Extensions of the two-phase double-point material point method to simulate the landslide-induced surge process
Introduction
Obtaining comprehensive hazard mechanisms, such as avalanches, landslides, and landslide-induced dammed lakes, has been and is still a major challenge for hazard assessment [13], [42], [46]. Rock avalanches and landslides can reach extremely high velocities along subaerial slopes; as a consequence, the remarkable kinetic energy of the sliding masses can be the origination of large waves or surges in water bodies. The landslide-induced surge process is an essential link of disaster chains in near-water regions, which establishes a connection between the landslide mass and water bodies, such as rivers, lakes, fjords and reservoirs, and directly affects the safety of infrastructure and residents both upstream and downstream. Therefore, the analysis and assessment of the geological disaster process is the top priority in the prevention and control work of geological disaster chain.
With the continuous improvement of computer computing efficiency, numerical calculation has become an important mean of geological disaster analysis and assessment. Large deformation continuous numerical methods such as Smoothed Particle Hydrodynamics (SPH) [2], [19], [36], Material Point Method (MPM) [3], [6], [8], [9], [12], [21], [29], [33], [34], [40], [41], [43] and discontinuous numerical methods such as DDA [15], [16] , NMM [37], [38], [39] and DEM [23] are both widely used in this field. With regard to the large deformation of solid and flow of fluid problems in the landslide-surge disaster chain, the material point method is adopted in this paper since the meshless characteristic and the higher computational efficiency.
In addition to large deformation of landslides and flow of water, the landslide-surge disaster chain also involves a complex solid-liquid coupling process, which is difficult to simulate precisely. More recently, efforts have concentrated on simulating coupled hydromechanical processes in saturated or unsaturated soils with MPM. The interaction between solid and fluid phases is formulated in two different approaches in the material point method: adopting either one set of MPs (i.e., single point manner) [20], [43] or two separate sets of MPs (i.e., double point manner) [7], [22], [39], [45]. For the landslide-induced impulsive surge process, it should be mentioned that the water is not only liquid within the pores but also a free liquid in this issue. Therefore, we extended the two-phase double point material point method (TPDP-MPM) program to simulate and investigate this typical fluid-solid coupling process.
This paper is organized as follows: First, the theory of the two-phase double-point approach of the MPM is introduced. Subsequently, by comparing two numerical examples with the benchmark model test results, the material point method is shown to accurately reproduce the gravity-driven flow of water and the large deformations of the soil. Finally, the Lituya Bay landslide-induced surge process, including the impact stage of the landslide mass, and the propagation and run-up stage of impulsive waves [10], is reproduced by using the two-phase double-point MPM.
Section snippets
Efficient two-phase double-point material point method
In this section we will give a brief introduction to the two-phase double-point material point method; for more details, refer to [31]. The governing equation for describing the motion of saturated soils is the v–w formulation, where velocities or displacements of the solid and fluid phases are considered as the primary variables. The v–w formulation was extended to the MPM by Jassim et al., [20] where the velocities of each phase become fundamental unknowns of the coupled system.
Benchmark example 1
An experimental study on impulsive waves generated by a submarine block was conducted by P. Heinrich [17]. The submarine triangular block was allowed to slide freely along a 45° slope, and a buffer was set to stop the block on the bottom. The initial state of this model and other information are described in Fig. 4(a).
The surface of the submarine block, the two inclined slopes, and the bottom were frictionless during the experiment. The elevation data of the free surface at 0.5 s, 1.0 s, and
Lituya bay landslide-induced surge analysis
On July 8, 1958, the Lituya Bay landslide was induced by an 8.3 Richter magnitude earthquake, resulting in an estimated 3 × 107 m3 of sliding mass in the Gilbert Inlet. Fig. 9 shows an aerial photograph of Lituya Bay with a graphical representation of the landslide area and the wave run-up area. There is a maximum bay depth of 122 m and a maximum run-up of 524 m above sea level on the opposite shore, which is partially overtopped. According to site conditions, the surge height of Lituya Bay is
Conclusion
In this study, the two-phase double-point material point method was used to reproduce this typical fluid-solid coupling process. By using OpenMP, the program was parallelized to analysis the dynamic process of surge initiation, wave propagation and the strong dynamic coupling between solids and fluids. The main conclusions resulting from this study are described as follows:
- (1)
The material point method was calibrated by reconstructing and simulating two model experiments regarding to submarine
Declaration of Competing Interest
The authors declare no conflict of interest.
Acknowledgments
The work reported in this paper is financially supported by the Youth Innovation Promotion Association CAS (no. 2021325), the International Partnership Program of Chinese Academy of Sciences Grant no. 131551KYSB20180042, and the National Natural Science Foundation of China (no. 51779250; no. 52179117).
A special acknowledgement should be expressed to China-Pakistan Joint Research Center on Earth Sciences that supported the implementation of this study.
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