To investigate the influence of the axial force and its distribution along the pile shaft on the response of laterally loaded piles, a generalized solution is proposed based on the transfer matrix approach, in which the transfer matrix coefficients for piles in the free, elastic, and plastic zones were analytically obtained through Laplace transformation. This proposed method can handle piles in multilayered soil deposits with any form of p-y curve. The proposed methodology is validated by comparing its predictions with the laboratory model pile test results. A good match between model prediction and the laboratory model pile test results implies that the proposed method can be used to evaluate the pile response under combined loads effectively. Moreover, the axial force distribution along the pile shaft is simplified as a constant, which equals to the vertical load applied at the pile head. Finally, the authors investigated the influence of vertical loads and the pile-embedded ratio on the ultima...

To study the mechanical properties of Y-shaped polypropylene fiber-reinforced subgrade fill, the strength characteristics of fiber-reinforced soil with different fiber contents, fiber lengths, and confining pressures were investigated through triaxial compression tests. The test results showed that fiber reinforcement significantly improved the strength and cohesion of the subgrade fill but had a limited impact on the internal friction angle. The fiber-reinforced soil specimens exhibited a failure pattern of bulging deformation, showing plastic failure characteristics. As the fiber content and length increased, the strength of the fiber-reinforced soil increased and then decreased. The optimal fiber content was 0.2%, and the optimal fiber length was between 12 and 18 mm in all test conditions. The strength of the fiber-reinforced soil increased with increasing confining pressure. An empirical model for predicting the failure strength of fiber-reinforced soil was established by analyzing the relationships between the failure strength of the fiber-reinforced soil and the fiber content, fiber length, and confining pressure. The stress-strain relationship of the fiber-reinforced soil exhibited strain-hardening characteristics and could be approximated by a hyperbolic curve. The Duncan-Chang model could be used to describe the stress-strain relationship of this fiber-reinforced soil. A calculation method to determine the model parameters (initial tangent modulus and ultimate deviator stress) was proposed.