Page 53 - Origin and Prediction of Abnormal Formation Pressures

36 G.V. CHILINGAR, J.O. ROBERTSON JR. AND H.H. RIEKE III
S
S
S

P
;:: ,,<: ............ , . . . . . .:

6
Stage A Stage B Stage C
~=1 L< 1 >0.465 ~.=0.465

Perforated Plates
Water
Fig. 2-7. Schematic representation of clay compaction, o- - grain-to-grain bearing strength, S = axial
component of total stress (overburden pressure), and p = fluid pressure, o- = S - p. (Stage A) Overpressure
system. (Stage B) Water is allowed to escape; springs carry part of the applied load. (Stage C) Compaction
equilibrium; load is supported jointly by the springs and the water pressure, which is simply hydrostatic.
)~ = Pp/Pt = p/S. (Modified after Terzaghi and Peck, 1948; in Hottman and Johnson, 1965, p. 718. In
Rieke and Chilingarian, 1974, fig. 5 I, p. 93.)

Another useful ratio of the effective intergranular stress to the total stress can be used,
which is expressed by the symbol X"
O -t
X -- (2-37)
(7

Hooke's law

Commonly, the overburden weight of sediments (force) creates the major stress, o- z,
which acts in a vertical direction. The lateral stresses, ox and ~r.v, lie in a horizontal plane
in all directions as a lateral restraining force. According to Hooke's law, the horizontal
strain (ex) can be expressed as follows"
O" x O- v O- z
ex = v--:- - v-- (2-38)
E E E
where e,, is horizontal strain, a~, a>,, a: are effective stresses along x and y (horizontal)
and z (vertical) axes, E is Young's modulus, and v is Poisson's ratio. Inasmuch as e~ is
essentially equal to zero and the lateral stress a, is equal to the lateral stress ay for rocks
in compression, then"
v
o x -- O-y -- o- h -- ~ o - z (2-39)
(1 - v)