Marine embankment slide and reinforcement simulation based on discrete numerical method

Hybird discrete numerical methods inclusive of DEM and XFEM were developed in the study to simulate the marine embankment slide in Zhejiang coast. The study derived the comprehensive fields that included the displacement, stress, internal forces and reliality factor. Therefore, the typical marine embankment slide simulation and reinforcement effect evaluation were completed. The methods and results were helpful for the marine embankment cases.


Introduction
A catastrophic slide went in the marine embankment of Zhejiang in China and the neighboring structures were destroyed heavily (Fig.1).

Fig.1 Collapsed marine embankment in-situ
The study adopted the discrete numerical method to simulate the birth of the disaster and the reinforcement technology [1,2] .

Discrete numerical method
Discrete element method (DEM) has been the most popular technique for the geo-materials physical behavior simulation.
DEM pays attention on the calculation on the intersecting forces, velocities and accelerations of the material particles as well as the interfaces. Here Newton's second law has been invited in the computation on the elements' velocities and accelations with the physical hypotheses on the connections between the discrete particles. Therefore, the goal physical fields on the structures can be ascertained during the diverse simulations on the non-linear behaviors [3] .
The internal law on the forcce and displacement of the interface can be expressed that the components of the interactive forces and the relative deformations in tangent and normal directions will be computed with the determination of tangent and normal rigidities. The model can be interpreted by the double-ball and wall-ball connection in Fig. 2. Particularly, the normal unit vector i n from double-ball model can be defined by Eq. (1).
XFEM was also applied in this study to predict the successive slide in the marine embankment. The subdomain integration has been invited in XFEM to realize the field summation on the discrete interpolative functions, by which the discrete functions' integreation were solved victorily. The goal numerical function can be expressed as Eqs. (3) and (4), where, designates the nodal freedom, refers to the additional nodal freedom due to the internal breach of the goal element, and represent the coupled items of the mass matrices on and , K , uq K , mat K and geo K define the global rigid matrix, the coupled item, the physical and geometrical rigidities, is the external force on , is the external force on .

Constitution of the marine embankment
The properties of the marine embankment were summarized into 5 categories, namely, debris, sliding zones, geo-matrix, revetment and riprap. The typical values of the 5 categories were shown in Tab.1 [4,5] , Mohr-Coulomb model was adopted to express the yielding characteristics of the geo-blocks in Eq. (5), where, and represent the shear strength indexes, and refer to the principal stresses.

Designs on boundary conditions
The initial sliding zones in the debris were depicted by 3point arcs that ran commonly into the embankment for 3m [6] . The debris bodies include two varities, i.e., sharp wallball and polygonal wall-ball zones that were shown in Fig.  3.

Results
The numerical results were derives with DEM and XFEM technologies as follows.

Discussions and conclusions
The stuff block more than 200 m 3 ran down into ocean during less than 12 s under the Sharp wall-ball B.C. The internal hydro-dynamic traction was the main cause and the collapsed debirs showed the radial mat distribution. The kinematic sliding zone with 5 m depth was swept into ocean under the internal seeping pressure which kept at the level of 10 kPa. The destroyed volume of the stuff block was more than 600 m 3 . The maximal value of stuff sliding loss was 630m 3 /35s under under the internal seeping pressure. The designed revetment system reinforced the marine embankment the internal friction density of which kept at the level of 2 MPa. Moreover, the level of interfacial open was less than 1 mm.
The reinforced depth in the embankment was more than 16m and the global reliability factor attained 2.6 which indicated that the designed revetment system was the admirable one.