Tomofumi Koyama

DEVELOPMENT OF COUPLED DISCONTINUOUS DEFORMATION ANALYSIS AND NUMERICAL MANIFOLD METHOD (NMM–DDA)

Discontinuous Deformation Analysis (DDA) and Numerical Manifold Method (NMM) have been widely used for the analyses of discontinuous rock masses. Recently, these discontinuum-based numerical methods have been applied to the simulations for slope failure due to earthquakes, where one of the key issues is the estimation of traveling velocities and distances for the collapsed rock blocks. For the dynamic response analysis of rock slopes, it is necessary to consider the local variation of seismic forces, especially when the slope size is large and/or the slope geometry becomes complicated. In DDA, there is difficulty to consider the local displacements and stress condition of the single block for the basement because of mathematical principle (in DDA, the displacement function is defined at the gravity center of the blocks and the strain in the block is uniform). On the other hand, NMM can simulate both continuous and discontinuous deformation of the block systems. However, the rigid body rotation of blocks cannot be treated properly because NMM does not deal with the rigid body rotation in explicit form. According to the above-mentioned features and drawbacks, it is reasonable to combine DDA and NMM from practical point of view. In this paper, the formulation for the coupled NMM and DDA (NMM–DDA) was presented. For the formulation, NMM and DDA can be easily combined by choosing displacements of the DDA blocks and NMM cover nodes as unknowns, because the processes to establish the equilibrium equations (minimizing total potential energy) and kinematics for block system are same between DDA and NMM. In this paper, some applications of the NMM–DDA to both dynamic and static problems were also presented and the validity and applicability of newly developed DDA–MM were discussed.

Coupled shear-flow tests for rock fractures with visualization of the fluid flow and their numerical simulations

Abstract A series of laboratory coupled shear-flow tests for fracture replicas under normal stresses was performed with visualization of fluid flow using a newly developed coupled shear-flow-tracer testing equipment and these laboratory tests were simulated by using FEM, considering evolutions of aperture and transmissivity with large shear displacements. The distributions of fracture aperture and its evolution during shearing and the flow rate were calculated from the initial aperture and shear dilations and compared with results measured in the laboratory coupled shear-flow-tracer tests using transparent fracture replicas and a CCD camera that provides continuous images of contact area and flow path evolution in real-time of the shearing tests. Numerical simulation results such as aperture and contact distributions agree well with the images obtained from the coupled shear-flow tests of fracture specimens with visualization of the fluid flow. The numerical models captured complex behavior of fluid flow in fracture samples and agree well with the experimental flow rate results.

STABILITY ANALYSES FOR ANCIENT MASONRY STRUCTURES USING DISCONTINUOUS DEFORMATION ANALYSIS AND NUMERICAL MANIFOLD METHOD

In this paper, the stability including stress distribution of two ancient masonry structures, the pyramid of the Pharaoh Khufu, Egypt and the Pont of Gard, were analyzed using discontinuous deformation analysis (DDA) and numerical manifold method (NMM). For the simulation using NMM, the newly developed four-node isoparametric element was used. The stress distributions/concentration were calculated and compared between the two methods. The calculated results show qualitative agreement with observations. DDA and NMM are applicable to simulate the physical phenomena of masonry structures.

A numerical study on the effect of shear resistance on the landslide by Discontinuous Deformation Analysis (DDA)

Japan is located in Circum-Pacific earthquake zone, which is one of the most seismologically active areas in the world. As a result, landslides have occurred frequently and often cause serious damage not only to human lives but also to the various important structures such as national roads, railway, electric power plans etc. From the engineering point of view, to investigate the mechanism of landslide due to earthquakes and estimate the damage caused by landslides are important issues. In this study, as the first step, to check the validity of DDA simulation for the seismic problems, a series of shaking table tests were carried out in the laboratory and simulated by DDA. Then, one of the largest landslides occurred in Aratozawa Area, Miyagi, Japan in 2008 caused by Iwate-Miyagi Nairiku Earthquake was simulated using DDA and discussed the mechanisms of the landslide. The 2-D DDA model for one of the survey lines was created based on the geological survey, and physical properties were determined from the laboratory tests using rock/soil samples obtained from the landslide site. In this study, to discuss the mechanism of the landslide, a series of parametric study in terms of shear resistance along the fractures was conducted.

Application of Manifold Method (MM) to the stability problems for cut slopes along the national roads

Recently one of the most challenging problems for civil engineers is how to construct new structures/infrastructures adjacent pre-existing ones and how to evaluate the effect of the new construction on the pre-existing structures (so-called neighbouring construction). The Manifold Method (MM) is one of the discontinuum based numerical approaches to simulate the mechanical behaviour of fractured rock masses including large deformation/displacement along fractures as well as stress/strain conditions of the rock blocks/masses. In this study, the MM was used to investigate the stability of the cut slope in the highly fractured rock masses along one of the national roads in Japan, focusing on the effects of new construction on the pre-existing structures/infrastructures. The effect of reinforcement during the construction such as rock bolts, anchors, etc. was also investigated and evaluated quantitatively by numerical simulations using MM.

Recent insights into analytical precision and modelling of DDA and NMM for practical problems

This paper discussed the analytical precision on equations of motion in some practical studies that use 2-D DDA, 2D-Coupled analysis of NMM & DDA, and 3D-DDA. We point out the main reason for numerical instability in DDA is loss of the effective digits when superposing the global stiffness matrix under the variable conditions of large and the small blocks. Categories of analyses are distributed in 2D-DDA static masonry structures such as the Great Pyramid and the Pont du Gard, 2D-DDA dynamic rock fall problems and the sensitivity of its analysis on the velocity ratio and the penalty, earthquake response analysis of rock slopes, 2D-NMM, 2D-coupled analysis of DDA and NMM and 3D-DDA rock fall problem. The selected examples on the Great Pyramid, Pont du Gard and Bayon Temple at Angkor Thom are located in Egypt, France and Cambodia respectively as UNESCO world heritages sites. The authors evaluated the applicability of the methods and the reliability of the results by comparing different methods and site observations from the practical problems.

Establishment of Criteria for Traffic Regulations Along the National Road Based on Numerical Simulations During Torrential Rainfall

In this study, the risks for slope failure were evaluated by numerical simulations and the new criteria for announcing traffic regulation during rainfall were established. Firstly, the saturated-unsaturated flow analysis was performed by 2-D Finite Element Method (FEM) and the flow simulation results were used for the circular arc sliding computation for slope stability. The criteria for announcement of traffic regulation for a certain slope along the national road were established using the relation between rainfall in short time (hourly rainfall and/or rainfall every 10 min) and accumulated rainfall, when the safety factors calculated from circular arc sliding computation become lower than 1.0. The risk of the slope failure was assessed by drawing snake curves (plotting rainfall in short term against the accumulated rainfall) using previous torrential rainfall data. In the simulations, the effect of different rain intensity based on the rainfall every 10 min and/or 1 h recorded by Japan Meteorological Agency on the rainwater infiltration into the slope as well as slope stability were also investigated.

Development of a numerical model for grout injection and its application to the in situ grouting test at the Grimsel test site, Switzerland

Grouting is commonly used to decrease the hydraulic conductivity of fractured rock masses and control the groundwater inflow. Since underground facilities are constructed in various geological conditions, different types of grout material and mixing/injection methods have been developed for effective and economical grout injection. It is also important to evaluate the grout arrival distance and the range of the altered hydraulic conductivity field after grout injection. However, the mechanism of the grout injection process has not yet been clarified sufficiently due to complex chemical and physical processes during grout injection. In this study, to simulate the grout injection process, a three-dimensional numerical model based on an equivalent continuum approach was developed and applied to the in situ grout injection tests at the Grimsel test site, Switzerland. In the simulations, the injection pressure and/or the injection rate was given as a boundary condition and the total amount of injected grout (silica sol) was calculated. The breakthrough curves (grout arrival time and the time evolution of grout density) at the observation boreholes and the distribution of the altered hydraulic conductivity field were also investigated. The simulation results were also compared with the ones obtained from in situ measurements/monitoring, which showed qualitatively good agreement.

Chapter 22 – Experimental and Numerical Study of the Geometrical and Hydraulic Characteristics of a Single Rock Fracture during Shear1

Coupled shear–flow tests were conducted on two artificial rock fractures with natural rock fracture characteristics under constant normal loading boundary conditions. Numerical simulations using three-dimensional Navier–Stokes equations taking account of the inertial effects of fluid were conducted using void space geometry models obtained from the coupled shear–flow tests. The test and numerical simulation results show that the evolution of geometric and hydraulic characteristics of rock fracture exhibit a three-stage behavior. Transmissivity of a certain void space geometry within a fracture is related to the Reynolds number of fluid flow due to the inertial effects of fluid, which can be represented by Navier–Stokes equations. The mechanical aperture is usually larger than the hydraulic aperture back-calculated from measured flow rate, and the difference between them relates strongly to the geometric characteristics of fractures. A mathematical equation is proposed to describe the relation between hydraulic aperture and mechanical aperture.

Application of coupled elasto-plastic NMM-DDA procedure for the stability analysis of Prasat Suor Prat N1 Tower, Angkor, Cambodia

There are many historic remains in the world and among them many masonry structures are in danger of collapse. To select suitable methods for restoration and preservation, it is important to evaluate the stability of masonry structures considering the interaction between foundation ground and masonry building, and accurate calculation of stress distribution inside the masonry structure is required. In the previous studies, NMM–DDA (coupled numerical manifold method and discontinuous deformation analysis) one of the discontinuum-based numerical methods was developed to satisfy these requirements and used for the stability analysis of Prasat Suor Prat N1 Tower in the Angkor monuments, Cambodia. However, the original NMM–DDA code treat only elastic bodies (for both DDA blocks and NMM elements) and cannot treat the failure of soil. Hence, in this study, the elasto-perfectly plastic constitutive law (Drucker–Prager model) was newly introduced to the original NMM–DDA code, and the model was verified by performing biaxial test numerically and comparing with analytical solution. The newly developed elasto-plastic NMM–DDA was applied to the stability analysis of Prasat Suor Prat N1 Tower. The simulation results were compared with the on-site observation/investigation and the applicability of elasto-plastic NMM–DDA was also discussed.