The red clay samples were taken from the Central South University of Forestry and Technology area in Changsha, Hunan province, China. The depth of the red clay samples was 50–70 cm, and the soil was brown-red. According to GB/T50123-2019, the physical properties of the soil were measured. The natural moisture content of undisturbed soil is 25.66%, the liquid limit is 49.0%, the plastic limit is 22.7%, the plastic index is 26.3, the dry density is 1.47 g/cm³, the specific gravity is 2.74, the maximum dry density is 1.694 g/cm³, the optimum moisture content is 20.2%. The performance parameters of coir fiber are shown in Table 1.

The sample sizes commonly used in triaxial studies of fiber-reinforced soils are currently of two types, 39.1 and 50 mm in diameter, under restricted test conditions. According to Ang and Erik Loehr (2003), the sample diameter exceeds 70 mm, and the sample is more likely to represent the strength of fiber-reinforced soil reasonably. Therefore, in order to avoid side effects and to consider the laboratory conditions, the tests in this paper used larger samples than previous sizes to investigate the strong pattern of coir fiber-reinforced soils. The sample diameter is 61.9 mm, and the height is 125 mm, as shown in Figure 1. The preparation process was carried out about the Standard for Geotechnical Test Methods (GB/T50123-2019). According to the calculation results, the prepared coir fibers with different contents were added to the soil particles in proportion to the mix well. It was put into the three-valve membrane, in turn, to compact it, thus forming a new soil structure. The distribution of coir fibers in the sample is shown in Figure 2. The compaction method was used to make the sample, and the control compaction degree was 95% of the maximum dry density. To simulate the pore state of the soil in the actual project, the prepared samples were put into the vacuum saturator (Apparatus No. 21110155LQ, apparatus located in Room 301 of the Civil Engineering Experiment Center). After the saturation was finished, the samples were encapsulated and stored in cling film.

According to the experimental conditions, the stress-strain relationship of coir fiber-reinforced soil study by the unconsolidated and undrained triaxial shear test method. The experiment was carried out on a Nanjing TKA triaxial tester (Apparatus No. 202001007, apparatus located in Room 301 of the Civil Engineering Experiment Center), which consists of a computer, an axial compression system, a confining pressure system and a pressure chamber. It can automatically control the test process and data acquisition.

The test process is as follows: the coir fiber-reinforced soil sample covered with latex film is placed in the pressure chamber and filled with water. Apply specific confining pressure with a confining pressure system. When the confining pressure reaches a predetermined value, the sample is sheared by a computer-controlled axial compression system at a constant axial loading rate. According to the test code, the shear strain rate was calculated to be 0.625 mm/min. A computer collects and processes the data of axial pressure, deflection stress, and axial deformation during loading. The maximum deviated stress value was used as the damage standard of the sample in the test. Four different circumferential pressures were selected for the tests, 50, 100, 150, and 200, respectively. Fiber content was chosen by mass percentages, 0, 0.1%, 0.2%, 0.3%, and 0.4%, respectively. The fiber lengths were 10, 20, 30, and 40 mm. The test conditions for the specific samples are shown in Table 2.

Influenced by the coir fiber, the samples underwent obvious plastic deformation during the test. As shown in Figure 3A, without adding coir fibers, the soil samples showed an obvious diagonal crack during the damage, which exhibited brittle damage; as shown in Figure 3B, after the addition of fibers, the damage showed bulging damage. Although a certain shear surface was also generated, the degree of shear was substantially reduced compared with that without the addition of coir fibers. Therefore, the damaged form of the coir fiber-reinforced soil is a mixture of ductile and brittle damage. This intuitively indicates that coir fiber can reduce the degree of damage to soil samples.

After the above analysis, the strength properties of the fiber-reinforced soil samples exhibited the optimum situation at a fiber length of 30 mm and a fiber content of 0.3%, and their stress-strain curves are shown in Figures 6, 7. The stress-strain curves of the fiber-reinforced soil samples under different test parameters were similar in shape, and all of them retained the essential characteristics of hyperbolic curve. For the fiber-reinforced soil samples, the damage stage is significantly different from that of the red clay soil. After the red clay soil samples reached the damage stage, the stress decreased with the increase of axial strain. In contrast, after the fiber-reinforced soil reached the damage stage, the stress continued to increase with the growth of axial strain, and the damage form showed a hardening characteristic. After the addition of fibers to the soil, the combination of the two forms a new structure. The incorporation of fibers has a significant impact on the mechanical properties of the sample. Soil particles in contact with fibers form a new arrangement. Their structural composition is changed, manifested by a decrease in density and compaction, and a substantial increase in plastic deformation capabilities. The stress-strain characteristics are as follows: when the plastic deformation is small, the stress-strain curve rises faster, or the stress increase is more prominent. When the plastic deformation is larger, the deviator stress of some samples appears to fall and then increase. With the further growth of strain, the stress-strain curve gradually tends to flatten out, and the deviator stress will keep growing slowly. Therefore, adding fiber can effectively limit the deformation of the soil, improve the soil’s strength index, and effectively change the soil’s original stress-strain field, thus optimizing the engineering performance of the soil.

The structural damage law promoted by Shen and Zhang (1998) regards the structural state of soil as two different forms: the non-damaged state and the remodeled state. The soil body is in a combination of both the non-damaged state and the remodeled state when the force deforms it, and with the gradual increase of the load, the state in which the soil sample is in can be expressed by the formula S = 1 − ω S i + ω S d (1) In the formula: S is the mechanical parameter of the soil; S_i is the strength property of the soil in the lossless state; S_d is the strength property of the soil in the remodeled state; ω is the damage ratio, the proportion of the soil in the remodeled state to the whole soil.

Eq. 1 is brought into the Duncan-Chang model to derive the modified hyperbolic function ε 1 σ 1 − σ 3 = a m + b n ε 1 (2) In the formula: a m = 1 1 − ω E i 1 + ω E i 2 ; b n = 1 1 − ω σ 1 − σ 3 u 1 + ω σ 1 − σ 3 u 2 ; ω = 1 − e − ε 1 ε 1 u − ε 1 ; E_i1 and E_i2 are the elastic modulus of the first and second stages, respectively; (σ₁-σ₃)_ult1 and (σ₁-σ₃)_ult2 are the deviator stress limit values of the fitted straight lines of the first and second stages, respectively; ω is the damage ratio; ε_1u is the axial strain corresponding to the soil body at the time of damage.

By analyzing the triaxial test data, the undamaged structural stage and the structural gradually damaged stage of the reinforced soil sample are regarded as the first stage of strength deformation; then the structural completely damaged stage is made the second stage of strength deformation.

In Figure 7, the stress-strain relationship curve ε₁/(σ₁-σ₃) ∼ ε₁ consists of two stages, ε₁ is at 0%–0.5% and ε₁ is greater than 0.5% after. Two straight lines can be fitted to these two stages respectively. Since the yield stress state of the soil changes with the change in loading conditions. As the stress changes, the sample gradually produces damage, and when the stress changes to a large enough, the damage will be more obvious, which is shown as the appearance of a turning point on the ε₁/(σ₁-σ₃) ∼ ε₁ curve, and this turning point is regarded as the turning point of the two straight lines of the first and second stages. The turning point’s appearance indicates that the sample’s damage has developed from the first stage to the second stage, and its elastic modulus and ultimate deviator stress will also change significantly, which is presented in the coordinate system in Figure 7 as the change of intercept and slope.

As shown in Figure 7, each stage can be fitted linearly, and the corner mark k refers to two different steps in the hardening process. The formula is expressed as y = a k + b k x k = 1,2 (3)

The asymptotic values of elastic modulus and deviator stress at each stage are obtained from the following equations. E i k = 1 / a k k = 1,2 (4) σ 1 − σ 3 u l t k = 1 / b k k = 1,2 (5)

In this paper, the stress-strain curve of coir fiber-reinforced soil is fitted using the hyperbolic function of Eq. 2. First, a part of the data with abnormal values will appear at the beginning of the test. After removing these anomalous data, the relationship image of ε₁/(σ₁-σ₃)∼ε₁ was plotted by data processing software. The stress-strain relationship is shown in Figure 7, and there are two obvious phases in the image. Point P is the turning point. A straight-line fit was performed for each of the two phases, and the fit was above 97%. Then, the values of parameters E_i1, E_i2, (σ₁-σ₃)_ult1, and (σ₁-σ₃)_ult2 are determined according to the Eqs 3–5. The same method was adopted to fit the data of each sample into a straight line to find out the values of the above four parameters. The calculated parameters are shown in Table 3.

The elastic modulus of stage 1 and stage 2 are shown in Table 3, showing the relationship between elastic moduli and fiber content, fiber length, and confining pressure under different test parameters. With the increase in fiber content and length, the elastic modulus of coir fiber-reinforced soil shows a trend of increasing first and then decreasing. The elastic modulus reaches the maximum value when the fiber content and length reach 0.3% and 30 mm, respectively. If the fiber content and length continue to increase, the elastic modulus decreases, and the ability to resist deformation of the sample decreases. For the same fiber content and length, the higher the confining pressure, the greater the elastic modulus. That is, the higher the resistance to deformation.

The values of ultimate deviator stress in stage 1 and stage 2 are shown in Table 3, showing the relationship between ultimate deviator stress and fiber content, fiber length, and confining pressure under different test parameters. The ultimate deviator stress value variation gradually increases when the fiber content is from 0.1% to 0.3%. Similarly, the ultimate deviator stress increases gradually when the fiber length is 10–30 mm. As the fiber content and fiber length continue to grow, the strength of the sample begins to decrease after reaching the optimum content and optimum length. The relationship between the modulus of elasticity and the confining pressure is shown by the fact that for the same sample with the same fiber content and fiber length, the value of the ultimate deviator stress increases with increasing confining pressure, and the sample exhibits higher strength. As can be seen from Table 3, the values of ultimate deviator stress (σ₁-σ₃)_ult1 for the same group of samples are all higher than (σ₁-σ₃)_ult2, indicating that the samples reinforced with coir fiber are suitable for modified Duncan-Chang model.

Based on the model and the pattern exhibited by the experimental results, the sample deviator stress also increases when the fiber content increases from 0.1% to 0.3%. When the fiber content was 0.4%, the sample deviator stress still kept increasing, but the value was less than 0.3% of fiber content. It indicates that the fiber content significantly changes the reinforcement effect of red clay samples at 0.3%. Similarly, based on the test conditions and experimental results, it can be concluded that the fiber length is optimal when it reaches 30 mm.