Answered: Consider excavation of a simple long…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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(a) Calculate the area of the joint and the weight of the wedge (W) in MN assuming a unit length along the out of plane direction (normal to the plane of the figure). (b) Calculate the normal force (N) on the joint plane before and after excavation. (C) Calculate the shear force (T) on the joint plane before and after excavation. d) Calculate the frictional shear strength force (S¢) on the joint plane before and after excavation. (e) Calculate the cohesive shear strength force (Sc) on the joint plane before and after excavation. (f)Calculate the total shear strength force (S = Sc + So) on the joint plane before and after excavation. (g) Calculate the partial factor of safety before and after excavation () due to friction only (FoS¢), (i) due to cohesion only (FoSc), (iii) total factor of safety due to both friction and cohesion ((FoS= FoSc+ FoS). (h) Determine dip, dip direction, strike and pole of both planes (slope and joint planes). Discuss the stability of the wedge against shear sliding. (i) Plot schematically all your results from item (h) above on a stereonet projection circle, Assess the stability of the wedge when the joint cohesion c= 0. (j) Calculate the resulting friction angles for a unit factor of safety before and after excavation, i.e, FoS = 1.0.

Consider excavation of a simple long trapezoidal pit with a joint highlighted in the pit slope,
forming a potentially unstable wedge (ABE), as shown in Figure 1 below. Both planes of the
slope and joint strike North-South. Angle of the pit wall slope with the horizontal axis, p =
57°. Angle of the joint plane with the horizontal axis, = 34°. The unit weight of the rock, y=
27 kN/m³, the depth of the pit, D = 93 m, the depth of the wedge, H = 72 m and the width of
the wedge at the crest, a = 44 m. From experimental measurements, it was found that the
ratio of the horizontal stress to vertical stress before excavation is K = 2.2. The friction angle
() and the cohesion (c) or cohesive shear strength of the joint are as follows:
0.007 MPa.
= 28° and c =
a
E
N
S
Z
σ₁₁ = y.z
Open Pit
Excavation
H
T
D
Oh
Joint Plane
F.S=
S C+N.tan()
T
=K.Ov
=K.y.z
Ground
stresses before
excavation
Figure 1. Excavation of a long pit in a jointed rock formation
B
d

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