Investigation of the Shear and Pore Structure Characteristics of Rubber Fiber-Reinforced Expansive Soil

Abstract

In recent years, many researchers have evaluated the sustainable use of waste tire rubber as an aggregate in soil. Its effectiveness has been widely acknowledged. The main objective of this work is to study the influence of rubber fibers on shear strength and pore structure characteristics in relation to expansive soil. In this context, we conducted a series of experiments that were carried out on reinforced expansive soil with rubber fiber contents of 0, 5, 10, 15, and 20%. The results show that the shear strength and maximum dilatation angle increase gradually with rubber fiber content. Due to the pore water pressure and creep effects, the deviator stress and effective cohesion of the samples under the consolidated drained conditions were higher than those under the undrained conditions. The converse was true for the internal angle. The addition of an appropriate amount of (5–10%) rubber fiber can effectively inhibit the development of soil cracks and reduce the porosity of the samples. The results obtained can highlight the beneficial effects of rubber fiber, which is highly desirable in many backfill applications.

1. Introduction

Expansive soil is rich in strong hydrophilic minerals such as montmorillonite and illite. It is generally considered a problem soil with a high expansion potential, with expansion contractility, multi-fracture, and over-consolidation [1]. The internal factors affecting soil expansion and contraction include mineral composition and microstructure. Meanwhile, the external factors include water and climatic conditions. Expansive soil is known as “catastrophic soil” because of the cyclic process of shrinkage and expansion: it characteristically expands when it absorbs water and contracts when it loses water [2]. This generally damages the superstructure, particularly the slight structure, e.g., cracking and destruction of foundations [3], roadbeds [4], dams [5], and channels [6]. According to statistics, the losses caused by expansive soil worldwide amount to billions of dollars. Within this, 10 million square meters of houses were destroyed due to expansive soil in China, and the economic losses exceeded USD 1 billion [7]. Therefore, it is necessary to improve expansive soil foundations to reduce the adverse effects of expansive soil on project services.

The currently proposed methods to improve the engineering properties of expansive soil mainly involve chemical, physical, and biological aspects. Chemical methods improve the soil conditions through the use of additives, such as fly ash, cement, and lime [8,9,10,11,12]; physical methods improve soil conditions via geosynthetics, soil substitution, and moisture control [13,14,15,16,17]; and biological methods improve the soil conditions through the catalytic action of biological enzymes [18,19,20,21,22]. The use of soil replacement methods may considerably increase construction costs. Although the use of additives such as cement effectively suppresses the expansion and contraction of expansive soil, the carbon dioxide emitted during the production of cement is uncontrollable. This has an adverse impact on the environment and a low long-term advantage. Therefore, it is necessary to study energy-saving and environmentally friendly methods to improve expansive soil.

The resource utilization of solid waste is an important part of China’s green, low-carbon, and circular economic system. Additionally, it is a strategic measure to achieve “carbon peak and carbon neutrality”. In February 2022, to promote the standardized utilization of renewable resources, eight departments, including the Ministry of Industry and Information Technology, issued the “Implementation Plan on Accelerating the Comprehensive Utilization of Industrial Resources”. It promotes the comprehensive utilization of renewable resources such as scrap steel, waste non-ferrous metals, waste tires, waste paper, and waste mobile phones. Research has shown that solid waste recycling and reuse are key to achieving eco-friendly, eco-efficient, and sustainable infrastructure development on a global scale.

The growing number of scrap tires, one of the largest sources of solid waste, has generated severe disposal challenges. It is estimated that a billion tires are discarded globally annually. This number is projected to increase to 1.2 billion by 2030 [23]. In the past ten years, rubber generation and recycling volumes in China have increased, as shown in Figure 1. In 2022, the amount of waste tires generated was 13.5 million tons, and the recycling volume was 6.5 million tons. This corresponded to a recycling rate of waste tires of 48.15%. The rate is relatively low, and the recycling capacity is relatively insufficient. This implies that there are relatively abundant waste tires for recycling and advantageous reuse. With the increasing awareness of environmental protection and resource conservation, the reuse of waste resources has become a new trend in scholarly research. Studies have shown that adding rubber fibers to soil can mitigate swelling potential, improve ductility, and increase shear strength. Abbaspour et al. [24] found that rubber fibers can mitigate the swelling characteristics of expansive soils by up to 44% of the swelling deformation of expansive soils. Özkul and Baykal [25] evaluated the effect of rubber fibers on the shear properties of clays using triaxial and permeability tests and found that rubber fibers increased the shear strength of clays; however, the change in permeability was not significant.

The main problem of expansive soil is that its strength is generally low. It generally varies with alterations in the load and drainage conditions. Moreover, it may differ in strength and deformation behavior under drained and undrained loading conditions. For example, Li et al. [26] evaluated the effects of confining pressure, initial dry density, initial moisture content, and drainage conditions on the mechanical properties of expansive soil based on consolidated drained and undrained tests. They determined that a hyperbolic model could be used to fit the strain–hardening curves in the drained tests, and an exponential curve model could be used to fit the strain–softening curves in the undrained tests. Tajdini et al. [27] investigated the effects of rubber chips on the mechanical properties of kaolinite clay via undrained and drained triaxial tests. They determined that the shear strength, dilatation angle, and shear stiffness of reinforced soil were higher under drained conditions than under undrained conditions. Fiber reinforcement is an effective method to improve the shear strength and ductility of soil. It is necessary to study the drainage response of fiber-reinforced soil to evaluate its long-term stability. Furthermore, it is necessary to investigate the effect of drainage conditions on the mechanical properties of fiber-reinforced soil.

The purpose of this study was to explore the drainage conditions and the mechanical properties of rubber fibers to improve expansive soil. The effects of rubber fibers on the shear strength, maximum dilatation angle, and pore diameter of expansive soils were quantified. Additionally, the effect of rubber fibers on the pore distribution of expansive soil was analyzed quantitatively. The test results can help evaluate the improvement effect that rubber fibers had on expansive soil, realize the utilization of waste tires to improve the environment, and provide theoretical support for the use of waste rubber in expansive soil engineering.

2. Materials and Methods

2.1. Test Preparation

2.1.1. Test Materials

The expansive soil used in this study was the Henan remodeled expansive soil. Its gradation curve is shown in Figure 2. Physical property indices, such as optimum water content, maximum dry density, liquid–plastic limit, and other physical properties of the expansive soil, were tested according to the standard geotechnical test methods. The results are shown in

Table 1. Physical properties of expansive soil.

Properties	Value
Natural moisture content	6.10%
Optimum moisture content	16.00%
Maximum dry density	1.853 g·cm−3
Specific gravity	2.73
Plastic limit	22.30%
Liquid limit	57.80%
Plasticity index	35.50
Free swell ratio	71.00%

. The expansive soil was dried and crushed through a 1 mm sieve to make soil powder for subsequent use.

Rubber is a composite material with high elasticity, durability, and friction resistance. The rubber fibers used in the tests were produced at the tire processing plant in Deyang, Sichuan, China. It was sieved to remove fine particles and coarse debris. Then, fibers with a length of approximately 15 mm and a diameter of approximately 1 mm were selected.

2.1.2. Sample Preparation and Saturation

The soil was initially prepared with an optimal moisture content. Then, it was mixed with fibers until the mixture was homogeneous. Subsequently, the sample was prepared. A mixture of rubber fibers and expansive soil was prepared via layered compaction to improve the random and uniform distribution of fibers in the sample. During the compaction process, the layers were scraped to ensure good bonding between adjacent layers of the mixture. The prepared samples were saturated using the pumping saturation method, placed in a vacuum saturation cylinder for 2 h, and then saturated by immersion in water for 48 h.

In this study, the rubber fiber content was defined as the ratio of the total mass of rubber to that of the rubber fiber-reinforced expansive soil. This is shown in Equation (1). Soltani et al. [28] found that when the rubber content exceeds 10%, the performance of the specimen changes greatly. Therefore, 0, 5,10, 15, and 20% rubber contents were selected for this study.

$$f=\frac{m_R}{m_s+m_{\omega }+m_R}\times 100\%$$

(1)

where $m_R$ is the mass of rubber fibers, $m_s$ is the mass of soil, and $m_{\omega }$ is the mass of water in the mixture.

2.2. Triaxial Test

The test instrument was a TSZ automatic triaxial instrument with computer control and automatic data acquisition systems. A pressure transducer was used to measure the pore water pressure inside the sample. A load cell and linear variable differential transducer (LVDT) measured the load and strain.

The displacement-controlled undrained shear tests were performed at a rate of 0.08 mm/min. The confining pressure ${p^{\prime }}_0$ was set to 100, 200, and 300 kPa, respectively. The displacement-controlled drained shear tests were performed at a rate of 0.0096 mm/min with the above-mentioned confining pressure. The triaxial test scheme for the rubber fiber-reinforced expansive soil is presented in

Table 2. Triaxial test scheme for the rubber fiber-reinforced expansive soil.

Sample	Rubber Fiber Content $\mathit{f}$ (%)	Shearing Rate (mm min−1)	Drainage Condition
ESR-1	0	0.08	undrained triaxial test
ESR-2	5
ESR-3	10
ESR-4	15
ESR-5	20
ESR-6	0	0.0096	drained triaxial test
ESR-7	10

.

2.3. Nuclear Magnetic Resonance (NMR) Test

The nuclear magnetic moment formed by the nuclear spin absorbs energy and transitions to a high-energy state. This releases energy in the form of electromagnetic waves to form a receptible radio signal known as NMR. It is a highly effective tool for studying water migration, pore size, and characteristic distribution in porous media. A PQ001-PM NMR analyzer (Suzhou Niumag Analytical Instrument Corporation, Suzhou, Jiangsu Province, China) was used. The triaxial test scheme for the rubber fiber-reinforced expansive soil is listed in

Table 3. Nuclear magnetic resonance test scheme.

Sample	Rubber Fiber Content $\mathit{f}$ (%)	Frequency (kHz)	Echo Interval (ms)
ESR-8	0	333	0.08
ESR-9	5
ESR-10	10
ESR-11	15

.

3. Results and Discussion

3.1. Undrained Behavior of Expansive Soil-Rubber Fiber (ESR)

Figure 3 shows the deviator stress, effective stress path, and pore water pressure for the ESR with different rubber fiber contents at a confining pressure of 200 kPa. The test results show that the deviator stress of the ESR increased with the rubber fiber contents. The deviator stress of ESR-1 is the smallest and that of ESR-3 is the largest.

Compared with ESR-1, the stress–strain response of ESR varied with the addition of rubber fibers, as shown in Figure 3a. ESR-1 exhibits an initial strain hardening behavior in the nonlinear deviator stress–strain curve. It attains a peak deviator stress of 116.2 kPa under 14% axial strain. As the shear proceeds, the ESR tends to display strain softening behavior. This is manifested by a decrease in deviator stress. The peak deviator stress decreases from 116.2 kPa to 112.1 kPa. This agrees with the results of Alam et al. [29]. That study investigated the mechanical response of root-reinforced loess by triaxial tests. ESR-2, ESR-3, ESR-4, and ESR-1 showed similar deviator stress–strain trends. Moreover, significant deviator stress peaks were observed, namely, 128.6 kPa, 134.5 kPa, and 124.4 kPa, respectively. Conversely, no significant peak deviator stress was observed for ESR-5. Figure 3d shows the pore water pressure curves for the ESR. These exhibit a trend similar to that of the deviator stress. The maximum pore water pressure (80.5 kPa) was obtained for ESR-4, and the minimum (73.2 kPa) was obtained for ESR-1. During the undrained shear test, the pore water pressure was related to the tendency of contraction and expansion. The effective stress path of ESR is shown in Figure 3c. The slope of the ESR stress path to the left indicates that it generates a positive pore water pressure during shearing, which reflects the contraction behavior of the ESR (Figure 3c). The deviator stress-strain curve for the ESR in the 0-4% strain range was selected, as shown in Figure 3b. Figure 3b shows that under equal deviating stress, the strain of the rubber fiber-reinforced expansive soil was higher than that of the unreinforced expansive soil. This indicated that the rubber fibers reduced the initial stiffness of the expansive soil.

The undrained triaxial test results of the ESR at confining pressures of 100, 200, and 300 kPa are shown in Figure 4 and Figure 5. The results reveal that the incorporation of rubber fibers increased ESR deviator stress, which was more significant at higher confining pressures (200 and 300 kPa). However, the effect on the deviator stress at 100 kPa was negligible. This is consistent with the results reported by Freilich et al. [30], who observed that the effectiveness of fibers for soil shear strength enhancement increases with an increase in confining pressure. Prior to shearing, the interaction between the soil particles and fibers improved owing to the increased confining pressure, and the fibers stretched gradually. As the presence of well-dispersed rounded particles destroys the sliding surface to increase the shear strength, the rougher surface of the rubber fibers makes the adhesion between the fibers and the soil play a significant role. The adhesion between the rubber fibers and the soil particles is greater than the friction force within the soil.

At the beginning of the shear phase, the fibers improved the distribution of the applied shear stress over a wider area. However, at lower confining pressures, the fibers may not interact effectively with the soil particles and may slip in shear. Thus, at relatively low confining pressures, fibers may not effectively confine soil particles or increase the strength of fiber-reinforced soil.

The pore water pressures of reinforced expansive soil and unreinforced soil under undrained conditions are shown in Figure 5. With the increase in rubber fiber content, the pore water pressure gradually increased and then decreased, and the maximum was obtained at ESR-4. The pore water pressures at 100, 200, and 300 kPa of ESR-1 were 40.6, 81.1, and 92.3 kPa, respectively, while the corresponding pore water pressures of ESR-4 were 44.3, 83.9, and 98.1 kPa, which were 9.1%, 3.5% and 6.3% higher, respectively. This indicated that the increase in pore water pressure is related to the distribution of fibers in the soil. It was noted that the effect of the confining pressure on the pore water pressure gradually increased as the confining pressure increased.

3.2. Drained Behavior of ESR

The deviator stress–strain curves and volume strain–strain curves of the ESR with 0 and 10% rubber fiber content in the drained tests are shown in Figure 6 and Figure 7, respectively. The tested ESR showed different damage patterns. The middle part of the unreinforced expansive soil (ESR-6) showed a significant uplift, whereas the uplift of the rubber fiber-reinforced expansive soil (ESR-7) was distributed uniformly along the height of the sample. This indicated that the rubber fibers played an important role in transferring the stress and strain inside the sample.

As anticipated, the deviator stress and shrinkage increased as the rubber fiber content and confining pressure increased. Under equal confining pressure, the strain of the reinforced soil when attaining the maximum deviator stress was significantly higher than that of the unreinforced soil. This indicated that the rubber fiber significantly improved the ductility of the soil. This was in agreement with the study of the effect of plant roots on the mechanical properties of the soil by Xu et al. [31]. With an increase in strain, the deviator stress of ESR-6 attains a peak at 16% strain. After the plastic deformation of ESR-7, the resistance of the fibers was activated. There was no apparent peak deviator stress, which was manifested in the form of strain hardening. At confining pressures of 100, 200, and 300 kPa, the deviator stress of ESR-7 increased from 111.8, 130.6, and 204.3 kPa to 130.4, 177.8, and 210.8 kPa, respectively. This corresponded to increases of 16.6%, 36.1%, and 3.2%, respectively. Safdar et al. [32] indicated that this could be owing to frictional interactions between the particles and fibers, as well as an increase in tensile strength provided by the fiber modulus.

With regard to the volume strain–strain response, the volume strain–strain curves of ESR-6 and ESR-7 exhibit compressive behavior throughout the shear process until the end of the test, as shown in Figure 7. Under equal confining pressure, the volume variations of ESR-6 and ESR-7 were marginally different. ESR-7 exhibited a larger initial shrinkage than ESR-6 and was distributed over a larger strain range. This may have been owing to the compression of the rubber fiber. Correia et al. [33] also observed that fiber-reinforced soil contracts more than unreinforced soil during shearing.

3.3. Strength Characteristics

The relationship between the shear stress and effective stress for the unreinforced expansive soil and 10% rubber fiber-reinforced expansive soil is shown in Figure 8. Here, the deviator stress of the undrained samples is lower than that of the drained samples. The difference decreases with an increase in the effective stress. Simultaneously, the effective stress of the undrained samples shifts to the left and the slope of the curve decreases owing to the pore water pressure.

For the drained and undrained conditions, the effective cohesion under the drained conditions was higher than that under the undrained conditions. The converse was true for the effective angle of internal friction. This is attributed to the effects of the pore water pressure and creep at the fiber–soil interface. Under drained conditions, owing to the lower strain rate, the test time increased significantly, and the influence of time on the interfacial strength (such as the time-varying slip or rearrangement of soil particles) was more evident. However, the pore water in the drained conditions was drained out of the soil, the stress was sustained by the soil skeleton and rubber fibers, and the occlusion capacity between the soil particles and fibers improved. Similarly, Freilich et al. [30] conducted consolidation undrained and consolidation drained triaxial tests on polypropylene fiber-reinforced soil. They observed that the effective shear strength parameters of the reinforced soil were higher under the undrained conditions. Özkul and Baykal [25] evaluated the shear strength of rubber fiber-reinforced soil under undrained and drained conditions. They observed that although the angle of internal friction was approximately equal for both conditions, the cohesion under the undrained conditions was higher than that under the under drained conditions.

The addition of rubber fibers increased the effective cohesion of the samples from 12.4 kPa (ESR-1) to 15.5 kPa (ESR-3). This corresponded to an increase of 25%. From ESR-6 to ESR-7, the effective cohesion increased from 21.3 kPa to 32.5 kPa (an increase of 52.6%). Meanwhile, the effective internal friction angle varied marginally. This is similar to the results obtained by Valipour et al. [34]. This indicates that rubber fibers can effectively interlock soil particles, improve the interaction between the fiber surface and soil matrix, and increase the effective cohesion [35,36].

3.4. Stiffness Characteristics

3.4.1. Structural Characterization Based on Tangential Stiffness

Observing that ESR yields under shear, Malandraki and Toll [37] and Wang et al. [38] indicated that the yield point can be determined from the curve of the tangential stiffness $E_{\tan }$ and axial strain in double logarithmic coordinates. The formula for calculating $E_{\tan }$ refers to the generalized Hooke’s law, as shown in Equation (2):

$$E_{\tan }=\left(\mathrm{d}{{\sigma }_1}^{\prime }-2\nu \mathrm{d}{{\sigma }_3}^{\prime }\right)/\mathrm{d}{\epsilon }_1$$

(2)

where $\mathrm{d}{{\sigma }_1}^{\prime }$ is the first effective principal stress increment, $\mathrm{d}{{\sigma }_3}^{\prime }$ is the third effective principal stress increment, $\mathrm{d}{\epsilon }_1$ is the axial strain increment, and $\nu$ is Poisson’s ratio.

From the consolidated drained condition, ${{\sigma }_3}^{\prime }$ is a constant, and $\mathrm{d}{{\sigma }_3}^{\prime }=0$. The shear tangential stiffness $E_{\tan }$, can be expressed as follows:

$$E_{\tan }=\frac{\mathrm{d}{{\sigma }_1}^{\prime }}{\mathrm{d}{\epsilon }_1}$$

(3)

To eliminate the influence of the average effective stress on the tangential stiffness during the shear process, $E_{\tan }$ was normalized. Figure 9 compares the $E_{\tan }/p^{\prime }$–${\epsilon }_1$ relationship curves for different rubber fiber contents at a confining pressure of 100 kPa with that of rubber-reinforced soil determined by other scholars [36,39,40]. From the figure, when ${\epsilon }_1<1.2\%$, the ESR of $E_{\tan }/p^{\prime }$ remained at approximately 20, although it reduced marginally. However, the magnitude of the reduction was not apparent. When $1.2\%<{\epsilon }_1<15\%$, as the shear progressed, the samples began to yield structurally, and $E_{\tan }/p^{\prime }$ decreased gradually with the increase in ${\epsilon }_1$. When $15\%<{\epsilon }_1$, the rate of variation in the normalized stiffness with the axial strain further increased, the curve was essentially close to being vertical, and the samples underwent overall failure. The relationship between $E_{\tan }/p^{\prime }$ and ${\epsilon }_1$ reveals an apparent yield point in the unreinforced soil. It corresponds to the destruction of the original arrangement and cementation of soil particles. After the addition of rubber, there was no apparent yield point in the reinforced soil. Yadav and Tiwari [38] indicated that the stretching of rubber would prevent the formation of face-to-face arrangement of soil particles.

Although the addition of rubber increased the shear strength of the mixture, $E_{\tan }/p^{\prime }$ decreased gradually as the rubber content increased. This is attributed to the temporary compression of the rubber fibers when subjected to confining pressure or kinking. This is in agreement with the observations of Akbarimehr et al. [39] and Özkul and Baykal [25]. Similarly, Gray and Ohashi [41] determined that fibers with a higher modulus tended to increase the shear strength and failed to increase the stiffness of the mixture. Meanwhile, Michalowski and Čermák [42] demonstrated that fibers reduce the stiffness or modulus.

3.4.2. Maximum Dilatation Angle

In continuum mechanics, the most widely used parameter for quantifying expansion is the dilation angle $\psi$. It can be obtained from triaxial tests as the ratio of the volume strain increment to the axial strain increment. Zhao and Cai [43] defined the physical significance of $\psi$ as frictional sliding along microcracks or particles.

The maximum dilatation angle under triaxial conditions was estimated according to the equation proposed by Vaid and Sasitharan [44]:

$${\psi }_{\max }={\sin }^{-1}\left(\frac{2}{\frac{3}{{\left|\mathrm{d}{\epsilon }_{\mathrm{v}}/d{\epsilon }_1\right|}_{\max }}-1}\right)$$

(4)

where ${\left|\mathrm{d}{\epsilon }_{\mathrm{v}}/d{\epsilon }_1\right|}_{\max }$ is the maximum rate of volume variation or expansion.

Figure 10 shows the variation in the maximum dilatation angle ${\psi }_{\max }$ with the rubber fiber content. It is positively correlated with the rubber fiber content for a given confining pressure [40,45]. It is demonstrated that the rubber affects the maximum dilatation angle of the ESR. This is because when the ESR sustains pressure, the rubber fiber sustains part of the stress transmission. Because of its deformable characteristics, the porosity ratio of the sample reduces. This considerably increases the compressibility of the sample. Perez et al. [46] determined that an increase in the size of the rubber also increases the maximum dilatation angle.

3.5. Effect of Rubber Fibers on Pore Size Distribution

Relaxation refers to the process by which the spin of a proton is stabilized from an excited state to an equilibrium state. Transverse relaxation refers to the time required for the maximum excited state to approach zero. The transverse relaxation time is determined using the proton relaxation time $T_{2\mathrm{B}}$ and surface relaxation time $T_{2\mathrm{S}}$.

$$\frac{1}{T_2}=\frac{1}{T_{2\mathrm{B}}}+\frac{1}{T_{2\mathrm{S}}}\approx {\rho }_2\left(\frac{S}{V}\right)$$

(5)

where ${\rho }_2$ is the surface relaxation rate, which is related to the physicochemical properties of the soil. $S$ and $V$ are the surface area and pore volume, respectively, of the porous medium.

The porosity and pore distribution characteristic parameters of the soil were calculated using the NMR transverse relaxation time $T_2$ spectrum. The relationship between the relaxation time and pore size is shown in Equation (6). From this equation, $T_2$ is linearly related to the pore size. Therefore, if the value of the surface relaxation rate ${\rho }_2$ is known, the pore-size distribution in the ESR can be obtained by measuring $T_2$. According to Lu [48], the ${\rho }_2$ of expansive soil is considered as 3 μm s⁻¹.

$$\frac{1}{T_2}\approx {\rho }_2\left(\frac{S}{V}\right)\approx {\rho }_2\left(\frac{2}{R}\right)$$

(6)

Figure 11 shows the relaxation curves of the ESR for different rubber fiber contents. The variation characteristics of the $T_2$ spectrum for different rubber fiber content were almost identical. This indicates that the distribution of internal pores was approximately identical. The $T_2$ spectra of the ESR with different fiber contents consist of two spectral peaks: a primary peak and secondary peak. The secondary peak is significantly smaller than the main peak. This indicates that the internal pore size had good continuity. Using ESR-8 as an example, the relaxation time corresponding to the vertex was 1.589 ms. Of this, the main peak accounted for 97.6%. To compare the data more visually, the spectral distributions of the other rubber fiber contents are presented in

Table 4. $T_2$ spectrum distribution of the ESR for different rubber fiber content.

Sample	Beginning and Ending Relaxation Times of Spectrum Peaks (ms) (Peak Percentage)
	Primary Peak	Secondary Peak
ESR-8	0.561–9.011 (97.6%)	9.659–36.123 (2.4%)
ESR-9	0.455–7.843 (97.6%)	8.407–33.701 (2.4%)
ESR-10	0.488–8.407 (97.4%)	9.011–31.440 (2.6%)
ESR-11	0.644–9.011 (97.3%)	9.659–36.123 (2.7%)

. As shown in Figure 11, the $T_2$ spectrum curve shifts to the left to a certain extent as the rubber fiber content increases. Comparing ESR-8 and ESR-11, the relaxation time corresponding to the main peak is equal (1.589 ms). However, the peak area of ESR-11 is larger than that of ESR-8. This indicates that when the rubber fiber content attained 15%, the pores in the sample were destroyed because of the excessive rubber fiber content. The fibers were intertwined into a clump, and the porosity increased. This affected the mechanical properties of the expansive soil. When the rubber content is 5–10%, the relaxation time of the main peak of the spectrum is 1.383 ms. This is less than that of ESR-8 and ESR-11. This result reveals that when the rubber fiber content is in the range of 5–10%, the interface between the expansive soil particles and rubber fibers displays effective bonding. This can effectively inhibit the development of soil cracks and reduce the pore space around the cracks.

To quantitatively analyze the pore number distribution of ESR with different diameters, it is necessary to subdivide the pore size of the ESR. The pore diameter of the ESR at different rubber fiber contents can be obtained using Equation (6). According to Zhou et al. [49], the pore diameters of soil can be divided into five types: macropores (>3 μm), medium pores (1–3 μm), small pores (0.2–1 μm), micropores (0.01–0.2 μm), and ultra-micropores (<0.01 μm).

Figure 12a, b show the pore size distribution curves and pore content curves, respectively, of the ESR with different rubber fiber content. As shown in Figure 12a, the pore diameters of the ESR were less than 0.5 μm. This reflected the tight pore structure inside the sample. After the addition of an appropriate amount of rubber fiber (5–10%), Amplifying the ESR pore size distribution curve, it was found that with the increase of rubber content, the ESR pore size distribution curve shifted to the left, and the proportion of peak pore size distribution decreased first and then increased. This indicated that the porosity of expansive soil could be reduced by adding rubber fiber.

The pore content curves of the ESR with different rubber fiber contents are shown in Figure 12b. From Figure 12b, the ESR micropores accounted for the largest percentage of the number of pores. It was followed by the ultra-micropores, and the fewest number of small pores. The pore size inside the ESR was mainly distributed between 0.01 μm and 0.2 μm. The pore size of approximately 0.02 μm accounted for the largest proportion (approximately 4.2% of all the pores in the ESR). The addition of an appropriate amount of fiber (5–10%) decreased the proportion of small pores and micropores and increased the proportion of ultra-micropores. However, the addition of more rubber fibers (15%) increased the percentage of small pores and micropores. This weakened the internal structure of the sample.

3.6. Shear Shrinkage Analysis Based on Classical Dilatation Equation

In recent years, scholars have proposed different forms of dilatation functions to describe the relationship between plastic volume strain and plastic strain.

Table 5. Several commonly used stress–dilatancy relationships.

Name of the Model	Formula
P.W. Rowe [50] model	$D=9(M-\eta )/(9+3M-2M\eta )$
Cambridge model	$D=M-\eta$
Modified Cambridge model	$D=(M^2-{\eta }^2)/(2\eta )$

summarizes the more commonly used stress–dilatancy relationship. Here, $\eta$ is the stress ratio, and $M$ is the critical stress ratio. The dilatancy rate and stress ratio of the triaxial rain test were orthogonalized according to the critical state parameters $M$ (plotted in Figure 13 and Figure 14) and compared with the dilatancy equation curves of the P.W. Rowe, Cambridge, and Modified Cambridge models.

The deviation between the model and the measured values is calculated using the root mean square error (RSME) method; the smaller the RSME, the more accurate the model is reflected. The relationship between the dilatancy rate and stress ratio for ESR-6 is shown in Figure 13. With an increase in the stress ratio, the dilatancy first increased to a peak and then decreased to zero. The Rowe model has a minimum RMSE of 0.26. The dilatancy equations of the Rowe model generally reflect the shear shrinkage pattern of ESR-6, whereas the Cambridge model and modified Cambridge model both overestimate its shear deformation. The relationship between the dilatancy rate and stress ratio of ESR-7 is shown in Figure 14. The figure shows that the confining pressure had a significant effect on the dilatancy rate of ESR-7. At low confining pressure (100 kPa and 200 kPa), it was found that the Rowe model could better describe the shear shrinkage of ESR-6 and ESR-7. Comparing the dilatancy rates of ESR-6 and ESR-7, the shear shrinkage deformation of ESR-7 was larger. This was more evident under a high confining pressure (300 kPa). At this time, the modified Cambridge model has the smallest RSME of 0.20; the dilatancy of ESR-7 was similar to that of the Modified Cambridge model. Similarly, To et al. [51] compared the dilatancy rate and dilatancy equation for fully weathered granite. They observed the Cambridge and Rowe models to be in better agreement with the test results. Meanwhile, the modified Cambridge model overestimated the dilatancy rate of granite.

4. Conclusions

To examine the effect of drainage conditions and rubber fibers on the mechanical properties of expansive soil, undrained triaxial, drained triaxial consolidation, and NMR ESR tests were performed in this study. The effects of rubber fibers on the ESR stress–strain relationship, tangential stiffness, maximum dilatation angle and pore size distribution were investigated. The main conclusions are as follows:

(1)

With an increase in strain, the ESR deviator stress and pore water pressure for different rubber fiber contents increased nonlinearly. The ESR showed compressive behavior during the shearing process. The rubber fiber-reinforced expansive soil showed a higher initial contraction than the unreinforced expansive soil.

(2)

The shear strength of ESR was affected significantly by the drainage conditions, which were influenced by the pore water pressure and creep of the fiber–soil interface. Under the consolidated drained conditions, the deviator stress and effective cohesion of the ESR were higher than those under the undrained conditions. The converse was true for the internal friction angle.

(3)

After the addition of rubber fibers, the shear strength of the expansive soil improved. However, its stiffness reduced. After a significant addition of rubber fibers to the unreinforced soil, the stretching effect of the rubber inhibited the formation of a face-to-face arrangement of soil particles. This alleviated the yield phenomenon of the ESR.

(4)

The addition of an appropriate amount of rubber fiber (5–10%) reduced the proportion of small pores and micropores in the ESR, increased the proportion of ultra-micro pores, and inhibited the development of soil cracks. When the rubber content was excessively high (15%), the fibers interweaved into clusters. This resulted in an increased porosity and a weakened internal structure of the ESR.

This study provides a reference for the application of rubber fibers in the backfill, and the beneficial reuse of recycled tires provides a sound environmental alternative to the safe disposal problems associated with waste materials.