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Far Field Stress
The Field Stress option is used to define the magnitude and orientation of the in situ principal stresses (i.e. stress state in the ground prior to excavation). In Examine2D there are two methods of defining the Field Stress:
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Constant
Gravitational
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The Field Stress parameters are entered in the sidebar, and depend on the analysis type - Plane Strain or Complete Plane Strain.
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Field Stress: Constant
The Constant Field Stress option assumes that the in situ principal stresses are constant in magnitude, and do not vary with depth or location. For excavations which are relatively deep below the ground surface, this is a common assumption (i.e. the gravitational stress gradient is negligible across the height of your model, compared to the overall stress magnitude).
Constant Field Stress Input (Plane Strain)
For a Plane Strain analysis, a Constant Field Stress is defined by the in-plane major and minor principal stresses (Sigma 1 and Sigma 3), the in-plane angle, and the out-of-plane principal stress (Sigma Z).
Sigma1 contours, constant field stress, angle = 20 degrees from horizontal
For Complete Plane Strain, the in situ principal stresses can be arbitrarily oriented with respect to the excavation axis. The magnitude and orientation of Sigma1, Sigma2 and Sigma3 are required, as well as the orientation of the excavation axis.
Constant Field Stress Input (Complete Plane Strain)
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Field Stress: Gravitational
The Gravitational Field Stress option assumes that the in situ stresses vary linearly with depth. The vertical stress at any point is calculated by multiplying the depth by the unit weight of the overlying material. The horizontal stress is calculated by multiplying the vertical stress by the Horizontal/Vertical Stress Ratios. Gravitational Field Stress is appropriate for surface or near-surface excavations.
Gravitational Field Stress Input (Plane Strain)
The depth can be measured from either:
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A single datum elevation
The actual ground surface of your model (i.e. ground surface boundary)
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The Use Ground Surface Boundary option is useful for models where the ground surface is not horizontal, since it provides a better initial estimate of the vertical in situ stress.
Sigma1 contours, gravitational field stress computed from depth below ground surface boundary
The vertical and horizontal stresses are calculated using the following equations:
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Sv = gamma*H
Sh = K*Sv
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where:
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gamma = unit weight of the soil/rock
H = depth below elevation or ground surface
Sv = Vertical stress
Sh = Horizontal stress
K = Horizontal stress ratio
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The equation for horizontal stress applies to both the in-plane and out-of-plane horizontal stresses.
For Complete Plane Strain and Gravitational Field Stress, the horizontal principal stresses can be arbitrarily oriented with respect to the excavation axis. The required input parameters are shown below.
Gravitational Field Stress Input (Complete Plane Strain)
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