}}$ (m)	${\mathit{L}}_{\mathit{r}}$ (m)	${\mathsf{\alpha }}_{\mathit{S}}$	${\mathit{f}}_{\mathbf{1}}$	${\mathsf{\delta }}_{\mathbf{1}}$ (°)
Value	0.06	0.65	1.0	0.745	36.7

was less than 1%. Therefore, the pull-out force values of single-sided tire strips under different normal stresses could well verify the reliability of the formula for the internal friction resistance of tires.

4.5.2. Outer Sidewall Friction of the Tire

In the double-sided pull-out test of tire strips, frictional resistance occurs on both the inner and outer sides of the strip. Based on the determination of the inner frictional resistance in the previous section, calculations can be performed using the formula for the outer frictional resistance of the tire. Given parameters such as the tread pattern ratio of the strip, apparent cohesion, and internal friction angle, the external friction angle δ₂ between the outer side of the strip and the filler in the outer frictional resistance Formula (8) of the tire is solved for.

According to the drawing test results of working conditions I and II and the material properties of waste tire double-sided strip, the calculation parameters in Equation (8) could be determined, of which the strip width $W_r$, strip length $L_r$, effective contact surface coefficient ${\alpha }_S$ were the same as in Equation (7), and other parameters were determined as follows.

(1)

Stripe surface pattern characteristics

$$\xi =0.2$$

(19)

(2)

Class cohesion

According to the weathered sand triaxial test molar stress circle, the shear strength index could be obtained:

$$\mathrm{c}=3.44 \mathrm{k}\mathrm{P}\mathrm{a}$$

(20)

(3)

Internal friction angle

$$\phi =29°$$

(21)

(4)

Effective principal stress

Consistent with the formula for calculating the inner friction resistance of tires, the following effective principal stresses were selected as reference values for calculation:

$${\sigma }_n=80 \mathrm{k}\mathrm{P}\mathrm{a}$$

(22)

(5)

Tire inner side friction

When the effective principal stress was 80 kPa, from Table 8:

$$P_{RII}=P_D-P_S=2.962 \mathrm{k}\mathrm{N}$$

(23)

(6)

Integrated interfacial friction coefficient

According to Equation (8), the interfacial friction coefficient could be calculated under known parameters as follows:

$$f_2={\displaystyle \frac{P_{RII}-(1-\xi )W_r{L}_r(c+{\sigma }_n\mathit{tan}\phi )}{{\alpha }_S{\xi W}_r{L}_r{\sigma }_n}}=2.358$$

(24)

(7)

Angle of external friction at the contact surface between the reinforcement and the soil

The coefficient of interfacial friction was related to the angle of external friction of the contact surface as shown in the equation:

$$f_2=\mathit{tan}{\delta }_2$$

(25)

$${\delta }_2={\mathit{tan}}^{-1}{f}_2=67.02°$$

(26)

Based on the above specific calculation process, the benchmark table of the parameters of the formula for calculating the friction resistance of the inner side of the tire given was as follows. Through further calculations, the external friction angles (δ₂) between the reinforcement material and soil under 20 kPa, 40 kPa, and 100 kPa were obtained as 70.6°, 68.7°, and 66.1°, respectively. The errors between these values and the calculated values in

Table 10. Calculation parameters of tire outer side friction model.

Calculation Parameters	$\mathsf{\xi }$	${\mathit{W}}_{\mathit{r}}$ (m)	${\mathit{L}}_{\mathit{r}}$ (m)	${\mathsf{\alpha }}_{\mathit{S}}$	${\mathit{f}}_{\mathbf{2}}$	${\mathsf{\delta }}_{\mathbf{2}}$ (°)	c (kPa)	φ (°)
Numerical value	0.2	0.06	0.65	1.0	2.358	67.02	3.44	29

were 5.37%, 2.54%, and 1.3%, respectively. The results showed that the calculation model for the external friction resistance of tires under high normal stress had better adaptability to the test results.

4.5.3. Tire End Resistance

In the pull-out test of tire grids, there is not only frictional resistance on the inner and outer sides of the strips but also end resistance generated by the transverse ribs. Based on the determination of the inner and outer frictional resistances of the tire, calculations can be performed using the formula for the tire end resistance. Given parameters such as the thickness of the transverse rib units, the number of transverse rib units, and correction coefficients, the lateral pressure coefficient k between the waste tire grid and the filler in the tire end resistance Formulas (9) and (10) is solved for.

According to the pulling test results of working conditions two and three and the nature of waste tire grid material, the calculation parameters in Equations (9) and (10) could be determined, in which the strip width $W_r$, strip length $L_r$, effective contact surface coefficient ${\alpha }_S$, class cohesion c, and the angle of internal friction $\phi$ were the same as those in Equation (8), and the other parameters were determined as follows:

(1)

Thickness of transverse rib unit

$$B=0.02 \mathrm{m}$$

(27)

(2)

Number of transverse rib units

$$n=3$$

(28)

(3)

Correction factor

The correction factor ${\alpha }_B$ was the ratio of the width of the transverse rib to the total width of the reinforcement:

$${\alpha }_B=0.5$$

(29)

(4)

Effective principal stress

Consistent with the formula for calculating the inner friction resistance of tires, the following effective principal stresses were selected as reference values for calculation:

$${\sigma }_n=80 \mathrm{k}\mathrm{P}\mathrm{a}$$

(30)

(5)

End Resistance Carrying Capacity

When the effective principal stress was 80 kPa, from Table 8, the tire end resistance load capacity could be seen:

$$P_{\mathrm{R}\mathrm{I}\mathrm{I}\mathrm{I}}=8.363 \mathrm{k}\mathrm{N}$$

(31)

(6)

Breaking the plane angle

Determine the damage plane angle of suitable weathered sand fillers based on the relevant literature:

$$\mathsf{\beta }=\mathsf{\pi }/2$$

(32)

(7)

Lateral earth pressure coefficient

Under the above known parameter conditions, the lateral earth pressure coefficients were determined according to Equations (9) and (10), based on the MD-3 modeling formulas:

$$\mathrm{k}=1.96$$

(33)

Based on the specific calculation process described above, the benchmark table of parameters for the end-resistance bearing capacity formula given was as follows. Through further calculations, the lateral earth pressure coefficients (k) under 20 kPa, 40 kPa, and 100 kPa were obtained as 2.18, 1.99, and 1.76, respectively. The results showed that when the normal stress was 40 kPa and 60 kPa, the calculated lateral earth pressure coefficients were close, indicating that the model had good reliability. However, when the normal stress was 20 kPa and 100 kPa, the error was about 10%, which suggested that the model needed further optimization to improve its accuracy under low or high stress conditions.

Analyzing the reasons, it might be that the interfacial friction between the tire reinforcement material and the soil was more sensitive to microscale changes (such as local redistribution of soil particles or slight deformation of the tire grid structure). Since the theoretical model assumed a uniform distribution of interfacial shear stress, this assumption oversimplified the actual discontinuous stress transmission state under low or high stress conditions. As a result, additional minor disturbances occurred at the interface under such conditions, leading to large deviations in the calculation results.

4.5.4. Comparison of Experimental and Theoretical Values

To comprehensively consider various influencing factors of the model under ideal conditions, the test parameters under a normal stress of 80 kPa were adopted as the benchmark parameters of the model. The reason is that under this normal stress, the numerical changes in the pull-out force load–displacement curve of the tire grid are more stable, which can reflect the actual engineering situation. Based on the calculation parameters determined in Table 9, Table 10 and

Table 11. Table of parameters for calculation of end-resistance bearing capacity formula.

Calculation Parameters	k	β	${\mathsf{\alpha }}_{\mathit{B}}$	B (m)	c (kPa)	φ (°)
Numerical value	1.96	π/2	0.5	0.02	3.44	29

, the data comparison graph between the theoretical pull-out value and the measured pull-out value of the waste tire grid was obtained, as shown in Figure 16, which showed that the theoretical pull-out value was well fitted with the measured pull-out value. The average error of the calculation model was 2.38% (with the maximum error being less than 5%), proving that the calculation model of the ultimate pull-out force of the waste tire grid was reliable.

5. Conclusions

This study reported the results of pull-out tests conducted on single-sided tire strips, double-sided tire strips, and tire grids subjected to varying normal stresses. The results indicated that tire grids displayed markedly superior tensile performance compared to single-sided and double-sided tire strips. The experimental data confirmed the accuracy of the calculation formula for the ultimate pull-out force of waste tire grids, offering theoretical support for interface bearing capacity assessments and stability analyses in subgrade reinforcement design.

(1)

Based on the limit equilibrium theory and the structural form of tire grids, considering the frictional characteristics of longitudinal rib interfaces and the loading characteristics of transverse rib structures, calculation formulas for the internal friction resistance, external friction resistance, and end resistance capacity of tires were proposed. A prediction model for the ultimate pull-out force of recycled tire grids was established by comprehensively considering interfacial friction and end resistance.

(2)

Under the same pulling displacement conditions, the pulling force of the three types of reinforced bodies increased with the increase in vertical pressure. The results indicated that the tensile strength of one side of the strip was approximately 43% of that of both sides, and the rough outer surface of the tire significantly enhanced the tensile performance of the strip. The overall rule of change presented an obvious non-linear phase change rule, and the strain softening characteristics of tire grids were more obvious than those of tire strips.

(3)

Under the same normal stress, the tensile strength of tire grids was approximately nine times that of single tire strips and about four times that of double tire strips. Consequently, processing tires into grid structures could significantly enhance their deformation resistance. The ultimate tensile strength of the three types of reinforcement increased linearly with the normal stress, with the normal stress coefficients in the corresponding fitting formulas being 0.02881, 0.06079, and 0.24589, respectively. The tensile strength of tire grids exhibited the highest growth rate.

(4)

Based on the pull-out test results, the baseline calculation parameters for the internal friction resistance, external friction resistance, and end resistance of the tire grid were determined and substituted into the formula for calculating the ultimate pull-out force of waste tire grids. The error between the theoretical and measured pull-out values was less than 5%, verifying the reliability of the mechanical model for predicting the ultimate pull-out force of waste tire grids.

In the future, we plan to continue in-depth research on the impact of cyclic traffic loads and rubber service life on the durability of waste tire grids, integrid methods such as finite element models and three-dimensional numerical simulations [24] to specifically present the development and changes in their fatigue. By clarifying the laws of their durability attenuation, it can effectively improve the safety, stability and service life of reinforced soil structures containing waste tire grids in complex traffic environments, reduce engineering maintenance costs, and have both important academic value and significant economic and environmental benefits, thus providing more comprehensive theoretical support for the engineering application of waste tire grids.