Quick analysis model for earthquake-induced landslide movement based on energy conservation

Abstract

The sliding process and characteristics of earthquake-induced landslides are complex, and many factors affect landslide movement. The damage caused by landslides is often closely related to their movement characteristics. Therefore, establishing an efficient and quick analysis model for earthquake-induced landslide movement is very important in considering multiple control factors in the sliding process. Based on the typical characteristics of earthquake-induced landslide movement, considering the influences of earthquake action, friction characteristics of sliding surfaces, topographic relief, and morphological changes in landslide masses, a widely applicable quick analysis model for earthquake-induced landslide movement (ELQA) is constructed based on energy conservation. Compared with the existing landslide movement models, this model can consider multiple control factors and significantly improve the applicability of the model. Through comparisons with theoretical analysis, model tests, and actual landslide (Kolka glacial detrital flow), the movement distance of the landslide front edge obtained by the ELQA model matches well with the comparison results, indicating that the ELQA model can reproduce earthquake-induced landslide movement more accurately and quickly. Based on the ELQA model, the influences of control parameters (terrain sampling point density, time step, calculated point number) and calculation parameters (internal friction angle, slip mass volume, terrain concavity, and convexity characteristics) on the calculation results are studied. The results show that control parameters such as terrain sampling point density, time step, and calculated point number have limited influence on the movement characteristics; as long as appropriate values are selected, the error rate can be controlled within 5%. The calculation parameters have a significant influence on the movement characteristics. For example, the influence of the internal friction angle on the coverage area reaches up to 83.75%. The slip mass volume has an insignificant influence on the maximum movement speed, but it on the coverage area reaches approximately 20%. The influence of the terrain concavity and convexity characteristics on the results is less than 10%. The ELQA model is suitable for in-situ estimation and can provide effective suggestions for disaster prevention and reduction in earthquake-prone areas.

Appendix

Let the absolute radius of curvature of the basic concave or convex terrain be constant as r^t_s.

The curvature of the terrain will cause centripetal or centrifugal movement of the slip mass (Fig. 22). Since the concave terrain f"(x) is positive and the convex terrain f"(x) is negative if defined:

$$r = \frac{1}{K} = \frac{{\left\{ {1 + [f^{\prime}(x)]^{2} ]} \right\}^{{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0pt} 2}}} }}{{f^{\prime\prime}(x)}}$$

(18)

where K is the curvature at a point on the terrain and f′(x) and f″(x) are the first derivative and second derivative of the topographic function, respectively.

Fig. 22

Basic terrain model

Then, for the three basic terrain models:

$$N = mg\cos \theta { + }m\frac{{v^{2} }}{r}$$

(19)

Considering the earthquake action, then:

$$N = mg\cos \theta { + }m\frac{{v^{2} }}{r} - (E_{x} sin\theta + E_{y} cos\theta )$$

(20)

After considering the effect of terrain curvature, the supporting force of the model will change, and an increment N_T related to velocity and curvature will be generated. A corresponding increment ΔW^t_T will be generated in the friction energy consumption, which is defined as terrain energy:

$$\Delta W_{{\text{T}}}^{t} = \mu N_{T} \Delta D_{s}^{t}$$

(21)