Civil Engineering Reference
In-Depth Information
Figure 11.28
Rotation of a two-dimensional rock wedge supported by two discontinuities
As an example, the stability against rotation of the wedge illustrated in Fig. 11.27 is con-
sidered. {R} intersects D1 and causes negative moments about the axes {r
k
} and {r
m
}.
Since the rotation about {r
m
} requires a positive moment, only a rotation about {r
k
} is
possible. According to the sign convention given above, the corresponding moment is
negative:
M
k
= - r
⋅
R,
(11.86)
where r and R are the lever arm and absolute value of {R} (Fig. 11.29).
According to the partial safety factor method, the stability against this rotation is
reached at the state of limit equilibrium with design values. The balance of forces and
the balance of moments require:
{R} + {Q
1
} + {Q
2
} = {0},
(11.87)
{M
k
} + {M
k1
} + {M
k2
} = {0},
(11.88)
where {Q
1
} and {Q
2
} are the reaction forces due to {R} on D1 and D2 and {M
k
},
{M
k1
} and {M
k2
} are axial vectors representing the moments caused by {R}, {Q
1
} and
{Q
2
} with respect to {r
k
}. At limit equilibrium the rock wedge is only supported at the
edges denoted in Fig. 11.29 with A and B. In consideration of the sign convention the
balance of moments can be written as
M
k
+ M
k1
+ M
k2
= - r
⋅
R + r
1
⋅
Q
1
+ r
2
⋅
Q
2
= 0
or
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