2.2.3. Distribution Form of Thrust Load of the Test Pile

(1) Selection of the distribution form of the thrust load

The distribution form of the landslide thrust behind the cantilever anti-slide pile is complex, and it does not change regularly along the pile depth. According to the Chinese specification (GB/T 38509-2020) [14], the distribution of landslide thrust in the loaded section of anti-slide pile can be divided into three forms: triangle, trapezoid, and rectangle, and the specific distribution form should be determined according to the nature and geometric characteristics of the sliding mass. The determination of the actual distribution form of landslide thrust is mostly based on an indoor model test, field test, and numerical simulation. Liu et al. [15] established a function model of the thrust distribution form based on the analysis of field measured data at home and abroad, indicating that the thrust distribution form of a sand and clay sliding mass should be considered as triangular or parabolic, and the distribution form between them should be trapezoidal. In the first section of this article, the rock slope behind the target anti-slide pile was covered with 0~1 m eluvial soil layer and 2~3 m strongly weathered rock layer. Therefore, it is more consistent with the actual working conditions to assume that the thrust distribution form behind the actual anti-slide pile is trapezoidal, as illustrated in Figure 3. The upper load and lower load of trapezoidal load are *q*<sup>1</sup> and *q*2, respectively, and the length of the loaded section is *l*.

**Figure 3.** Distribution of trapezoidal thrust load behind an anti-slide pile.

(2) Application mode of thrust

The distribution form of the trapezoidal thrust load behind the anti-slide pile mentioned above is a theoretical assumption, and the idealized trapezoidal thrust load should be simplified as a concentrated force in the indoor test. According to the mechanical characteristics of a cantilever anti-slide pile, it is regarded as a cantilever beam subjected to trapezoidal load. Based on the principle of equivalence (the same load location, the same total load value, and the economic and reasonable equivalent error), the trapezoidal load of an anti-slide pile is equivalently replaced by the concentrated force. In the process of replacement, the accuracy of the result of load equivalence is directly determined by the number, value, and position of the concentrated force. The existing research on the bearing performance of the anti-slide pile mainly concentrates on the bending moment and deformation, where the maximum bending moment of the pile and the maximum deflection at pile top are the main criteria. Therefore, the cantilever beam structure was taken as an example in this paper, and the maximum bending moment and maximum deflection of the cantilever beam were taken as the indicators to discuss the optimum equivalent scheme, so as to finally obtain the distribution form, number, location, and value of the corresponding concentrated load. The specific equivalent calculation method is as follows.


**Table 4.** Calculation results of the bending moment and deflection under trapezoidal load and concentrated load.


Note: *ω*<sup>0</sup> = *ql*4/(*EI*).

It can be seen from Table 4 that the greater the proportion of the upper load and lower load of the trapezoidal load (*n*), and the smaller the number of concentrated forces (*m*), the smaller the error of equivalent schemes (*D*), and *D*<sup>3</sup> is the smallest when *n* = 6 and *m* = 3. Therefore, three concentrated forces are finally loaded in this study, where *F*1, *F*2, and *F*<sup>3</sup> are located at 0.86*l*, 0.50*l*, and 0.14*l* of the loaded section of the test pile, respectively, and *F*<sup>1</sup> = *F*/6, *F*<sup>2</sup> = *F*/3, and *F*<sup>3</sup> = *F*/2, respectively.

$$y\_c = \frac{n+2}{3(n+1)}l \tag{1}$$

$$F = \frac{n+1}{2}ql$$

$$M = \frac{n+2}{6}ql^2\tag{3}$$

$$Mm = \sum\_{i=1}^{m} F\_i \* x\_i \tag{4}$$

$$
\omega = \frac{ql^4}{EI}(\frac{n-1}{30} + \frac{1}{8})\tag{5}
$$

$$
\omega\_m = \sum\_{i=1}^m \frac{F\_i \mathbf{x}\_i^2}{6EI} (3l - \mathbf{x}\_i) \tag{6}
$$

where *q* is the size of the upper load, and *E* and *I* are the elastic modulus and inertia moment of the cantilever beam, respectively.
