Geology Reference
In-Depth Information
Box 6-1.
As the rock or soil is compressed under self weight, it tries to
expand laterally and a horizontal stress is exerted. This is termed the
Poisson effect. Typically, in a soil pro
le at shallow depths (tens of
metres), the
in situ
horizontal stress (
h
) due to self weight will be
between about 0.3 (in loose sand) and 0.6 times (in dense sand) the
vertical gravitational stress. The value 0.3 to 0.6 is called the coef
σ
cient
of earth pressure at rest. In normally consolidated clay, the value is
about the same as for dense sand: 0.6. For most rocks, the Poisson
s
ratio is slightly less than 0.3. Most continental rocks weigh about
27 kN/m
3
, so at a depth of 500m the total vertical stress can
be anticipated to be about 13.5 MPa, and horizontal stresses (
'
σ
h
)
about 4 MPa.
Generally, stresses are estimated by calculating the total weight of a vertical column of soil based on unit
weight measurements. Effective stress is estimated by subtracting measured or estimated water pressure
from the total stress due to the bulk weight of the soil or rock (including contained water).
Sand above
water table
γ
=
16 kN/m
3
Sand
Water table
4 mbGL
Sand below
water table
γ
=
19 kN/m
3
8 mbGL
Clay
10 mbGL
Clay
γ
=
21 kN/m
3
Assume unit
weight of water
γ
=
10 kN/m
3
In
Figure B6-1.1,
a ground pro
le is shown with sand overlying clay. The water table (upper surface of
saturated ground) is 4m below ground level (mbGL).
The unit weight (
) of the damp sand above the water table is 16 kN/m
3
; the unit weight below the water
table, sand plus pores full of water (
γ
γ
sat
), is 19 kN/m
3
. The underlying saturated clay has unit weight
γ
sat
=
21 kN/m
3
. The unit weight of fresh water,
γ
w
, is about 9.81 kN/m
3
(10 is generally a near-enough
approximation given other assumptions).
We wish to estimate the vertical stress at the crown of a tunnel to be constructed at a depth of 10 mbGL.
As shown in
Figure B6-1.2.
