Lanhao Zhao

Finite element simulation of impulse wave generated by landslides using a three-phase model and the conservative level set method

A numerical model has been developed using the finite element method for the simulation of impulse waves generated by landslides. The fluid-like landslide is modeled as a generalized non-Newtonian visco-plastic fluid. A three-phase flow model based on the incompressible viscous Navier–Stokes equations is solved using the finite element method to describe the motion of the three types of fluid in landslide. The conservative level set method is expanded to n-phase flow cases and employed to capture the interface of the three phases: air, water, and the landslide. The overall performance of the approach is checked by a number of validation cases: a Rayleigh–Taylor instability problem to illustrate the capability of the proposed method to deal with interface capturing, a benchmark test of a subaerial landslide generated by an impulse wave is carried out and compared with the published experimental data and numerical results, and finally, the 1958 Lituya Bay landslide generated impulse wave, and its results are compared against a scaled-down experiment and other published numerical results. It can be noted that the current model has an excellent ability to capture the complex phenomena that occurs during the whole process of the landslide-generated impulse wave, and considering the simplified treatment of the landslide and the numerical model, fairly good agreement between computed and experimental results has been observed for all simulation cases.

Finite element modelling of local scour below a pipeline under steady currents

ABSTRACT Local scour has been identified as the main factor that causes failures of structures in offshore engineering. Numerous research efforts have been devoted to local scour around offshore pipelines in the past. In this paper, a finite element numerical model is established for simulating local scour below offshore pipelines in steady currents. The flow is simulated by solving the unsteady Reynolds-averaged Navier–Stokes equations with a standard k − ϵ turbulent model closure. A sand slide scheme is proposed for the scour calculation, and bed load is considered in the proposed scour model. To account for changes in bed level, the moving mesh method is adopted to capture the water–sediment interface (bed), and the change of bed level is calculated by solving Exner–Polya equation. All the equations are discretised within the two-step Taylor–Galerkin algorithm in this paper. It is found that the sand slide model works well for the simulation of the scour, and the numerical results are shown to be in good agreement with the available experimental data.

Mixed Finite Element Method for Static and Dynamic Contact Problems with Friction and Initial Gaps

A novel mixed finite element method is proposed for static and dynamic contact problems with friction and initial gaps. Based on the characteristic of local nonlinearity for the problem, the system of forces acting on the contactor is divided into two parts: external forces and contact forces. The displacement of structure is chosen as the basic variable and the nodal contact force in contact region under local coordinate system is selected as the iteration variable to confine the nonlinear iteration process in the potential contact surface which is more numerically efficient. In this way, the sophisticated contact nonlinearity is revealed by the variety of the contact forces which are determined by the external load and the contact state stick, slip, or separation. Moreover, in the case of multibody contact problem, the flexibility matrix is symmetric and sparse; thus, the iterative procedure becomes easily carried out and much more economical. In the paper, both the finite element formulations and the iteration process are given in detail for static and dynamic contact problems. Four examples are included to demonstrate the accuracy and applicability of the presented method.

Strength Reduction Method for Stability Analysis of Local Discontinuous Rock Mass with Iterative Method of Partitioned Finite Element and Interface Boundary Element

SRM (strength reduction method) with iterative method of PFE (partitioned fnite element) and IBE (interface boundary element) is proposed to solve the safety factor of local discontinuous rock mass. Slope system is divided into several continuous bodies and local discontinuous interface boundaries. Each block is treated as a partition of the system and contacted by discontinuous joints. The displacements of blocks are chosen as basic variables and the rigid displacements in the centroid of blocks are chosen as motion variables. The contact forces on interface boundaries and the rigid displacements to the centroid of each body are chosen as mixed variables and solved iteratively using the interface boundary equations. Flexibility matrix is formed through PFE according to the contact states of nodal pairs and spring flexibility is used to reflect the influence of weak structural plane so that nonlinear iteration is only limited to the possible contact region. With cohesion and friction coefficient reduced gradually, the states of all nodal pairs at the open or slip state for the first time are regarded as failure criterion, which can decrease the effect of subjectivity in determining safety factor. Examples are used to verify the validity of the proposed method.

A Novel Contact Algorithm Based on a Distance Potential Function for the 3D Discrete-Element Method

The combined finite–discrete-element method (FDEM) has made a groundbreaking progress in the computation of contact interaction. However, FDEM has a strict requirement on the element type, and the simulation result may be inconsistent due to a deficiency of physical meaning of the potential function. To address this problem, a new 3D discrete-element method based on a distance potential is proposed for a system consisting of a large number of arbitrary convex polyhedral elements. In this approach, a well-defined distance potential is proposed as a function of the penetration between the contact pairs. It exhibits a clear physical meaning and a precise measurement of the embedding between the elements in contact. The newly presented method provides a holonomic and accurate contact interaction without being influenced by the element shape. Therefore, the restraint of the element type in FDEM is removed and the proposed method can be used for arbitrary convex polyhedrons. In addition, an improved contact detection algorithm for non-uniform block discrete elements is provided to overcome the constraint of elements with the same size in the Munjiza-No Binary Search contact detection method. The new approach retains the merits of the FDEM and avoids its deficiencies. It is validated with well-known benchmark examples including an impact simulation, a friction experiment, a joint structure of a sliding rock mass, pillar impact, block accumulation, and analysis for the failure process of wedge slope. The results of this proposed method are in excellent agreement with the existing experimental measurements and analytical solutions.

Single Spring Joint Element Based on the Mixed Coordinate System

As a FEM for reinforced concrete bond-slip problems, one important feature of the typical double spring joint element method is the selection of the normal stiffness, which may cause the mutual embedding problem and bring challenges to the calculation. In this paper, a novel single spring joint element method based on the mixed coordinate system is proposed to simulate the interaction of two materials. Instead of choosing the normal stiffness arbitrarily, the proposed method makes DOFs of two materials in the normal direction equal to ensure deformation compatibility. And its solid elements for the concrete are solved in global coordinate system, while the beam elements for the steel bar are solved in local coordinate system. In addition, the proposed method can also be applied to RC structures with irregular arrangements of steel bars. Numerical examples demonstrate the validity and accuracy of the proposed approach. Furthermore, the bond model is applied to RC beams with the description of the damage process.

Implementation of Fictitious Crack Model Using Contact Finite Element Method for the Crack Propagation in Concrete under Cyclic Load

The mixed freedom finite element method proposed for contact problems was extended to simulate the fracture mechanics of concrete using the fictitious crack model. Pairs of contact points were set along the potential developing path of the crack. The displacement of structure was chosen as the basic variable, and the nodal contact force in contact region under local coordinate system was selected as the iteration variable to confine the nonlinear iteration process in the potential contact surface which is more numerically efficient. The contact forces and the opening of the crack were obtained explicitly enabling the softening constitutive relation for the concrete to be introduced conveniently by the fictitious crack model. According to the states of the load and the crack, the constitutive relation of concrete under cyclic load is characterized by six contact states with each contact state denoting its own displacement-stress relation. In this paper, the basic idea of the mixed freedom finite element method as well as the constitutive relation of concrete under cyclic load is presented. A numerical method was proposed to simulate crack propagation process in concrete. The accuracy and capability of the proposed method were verified by a numerical example against experiment data.