The main goal of the paper is to give a variational formulation of the behaviour of bolt systems in rock mass. The problem arises in geomechanics where bolt systems are applied to reinforce underground openings by inserting steel bars or cables. After giving a variational formulation, we prove the existence and uniqueness and some other properties.
The main goal of the paper is to describe a reinforcement consisting of fully grouted bolts, which is applied to stabilizing underground openings and tunnels. After a variational formulation is given, the existence and uniqueness is proved. Some asymptotic results that make it possible to replace the real system with a continuous one more suitable for discretization are presented. Some other types of reinforcements and properties are studied.
A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic problem connected...
In this paper the stability of two basic types of cable stayed bridges, suspended by one or two rows of cables, is studied. Two linearized models of the center span describing the vertical and torsional oscillations are investigated. After the analysis of these models, a stability criterion is formulated. The criterion expresses a relation between the eigenvalues of the vertical and torsional oscillations of the center span. The continuous dependence of the eigenvalues on some data is studied and...
In this paper a dynamic linear model of suspension bridge center spans is formulated and three different ways of fixing the main cables are studied. The model describes vertical and torsional oscillations of the deck under the action of lateral wind. The mutual interactions of main cables, center span, and hangers are analyzed. Three variational evolutions are analyzed. The variational equations correspond to the way how the main cables are fixed. The existence, uniqueness, and continuous dependence...
A method for the detection of the initial stress tensor is proposed. The method is based on measuring distances between pairs of points located on the wall of underground opening in the excavation process. This methods is based on solving twelve auxiliary problems in the theory of elasticity with force boundary conditions, which is done using the least squares method. The optimal location of the pairs of points on the wall of underground openings is studied. The pairs must be located so that the...
In this paper a method for the detection of initial stress tensor is proposed. The method is based on measuring distances between some pairs of points located on the wall of underground opening in the excavation process. This methods is based on the solution of eighteen auxiliary problems in the theory of elasticity with force boundary conditions. The optimal location of the pairs of points on the wall of underground work is studied. The pairs must be located so that the condition number of a certain...
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