671017.pdf

1 2 34567 8 9 10 11 1 2 13 14 15

Normal stress (kPa)

Solutions for cavity expansion

in an infinite space

Present solutions

D/a

−1. 0

−0. 9

−0. 8

−0. 7

−0. 6

−0. 5

−0. 4

−0. 3

−0. 2

−0. 1

0. 
   

h=7a

h=7a

h=8a

h=8a

D o

r

z

h

(a) Normal stress

1 2 34567 8 9 10 11 1 2 13 14 15

Shear stress (kPa)

Present solutions

Solutions for cavity expansion

in an infinite space

D o

r

z

h

D/a

h=7a

h=7a

h=8a

h=8a

−0. 20

−0. 15

−0. 10

−0. 05

0. 00


1. 05


2. 10


3. 15


4. 20

(b) Shear stress

Figure 8: Stress along the horizontal free surface.

the introduction of the correction functions. Figures9(a)
and9(b)show that, after being corrected, both the normal
and shear stresses still have larger values in the range1⩽
퐷/푎 ⩽ 4andthendecreasewithfurtherincreaseof퐷/푎.
The larger distance of퐷/푎, the smaller the stresses on the
slope surface will be produced. The condition of zero stress at
the horizontal and sloping free surface is not strictly satisfied.
However, this approximate approach is purposeful in reality.
From Figures 8 and 9 , the stresses, particularly the shear
stresses, on the two free surfaces are close to zero after
correction. Thus, the stresses will decrease until zero if the
correction processes are iterated continually. It is obvious
that the stresses on the free surface decline slowly with the

1 2 34567 8 9 10 11 1 2 13 14 15

Normal stress (kPa)

0. 0

0. 5

1. 0

1. 5

2. 
   


3. 5

3. 0

Present solutions

Solutions for cavity

expansion in an infinite

space

l= 4a

l= 4a

l= 5a

l= 5a

D/a

h l

z

D

o r

(a) Normal stress

1 2 34567 8 9 10 11 1 2 13 14 15

Shear stress (kPa)

Present solutions

Solutions for cavity

expansion in infinite

−1. 5

−1. 2

−0. 9

−0. 6

−0. 3

0. 
   


1. 3


2. 6


3. 9


4. 2


5. 5

l= 4a

l= 4a

l= 5a

l= 5a

D/a

h l

z

D

o r

(b) Shear stress

Figure 9: Stress along the sloping free surface.

iteration increase, so further trivial corrections are not carried

out here.

The displacement of soil induced by the cavity expansion

is discussed in this section.Figure 10illustrates that the

slope and its inclination angles have pronounced influence

on the distributions of the displacements induced by a

cavity expansion source. The displacement decreases with the

increase of the distance(푡 + 푟)/푎.Similarly,thedisplacement

decreases rapidly in the range1 ⩽ (푡 + 푟)/푎 ⩽ 3,

but then more slowly with further increase of(푡 + 푟)/푎.

Meanwhile, the displacement induced by a cavity expansion

source approaching a free surface, in general, is larger than

that in infinite medium (no boundary effect). The findings

are in accordance with the results proposed by Keer et al. [ 16 ]