**1. Introduction**

Due to the advantages of a flexible structure and strong resistance, anti-slide pile has become the most widely used slope prevention technology in the field of geotechnical disaster prevention and mitigation since the 1930s [1]. However, with the anti-slide pile structures gradually entering the middle or even aging stage of their service life, how to evaluate their service status in the whole life cycle has become one of the most important key issues in this field. The service performance of an anti-slide pile depends heavily on its initial design level and service conditions. However, at present, the structural design of the anti-slide pile depends more on engineering experience and the industry standard, and the relevant theoretical system is still far behind the engineering application. There

**Citation:** Jin, H.; Ren, Q.; Xiao, S. Study on the Evolution Law of Internal Force and Deformation and Optimized Calculation Method for Internal Force of Cantilever Anti-Slide Pile under Trapezoidal Thrust Load. *Buildings* **2023**, *13*, 322. https://doi.org/10.3390/ buildings13020322

Academic Editor: Binsheng (Ben) Zhang

Received: 24 December 2022 Revised: 16 January 2023 Accepted: 17 January 2023 Published: 21 January 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

are many cases of economic waste caused by an over-conservative design of anti-slide pile structures, and more and more cases of early instability and failure due to insufficient control of the structure itself and geological environment conditions. With the temporal and spatial evolution of the service environment, the working state of the anti-slide pile will always be in a dynamic process during the service period. It is particularly urgent to strengthen the monitoring of the stress and deformation of the anti-slide pile to obtain the bearing characteristics and then evaluate the preventive effect or service status.

The research methods of internal force and deformation of the anti-slide pile mainly include field monitoring or numerical simulation for outdoor prototype piles and physical model tests or numerical simulations on indoor scale piles. Zhang et al. [2] and Zhou et al. [3] used a vibrating wire reinforcement meter or strain gauges to monitor the stress state of steel bars in anti-slide piles for a long time and obtained the stress characteristics of piles. Zhang et al. [4] and Zhang et al. [5] conducted long-term dynamic monitoring on the target anti-slide pile by laying optical-fiber-sensing equipment and carried out the inverse analysis on the internal force of the pile. However, due to the lack of monitoring equipment at the initial stage of the construction of some in-service prototype piles and the complexity of on-site monitoring, the physical model test or numerical simulation on indoor scaled piles have become a very effective method to analyze the bearing performance of anti-slide piles [6]. Hu et al. [7] and Zhang et al. [8] obtained the distribution law of the bending moment of the test anti-slide pile at the initial stage of loading by monitoring the strain evolution process of the pile concrete. Wei et al. [9] and Xie [10] obtained the internal force distributions at different sections of the large test pile by welding reinforcement meters on the steel bars. Cao [11], Li et al. [12], and Li et al. [13] monitored the evolution law of internal force in the whole loading process of test piles by laying steel strain gauges. As indicated above, all studies deduced the distribution of internal force of the test pile by monitoring the stress and strain states of concrete and steel bars. However, the internal force of the test pile in the linear elastic stage was only analyzed [7,8], and the anti-slide pile was considered as a homogeneous elastomer in the whole calculation process of internal force [9–13]. In fact, the concrete and steel bars of the piles are all elastic-plastic materials, and ignoring the plastic characteristics of the concrete and steel bars will significantly affect the calculation results of the internal force. Moreover, the monitoring methods are only applicable to the stress monitoring of outdoor anti-slide piles due to the large size of reinforcement meter [9,10]. In conclusion, the calculation of internal force of the anti-slide pile in laboratory model test lacks reasonable theoretical analysis, the whole process analysis of internal force and deformation under external load has not been carried out, and the nonlinear characteristics and internal force calculation method of anti-slide piles need to be further studied.

In view of this, based on a cantilever anti-slide pile treatment project in Nan'an District of Chongqing City, China, an indoor physical model test on the bearing performance of the cantilever anti-slide pile under trapezoidal load was carried out in this study. Considering the evolution process of the stress–strain constitutive relationship of the pile materials, the optimized calculation method for internal force of the cantilever anti-slide pile was proposed, and the whole process of the stress and deformation and the nonlinear characteristics of the internal force of the pile was explored. It is expected to provide a reasonable evaluation standard for the working state of cantilever anti-slide piles during the service period, and further optimize the structural design.
