IN-SITU AND INDUCED EFFORT
IN-SITE STRESSES
Sheorey (1994): elostatic thermal stress model. the two horizontal stresses are seldom equal.
Therzagui y Richard (1952):horizontal stresses are more difficult to estimate than vertical stresses
TWO-DIMENSIONAL AND THREE-DIMENSIONAL MODELS
WORLD STRESS MAP
STRESS MEASUREMENT
EXAMPLE OF TWO-DIMENSIONAL STRESS ANALYSIS
Orientation of maximum horizontal compressive stress
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TWO-DIMENSIONAL: stress and displacement analysis in the rock surrounding the tunnel, where the length of the opening is much greater than the dimensions of its cross section
THREE-DIMENSIONAL: in the case of underground machines, chamber, crusher with an equidimensional shape and the effect of the end walls cannot be neglected
NUMERICAL SOLUTIONS
the horseshoe-shaped tunnel floor allows for upward shifting or lifting of the floor. sidewalls create high stress concentrations
preliminary design:
- in strong rocks at shallow depths the stress problems may be insignificant and the analysis continues.
the group of excavations can form a set of complex three-dimensional shapes
Due to faulting, dikes, rock properties are seldom uniform within the rock volume of interest.
METHODS FOR THE ANALYSIS OF STRESS-DRIVEN PROBLEMS
direct method
indirect method
boundary element methods
displacement discontinuity method
domain discretization methods
finite element method and finite differences
limit discretization methods
distinct element method
PROGRAMS: EXAMINED3D, PHASE2.
excavation limit is divided into elements and the interior of the massif as an infinite continuum
the interior of the massif is divided into geometric elements
only the limits of the geometry of the problem is divided into elements
displacements are resolved directly for the specified boundary conditions
find set of fictitious stresses
elongated slit solution in an elastic continuum and shear and normal displacements
problems involving nonlinear heterogeneous material propertiess
allows a very general constitutive modeling of the behavior in conjunction with the computational effort
in poor quality massifs or in very deep tunnels, the horseshoe shape is not suitable
the distribution of stresses in the massif that surrounds the tunnel can be improved by modifying the shape from a horseshoe to a circular one
tunnel shape
geological observations
earthquake focal mechanisms
volcanic alignments
fault slip interpretation
hydraulic fracturing
excavations and bursting of wells
regional characteristics:
- faults: the in situ stresses in the vicinity can rotate with respect to the regional stress field.
- analysis of induced stresses: in the new underground opening, the stresses in the new neighborhood are redistributed.
- the 3 stresses are mutually perpendicular but may be inclined in the direction of the stress applied in situ
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HYBRID APPROACHES: Combining methods to remove undesirable features while retaining advantages