Pore water pressure model for sands reinforced with randomly distributed fibers based on cyclic triaxial tests

Abstract

In this study, the pore water pressure accumulation laws in sand reinforced with randomly distributed fibers was investigated through cyclic triaxial compression tests. The effects of relative density, cyclic stress ratio, fiber content, and fiber length were examined. The test results showed that reinforcing the sand with randomly distributed fibers effectively delayed the pore water pressure accumulation and significantly increased liquefaction resistance. When the test conditions remained unchanged, the pore water pressure accumulation rate of the fiber-reinforced sand decreased as the fiber length and fiber content increased, and reached the lowest when fiber content reached 0.6% and fiber length attained 12 mm. Whereas, the accumulation rate of fiber-reinforced sand increased as the cyclic stress ratio increased, and reached the highest when relative density reached 30%, followed by 50% and 70%. Based on the test results, a three-parameter pore water pressure model that accounts for the effects of fiber content, fiber length, relative density, cyclic stress ratio, and sand particle diameter was established, and a method for estimating the parameters a and b was recommended. The predictions agreed relatively well with the test results, suggesting that the model is applicable to analysis the pore water pressure development laws in fiber-reinforced sands.

Introduction

The engineering properties of soils can be enhanced effectively by adding suitable reinforcing materials. Planar reinforcing materials, such as geotextiles and geogrids, improve the mechanical properties of a soil mass mainly through contact; therefore, they are unable to enhance the properties of the parts of a soil mass that are not in contact with them. After a suitable quantity of geosynthetic fibers are added into a soil mass, the soil particles mesh with the fibers at multiple points to reinforce the entire soil mass. Due to their high ultimate elongation and tensile strength, polypropylene (PP) geosynthetic fibers can be used to reinforce soils. When a soil mass reinforced with PP geosynthetic fibers under loading, the PP fibers generate a tensile force which limiting the lateral deformation of the soil mass, thereby increasing its shear strength. Additionally, the PP fibers can also provide a certain amount of tensile strength to the soil mass. The shear strength of soils under static loading increases considerably after fiber reinforcement. Compared with unreinforced soils, fiber-reinforced soils exhibit relatively high strength and flexibility, even after sustaining relatively large deformation [[1], [2], [3], [4], [5]]. The strength and modulus of a fiber-reinforced soil is affected by many factors, including the fiber content (FC), fiber length (FL), cyclic stress ratio (CSR) and relative density (D_r). Li and Ding [6] noted that the elastic modulus of a fiber-reinforced sand is controlled by various factors, including FC, confining pressure (σ₃), and number of loading/unloading cycles. Sadeghi and Beigi [7] noted that shear modulus (G) of fiber-reinforced clayey sand decreased with increasing of deviator stress ratio under high σ₃, and the loss rate of G for fiber-reinforced sand is lower than unreinforced specimens. Sahu et al. [8] concluded that the maximum G of hair fiber-reinforced sand is observed when FC=0.5% and D_r=80%, and the damping ratio of reinforced sand showed significantly variation when FC greater than optimum value. Maher and Woods [9] indicated that the dynamic modulus increased with increasing of fiber aspect ratio and FC, whereas damping was less affected than modulus. Sargin and Erken [10] observed the liquefaction phenomenon of saturated loose sand reinforced with PP fiber, and found that fiber addition made loose sand more resistant to liquefaction, whereas the initial elasticity modulus of fiber-reinforced sand decreased with the increasing of FC.

Moreover, studies have shown that fiber reinforcement increases the number of loading cycles leading to liquefaction (N_L) and increases liquefaction resistance (R_L), suggesting that adding fibers into sands increases their dynamic strength [[11], [12], [13]]. Eskisar et al. [14] examined the effects of FC and FL on the R_L of medium-density sands, and found that N_L increased with FC and FL, and the loading cycles (N) was significant effect on the pore water pressure (U). Ye et al. [15] investigated the R_L of a sand reinforced with fibers through dynamic triaxial and torsional tests, and found that randomly distributed fibers effectively improved the R_L of the sand and that loading conditions had no impact on the test results. Maheshwari et al. [16] found that the maximum U ratio of fiber-reinforced sand decreased with increasing of FC, and the R_L increased nearly 88% when FC=0.75%. Sonmezer [17] found fiber inclusion leading to increase of the R_L and cumulative liquefaction energy, and FC was more effective than FL to liquefaction effect. Krishnaswamy and Isaac [18] concluded that coir fiber was a effective reinforced material to improve R_L, especially at lower D_r. Amini and Noorzad [19,20] investigated the effect of FC, FL, σ₃, and D_r on the liquefaction behaviors of fiber-reinforced sand, and found fiber addition leading to increased of N_L and cumulative dissipated energy. Karakan et al. [21] noted that the N_L increased with increasing of FL and FC, and the U was affected by the N. Zhang and Russell [22] investigated the loading distributed mechanism by sand's skeleton, pore water, and fibers, and introduced a new U ratio which account for the direction of the principal stresses and fiber orientations.

The U is significant for liquefaction appraisal under dynamic loading, thereby the U models attracted researchers' widely attentions. Based on the CPT and SPT test results, Chiaradonna et al. [23] proposed a U model to analyze the seismic response of Kobe and Loma Prieta earthquakes, and the results indicated that the model can well predicted the site response. Zhao [24] established a new attenuation-type U model according to introduce the dynamic strength and equivalent dynamic stress level into Parr's equation, and verified the model by compared with test results. Based on finite-difference method, Abdollahi and Mason [25] coupled a seepage-deformation model to describe the U under tsunami loading, the results showed that the U head gradient depend on the water weight and pore water compressibility. Coupled the effects of temperature and mechanical load, Wang et al. [26] established a time-dependent model to predicted the U in stratified saturated soil, and verified the model by the analytical solution and model test results. Liu et al. [27] proposed a accumulation U model under wave loading, and concluded that the effect of residual U and seabed stress could accelerate accumulation of pore pressure. Based on dynamic triaxial tests, Wang et al. [28] established a increment model to predicted the U in fine sands under uniform cyclic loading, and found the new model can well predict the U, N_L, and R_L. Taken into account the effect of earthquake loading, Nhan et al. [29] developed a U and post-settlement model by introduced the Atterberg's limits as a constants. Zhang et al. [30] established a critical U equation based on the failure criterion, and concluded that the model is useful to predict the foundation stability. Wang et al. [31] established a U model based on the thixotropic fluid rate equation, and reasonably explained the generation and growth mechanism of pore pressure from the energy perspective.

Currently, research on fiber-reinforced sands under dynamic loading is primarily focused on R_L, and the establishment of U model is mainly based on sands. To date, there is little research investigating the characteristics of U in fiber-reinforced sands, especially establishing the U model. Therefore, this study examined a fiber-reinforced sand through extensive cyclic triaxial compression tests and analyzed the effects of various factors, such as the D_r, CSR, FC, and FL on the variations in U. Based on the experiment results, a U model that simultaneously accounts for the effects of various factors was established for fiber-reinforced sands, which provides a guideline for an intensive investigation of U patterns in fiber-reinforced sands.