International Journal for Numerical and Analytical Methods in Geomechanics

1984 International Journal for Numerical and Analytical Methods in Geomechanics

doi: 10.1002/nag.1610080501

Tassoulas, John L.; Kausel, Eduardo

1984 International Journal for Numerical and Analytical Methods in Geomechanics

doi: 10.1002/nag.1610080502

Circular ring footings on an elastic stratum are considered. The static and dynamic stiffnesses are calculated using an efficient numerical technique. The results indicate that the static torsional and rocking stiffnesses of a ring footing do not deviate significantly from the corresponding stiffness of the circular footing for values of the inner‐radius‐to‐outer‐radius ratio up to about 0.75. The static horizontal and vertical stiffnesses change considerably only for values of this ratio greater than about 0.60. The change in the stiffness and damping coefficients is small for values of the ratio between 0 and 0.5.

Sharma, K. G.; Rao, G.‐Venkatappa

1984 International Journal for Numerical and Analytical Methods in Geomechanics

doi: 10.1002/nag.1610080503

Numerical solutions have been obtained for stresses and displacements in a linear elastic half space due to distributed loads of circular, rectangular and elliptical shapes. The technique primarily involves use of a multi‐dimensional numerical integration technique to integrate point load solutions over the distributed loading after discretizing the area into a finite number of elements. Both uniform vertical and shear loads have been considered as well as vertical conical loads and inward shear loads. The technique evolved facilitates the determination of stresses and displacements by the use of mini‐computers and is neither as tedious and cumbersome as the use of tables and charts nor as costly as FEM solutions. A detailed comparison has been presented between the results obtained by the numerical solutions and those of the existing analytical solutions wherever they are available. It is found that the agreement between the two is within one per cent for displacements at all depths for the different cases studied. The matching is also good in the case of stresses, except at shallow depths.

Booker, J. R.; Carter, J. P.

1984 International Journal for Numerical and Analytical Methods in Geomechanics

doi: 10.1002/nag.1610080504

An analytical solution to the problem of a load applied to a portion of the wall of a circular tunnel installed deep in a homogeneous isotropic material has been found. The solution is obtained by taking a Fourier transform, in the axial direction, of the field quantities and then representing these as a Fourier series in the polar angle. The integration which is necessary for the inversion of Fourier transforms has to be performed numerically using Gaussian quadrature. The solution has been used to analyse the problem of uniform normal loading applied over rectangular patches of the tunnel wall. An indication of how the solution can be applied to the tunnel jacking problem is given.

Akagi, Tomoyuki; Ichikawa, Yasuaki; Kuroda, Hidetaka; Kawamoto, Toshikazu

1984 International Journal for Numerical and Analytical Methods in Geomechanics

doi: 10.1002/nag.1610080505

A rheological model which is able to explain the delayed failure phenomenon has been proposed and applied to the analysis of the time dependent behaviour of deep tunnels. The model is the three element Voigt type before yielding and becomes the five element Voigt type after yielding. This means that the stiffness of the model is decreased by yielding. It is assumed that the yielding takes place when the stored elastic energy density of distortion reaches a certain maximum value. Some experiments to determine material constants are proposed. The numerical results clearly exhibited a delayed failure state of the rock masses around the tunnel surface. It was found that the extension of the yielding zone due to tunnel excavation depends on the opening method.

Belytschko, Ted; Plesha, Michael; Dowding, Charles H.

1984 International Journal for Numerical and Analytical Methods in Geomechanics

doi: 10.1002/nag.1610080506

A simple rigid block model has been developed for analysing the stability of caverns and tunnels in jointed rock. Rigid block interactions are idealized as linear edge‐to‐edge contacts with a zero joint tension constraint and a Mohr‐Coulomb friction law. In the method, the minimum friction angle for stability is determined by sequentially eliminating tension and then minimizing the shear. It is demonstrated through examples that the minimum joint friction angle which results in a stable configuration is independent of the stiffness of the joint, and depends only upon the loading and geometry of the jointing and cavern. This insensitivity of stability to the normal and tangential joint stiffnesses, which can be difficult to obtain, is very useful for design purposes.

Michalowski, Radoslaw L.

1984 International Journal for Numerical and Analytical Methods in Geomechanics

doi: 10.1002/nag.1610080507

A differential slice technique is applied in order to obtain the solution for the pressure distribution on rigid retaining walls. The technique is based on a statical analysis of a plane differential slice, for which only the global equilibrium is required. An analytical solution to the problem is found for a non‐cohesive material and a linear slip surface. For more complicated cases the numerical solution is required.

Wood, D. M.

1984 International Journal for Numerical and Analytical Methods in Geomechanics

doi: 10.1002/nag.1610080508

1984 International Journal for Numerical and Analytical Methods in Geomechanics

doi: 10.1002/nag.1610080509