Introduction

As an effective soil improvement technology, reinforcement technology has been widely used in slope protection [1, 2], roadbed treatment [3,4,5], retaining walls [6,7,8], and other projects [9, 10]. The traditional reinforcement technology is to arrange the reinforcement material of the soil in a certain direction. The directional distribution will form a potential fracture surface in the soil and increase the soil’s anisotropy [11, 12]. The fiber reinforcement technology’s objective is to randomly distribute discrete fiber materials in the soil to achieve improvement of the soil’s mechanical properties [13, 14]; the randomly distributed fiber materials can well solve the problem of soil anisotropy caused by traditional reinforcement technology [15,16,17,18,19,20]. As a result, the fiber reinforcement technology is finding wider application in the field of geotechnical engineering, also becoming one of researchers’ major concerns.

Fiber-reinforced soil is a common roadbed treatment method, and its dynamic characteristics, especially its liquefaction characteristics under dynamic load, is an important research topic. Eyyüb [21] analyzed the liquefaction resistance of sand with different fiber content and different fiber length and found that the cycle number for liquefaction increased with the increase in fiber content and fiber length. Zhou [22] studied the liquefaction resistance of calcareous sands reinforced with polypropylene fibers, and the results indicated that increasing fiber content and fiber length could improve the liquefaction resistance of calcareous sands, especially when the fiber content was greater than 0.8%. Fardad [23] studied the liquefaction characteristics of Babolsar sand reinforced with randomly distributed fibers using an energy-based approach, and the results revealed that the addition of fibers increased the number of cycles required to liquefaction, resulting in higher cumulative dissipated energy. Maheshwari [24] conducted shaking table tests on saturated sand with three different reinforced materials (geogrid-plate, geosynthetic fiber, and natural coconut shell fiber) and found that the addition of the three reinforced materials would reduce the maximum pore water pressure ratio, especially with a higher fiber (or geogrid-plates) content. Vercueil [25] implemented cyclic triaxial tests on geosynthetics-reinforced sand and concluded that geosynthetics can significantly improve the sand’s liquefaction resistance. Li [26] discussed the effects of fiber content and fiber length on the excess pore water pressure and dynamic strength. The results showed that with the increasing of fiber content, the dynamic strength and liquefaction resistance increased, whereas the accumulation rate of excess pore water pressure decreased. Zhou [27] conducted a series of cyclic triaxial tests on sisal fiber reinforced sand and concluded that the fiber content has a significant effect on the excess pore water pressure in saturated sand, and the accumulation rate of excess pore water pressure was negatively related with the fiber content. In addition, the interlocking structure formed between fibers and sand particles can significantly improve the liquefaction resistance of sand. However, Wang [28] studied the liquefaction and settlement characteristics of fiber-reinforced saturated sand through centrifugal test and believed that the fiber had no significant influence on the excess pore water pressure and settlement.

Presently, only a few studies have focused on the liquefaction characteristics of fiber-reinforced saturated sand [29], and the conclusions drawn by existing studies are not consistent. Therefore, it is necessary to implement further research on the liquefaction characteristics of fiber-reinforced saturated sand. In this paper, the influences of fiber content (FC), cyclic stress ratio (CSR), and loading frequency (f) on the excess pore water pressure (EPWP) characteristics and the liquefaction characteristics of saturated sand and fiber-reinforced saturated sand were studied through cyclic triaxial test.

Test Materials and Testing Methods

Test Materials

The China ISO standard sand was selected as the test material, as shown in Fig. 1a, and the shape of the particles is sub-round to round. Figure 2 shows the particle size distribution (PSD) curve for the ISO sand, and Table 1 lists the physical and mechanical parameters such as the specific gravity and the maximum and minimum unit weights [30].

Fig. 1
figure 1

Test materials: a The ISO sand, b Basalt fiber

Full size image
Fig. 2
figure 2

PSD curve of the ISO sand

Full size image
Table 1 Physical and mechanical parameters of the ISO sand
Full size table

The fiber used in the test is basalt fiber, which is a fibrous material extracted from natural basalt and has the advantages of high strength, corrosion resistance, and high temperature resistance [31, 32]. In recent years, the mechanical properties of basalt fiber-reinforced soil have become a new research hotspot.

The length of the basalt fiber selected in this paper is 12 mm, as shown in Fig. 1b, and its basic technical index such as the density, the monofilament diameter, the tensile strength, the elastic modulus, and the elongation at break are all shown in Table 2.

Table 2 Basic technical index of basalt fiber
Full size table

Testing Methods

Testing Equipment

The consolidated undrained cyclic triaxial test was performed with DDS-70 to explore the liquefaction characteristics of basalt fiber-reinforced saturated sand. The equipment is mainly composed of a confining pressure control room, three-axis chamber, vibration exciter, electrical control system, and the equipment can be used for sand liquefaction test.

Testing Programs

This paper mainly analyzes the influence of basalt fiber content (i.e., the ratio of the basalt fiber’s weight to the dry sand’s weight, expressed as FC = 0, 0.2%, 0.4%; after 0.4%. This fiber content is reasonable for fibre-reinforcement because fiber contents less than 1% were usually used in previous investigations[24, 28, 33], In addition, we found in our preliminary tests that when the fiber content was above 0.4%, the mixing of soil-fiber was felt very difficult as the fibers are sticking together to form lumps.), the cyclic stress ratio (that is, the ratio of half of the dynamic load amplitude to the confining pressure, expressed with CSR, CSR = 0.30, 0.35, 0.40), and the loading frequency (f = 1, 3, 5 Hz) on the excess pore water pressure (EPWP) and the dynamic strength curve of basalt fiber-reinforced saturated sand. The confining pressure is 50 kPa, and the loading waveform is sinusoidal. The test is stopped when the strain reaches 5% or the EPWP equals confining pressure. The specific test programs are shown in Table 3.

Table 3 Dynamic triaxial testing programs
Full size table

Specimen Preparation

The diameter of the specimen was 39.1 mm and the height was 80 mm. The specimen was prepared by the layered moist compaction method. The weight of the sand and the basalt fiber required to prepare a specimen was calculated according to the materials’ dry density and fiber content, etc. Then the sand and the fiber were evenly mixed; a certain amount of distilled water was sprayed to ensure that the mixture had a certain pseudo-cohesion to facilitate specimen preparation. Afterward, the moist mixture was placed in a sealed glassware for 24 h to allow the moisture to be evenly distributed. The specimen was compacted with five layers with a height of 16 mm in each layer. Before pouring into the next layer, the top of previous layer had to be scarified prior to ensure good contact between the two different layers. After the specimen was prepared, it was installed in the triaxial cell for saturation. When the pore pressure coefficient (B) was greater than 0.95, the specimen was considered to be saturated. Then, isotropic consolidation was carried out under a predetermined confining pressure. Finally, dynamic load was applied to perform the test.

Test Results

Analysis of Typical Test Curves

Figures 3, 4, and 5 show typical test curves for saturated sand and basalt fiber-reinforced saturated sand obtained from cyclic triaxial test, where (a) is the time history curve for axial stress, (b) is the time history curve for axial strain, (c) is the time history curve for EPWP, and (d) is the hysteresis curve. It can be seen from Figs. 3, 4, 5 that: (1) the axial stress shows a sinusoidal wave trend, and as the loading progresses, the axial stress slightly decreases. (2) The axial strain presents a horn shape, and as the loading progresses, the axial strain increases in the form of sine wave until the axial strain reaches 5%. (3) The curves of EPWP and loading time can be divided into three stages. At the initial stage of loading (stage I), the EPWP presents irregular changes. In the middle stage of loading (stage II), the EPWP increases rapidly in a sinusoidal wave. At the later stage of loading (stage III), the sample achieves initial liquefaction and the EPWP increases slowly in the form of sine wave, and at this stage, there is a groove at each peak of sine wave. (4) As the time go on, the long axis of the hysteretic curve gradually shifts horizontally and the hysteresis curve becomes flat, which indicates that the specimen’s stiffness and elastic modulus are gradually reduced with loading. The hysteresis curve’s area also gradually increases with an increase in loading time, which indicates that the energy consumed by the specimen gradually increases; that is, the damping ratio of the specimen gradually increases.

Fig. 3
figure 3

Typical test curves for saturated sand: a time history curve for axial stress, b time history curve for axial strain, c time history curve for EPWP, and d hysteresis curve

Full size image
Fig. 4
figure 4

Typical test curves for basalt fiber-reinforced saturated sand (FC = 0.2%): a time history curve for axial stress, b time history curve for axial strain, c time history curve for EPWP, and d hysteresis curve

Full size image
Fig. 5
figure 5

Typical test curves for basalt fiber-reinforced saturated sand (FC = 0.4%): a time history curve for axial stress, b time history curve for axial strain, c time history curve for EPWP, and d hysteresis curve

Full size image

Analysis on Characteristics of Excess Pore Water Pressure Ratio

The Influence of Basalt Fiber Content on Excess Pore water pressure ratio

In the following analysis, the EPWP was normalized by the confining pressure and obtain the excess pore water pressure ratio (EPWPR). Figure 6 shows the influence of basalt fiber content on the curves of EPWPR with the cycle number N. Figure 6 shows that: (1) the EPWPR of saturated sand and basalt fiber-reinforced saturated sand varies with the cycle number, which can be divided into two stages: the EPWPR linearly increases with the cycle number less than 50; when the cycle number is more than 50, the EPWPR nonlinearly increases until it reaches 1.0. Simultaneously, liquefaction failure occurs to the specimen. (2) The EPWPR for a given cycle number decreases with an increase in basalt fiber content, and the cycle number for liquefaction also shows an increasing with the increase of basalt fiber content. For saturated sand, the cycle number for liquefaction is 204; when the basalt fiber content is 0.2%, the cycle number for liquefaction is 475, which is 132.8% higher than that of saturated sand, and when the basalt fiber content is 0.4%, the cycle number for liquefaction is 685, which is 235.8% higher than that of saturated sand. This indicates that the addition of basalt fiber can inhibit the generation and accumulation of EPWP in saturated sand, especially with a fiber content of 0.4% (in this paper, the fiber content is limited to 0.4%). This is consistent with the research conclusions of Maheshwari [24], Noorzad [33], and Boominathan [34].

Fig. 6
figure 6

The influence of basalt fiber content on the curves of EPWPR and N

Full size image

The Influence of CSRs on EPWPR

The influence of CSRs on the curves of EPWPR and cycle number are shown in Fig. 7. We can see that the EPWPR of both saturated sand and basalt fiber-reinforced saturated sand increases with an increase in CSR under at a given cycle number, and the cycle number for liquefaction also decreases with the increase of CSR. With an increase of CSR, the stress exerted on the saturated specimen also increases, thus the internal structure of the specimen is more prone to failure, and more excess pore water pressure is accumulated in the saturated specimen.

Fig. 7
figure 7

The influence of CSR on the curves of EPWPR and N: a Saturated sand, b Basalt fiber-reinforced saturated sand with FC = 0.2%, c Basalt fiber-reinforced saturated sand with FC = 0.4%

Full size image

The Influence of Loading Frequency on EPWPR

Figure 8 shows the influence of loading frequency on the curves of EPWPR with cycle number for saturated sand and basalt fiber-reinforced saturated sand (FC = 0.2%). As can be seen from Fig. 8 that for saturated sand and basalt fiber-reinforced saturated sand, the increase of loading frequency is conducive to the accumulation of EPWP and accelerates the process of soil liquefaction failure. When the loading frequency is higher, the time of one stress cycle applied to the saturated specimen is shorter, and the EPWP generated inside the specimen has not enough time to dissipate before the next cyclic loading begins. And it is easier to accumulate excess pore water pressure, thus the specimen is more prone to liquefaction failure.

Fig. 8
figure 8

The influence of loading frequency on curves of EPWPR and cycle number: a Saturated sand, b Basalt fiber-reinforced saturated sand with FC = 0.2%

Full size image

Empirical Model of EPWPR

To eliminate the influence of cycle number, it is normalized by the cycle number for liquefaction (i.e., cycle number ratio, N/Nf). The curves of the EPWPR and the cycle number ratio satisfy the hyperbolic form. According to Chen [35], the curves of the EPWPR and the cycle number ratio can be fitted by hyperbolic function, as shown in Eq. (1).

$$\frac{{u_{d} }}{{\sigma_{3} }} = \frac{{N/N_{f} }}{{a\left( {N/N_{f} } \right) + b}}$$
(1)

where \(u_{d}\) is the EPWP, \(\sigma_{3}\) is the confining pressure, \(N\) is the cycle number, \(N_{f}\) is the cycle number for liquefaction, a and b are the fitting parameters that determine the influence of cycle number. Equation (1) is used to fit the curves of EPWPR and cycle number ratio, and the fitting parameters a and b, and the correlation coefficients R2 are obtained as shown in Table 4; we know that the R2 are all greater than 0.90, which indicates that the empirical model can well predict the development of EPWP for saturated sand and basalt fiber-reinforced saturated sand well.

Table 4 Fitting parameters for Eq. (1)
Full size table

Dynamic Strength Curve

The cyclic number for liquefaction and the corresponding cyclic stress ratio were plotted in a graph, and we obtain the dynamic strength curves for saturated sand and basalt fiber-reinforced saturated sand with different fiber content as shown in Fig. 9. It can be seen that for both saturated sand and basalt fiber-reinforced saturated sand, the cycle number for liquefaction decreases with the increase of CSR. For a given cycle number, larger cyclic stress ratio was required for specimen to liquefaction as the fiber content increased. This also verifies that an addition in fibers greatly improve the liquefaction resistance of saturated sand. In this paper, when the fiber content is 0.4%, the liquefaction resistance of fiber-reinforced sand is the most optimal. Additionally, the curves of CSR and the cycle number for liquefaction are in the form of a power function, according to Zhou [36], it can be calculated by a power function, as shown in Eq. (2).

$${\text{CSR}} = m \cdot N_{f}^{n}$$
(2)

where m and n are fitting parameters, Eq. (2) is used to fit the dynamic strength curves for saturated sand and basalt fiber-reinforced saturated sand. The obtained fitting parameters and the correlation coefficients R2 are shown in Fig. 9. The correlation coefficients are all greater than 0.90, indicating that Eq. (2) can well describe the dynamic strength curves for saturated sand and basalt fiber-reinforced saturated sand.

Fig. 9
figure 9

Dynamic strength curves for saturated sand and basalt fiber-reinforced saturated sand

Full size image

Conclusion

This paper studies the liquefaction characteristics of saturated sand and basalt fiber-reinforced saturated sand by cyclic triaxial test and draws the following conclusions:

  1. 1.

    An addition in basalt fiber can effectively inhibit the generation and accumulation of EPWP and improve the liquefaction resistance of saturated sand; the liquefaction resistance of fiber-reinforced saturated sand increases with the increase of basalt fiber content, and the optimal basalt fiber content is about 0.4%.

  2. 2.

    For saturated sand and basalt fiber-reinforced saturated sand, the increase in CSR and the increase in loading frequency are beneficial to the accumulation of EPWPR and accelerate the process of soil liquefaction failure.

  3. 3.

    The curves of EPWP and loading time can be divided into three stages: stage I, the EPWP presents irregular changes; stage II, the EPWP increases rapidly in a sinusoidal wave; and stage III, the EPWP increases slowly in the form of sine wave. The curves of EPWPR and cycle number ratio for saturated sand and basalt fiber-reinforced saturated sand is in accordance with the hyperbolic function, and an empirical model to predict EPWP was proposed.

  4. 4.

    The cycle number for liquefaction decreases with the increase of CSR. The dynamic strength curves for saturated sand and basalt fiber-reinforced saturated sand conform to the power function.