Rock Mass In-Situ Stress - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 220

where γ S is the mean unit weight of the overlying sediments. If the clay is assigned to

behave isotropically and elastically and Poisson's ratio ν of the clay is assumed to reduce

as a result of consolidation and compaction, varies with overburden t, as illustrated in

Fig. 9.8. The horizontal stress in the element e at t = t 1 is then obtained by

ν

(9.13a)

When the fi nal thickness of overburden t n is reached, the clay has consolidated into a
claystone with Poisson's ratio ν n (Fig. 9.8) and the horizontal stress becomes

(9.13b)

When the sediments overlying the claystone are eroded away, both the vertical and the
horizontal stress in the element e reduce. However, during unloading the element be-
haves like a claystone with Poisson's ratio

ν n . Thus, at the fi nal ground surface the verti-
cal stress is zero and the horizontal stress reduces to

(9.14)

This remaining stress represents the additional horizontal stress Δσ Hn resulting from

diagenetic consolidation that needs to be added to the horizontal stress due to gravity
acting in the claystone at depth h:

(9.15)

where γ S is the unit weight of the claystone. Depending on the strength of the

claystone, this stress at a certain depth can lead to failure of the intact rock that may
be indicated by observed features such as slickensides and local shear zones (Chapter
2). In such cases, the horizontal stresses are considerably reduced and can no longer
be derived from Equation (9.15). In the area of Stuttgart, for example, theoretically
horizontal stresses of some 10 MPa can be derived when using Equation (9.15). In this
area, features such as slickensides have been observed, and the maximum horizontal
stress derived from monitoring results and stress measurements amounts to approx.
1 - 2 MPa only (Wittke 1991).

γ C >

A similar explanation of the origin of increased horizontal stresses due to erosion start-
ing from an originally hydrostatic stress state are given by Voight (1966a) and Brady &
Brown (2006).