Terzaghi, in his theory of slopes, uses the term 'secondary permeability' for the permeability which results from the pressure of open and continuous cracks and fissures in the rock. It depends on the width and spacing of these passages. Primary permeability is found in the voids of the intact rock located
212 Rock slopes and rock slides
between the fissures and is so minimal compared with secondary permeability that a tunnel driven through intact rock below the water-table appears to be dry.
If secondary permeability of the rock were uniform, the water-table would assume a more or less parabolic shape. But rock masses just behind the slope are frequently more fissured than those at a distance, making water per- colation easier.
If water were immobile in the fissures, the water-table would be horizontal, the uplift forces on the rock would be vertical, and lateral forces balanced.
When there is a flow of water a lateral pressure is exerted on the rock mass.
This is called 'cleft' water pressure and it is proportionate to the difference in water level on both sides of the rock mass. It can be calculated by using the methods for calculating water pressure in soils. Additionally, the water percolating through fissures filled with clay-like material will reduce the friction forces along these fissures. Combined effects of this type may weaken the foot of some slopes and cause a rock slide.
Bjerum (Norway) submitted a detailed survey of local conditions to the Austrian Society of Rock Mechanics in Salzburg (1963), which proved a definite connection between climate and rock slides. The area under observa- tion has severe winters with very heavy snowfalls. There is also a lot of rain during autumn. Most of the major slides take place in April. At that time the melting snow feeds large quantities of water into the rock joints, which are still plugged with ice. The resulting pressure build-up causes a rock fall or slide. There is a second peak-period in October-November.
The report also gives details of the rock slide which occurred at the south end of Loen lake (south-west coast of Norway) on 13 September, 1936.
The slope is located on granite gneiss with poorly developed foliation and rises at an average angle of 50° to a height of about 3600 ft above lake level.
The middle portion of the slope, at a height of about 1600 ft, is nearly vertical. The planes of foliation dip at an angle of about 65° towards the lake. The rock behind the vertical face is weakened, probably by sheeting joints situated parallel to the face, but the rock between the joints is practically impervious. During a heavy rainstorm the rock between the vertical face and one of the vertical joints, about 1-3 million yd3 in volume, dropped from the cliff and fell into the lake, causing a 230-ft-high wave which destroyed a village and killed many people.
Although Terzaghi believes that the effects of 'primary permeability' are negligible, there are cases where they are quite significant. Some rocks may absorb pore water quite easily. Phyllite for example, when soaked in water over a period of three days, may have its modulus of elasticity reduced by 50 or 70 %. This can only be explained if water penetrates in all the pores of the rock. Similarly, microfissured rocks (gneiss) may absorb water, even if it is at a slow rate. Some samples have disintegrated completely within a year of being put in water.
9.3.2 Statics of immersed or partly immersed rock
It is accepted in soil mechanics that the pore water reduces the shear strength of the soaked soil. When u is the pore water pressure, Coulomb's law becomes:
r = c + (a — u) tan <j>.
This law is also valid for rock as seen in chapter 8. In the case when rock cohesion is negligible:
T = (a — u) t a n <f>.
This very general remark can be used when discussing the stability of rock slopes immersed or partially immersed in water.
In fig. 9.6 the volume of rock, Vl9 is immersed in water, V2 is above water.
The stability of the rock mass, yr(V1 + V2) is considered where yr is the
Fig. 9.6 Fig. 9.7
specific weight of the solid rock materials, voids excluded, and y the specific weight of the water. Assuming n to be the volume of the pores then the vertical uplift force, U, on the rock mass is
and the weight is
W=yr(l-n)(V1+V2), and the vertical resultant is
n)Vx + yr{\ - n)V2.
There is no horizontal component from the water pressure. Figure 9.7 refers to conditions along the slopes of a lake or reservoir. There is a possibility for the rock mass BAC to slide along the plane sliding surface BC. The weight of the mass of rock BAC is
W = £yr(l - n)H2 (cot a - cot /S) = \yz{\ - n)H2 sin (fi - a) sin j8 sin a The uplift is
sin a sin
214 Rock slopes and rock slides
fory<H where y is a variable water depth, and
sin for y>H.
The force acting normal to the plane surface CB is (W — £/) cos a and the tangential force is (W — £/) sin a.
The condition for rock stability is a < <j> for all cases from y = 0 to y = H and y>H and does not depend on the uplift £/.
Conditions of stability along a circular surface are very similar. O is the centre of the arc of circle CB with radius r and W — C/ the resultant of the weights and uplift forces. On a small element of circle As the normal and
Fig. 9.8
tangential forces are AN and Ar. The three equations for equilibrium of masses are (fig. 9.8) (Lotti & Pandolfi, 1966a):
2 cos ex. AN + S sin aAr = W - U, S sin aAN — S cos aAr = 0,
r S AT=(W- U)a.
The condition for stability is:
Ar
at any point of the circular surface. This solution is identical to the approach used in soil mechanics. There are others which are also acceptable and these can be worked out using the general theorems of the mechanics of the centre of gravity of rock masses.
Hydrostatic forces acting on the rock masses never have any horizontal component. When there is a flow of interstitial water, hydrodynamic forces
A
- I f - - P tA z —TT—F^
A / / A / /
(a)
Fig. 9.9 Horizontal component of forces, AH, transferred to rock mass.
have a component of forces AH in the direction of the flow, (fig. 9.9) and the force AH transferred to the rock is equal and opposed to the restraining force AR on the flowing water, which is then:
AH = -AR = AzA = Az
—Ax = SA Ax,
and
= 2 SA
on the whole length of the water-table to be considered, where S is the slope of the water-table and A = cross-section area. The slope of the sliding surface does not matter and the force AH = —AR = 0 when Az = 0 (hydrostatic conditions, no flow).
Tests and measurements made in situ have proved that in most cases seepage of water in fissured rock masses can be simulated by the flow through porous media (sand and gravel), and a seepage factor can be calculated from in situ measurements.
^ 3 — - ^ C ^ j \ steady water / ^ ^ K ) level permanent (-\ ^7/
or semi-permanent seepage line
Fig. 9.10
Theories developed for ground water flow can be used for fissured rock masses. For example, fig. 9.10 shows the ground water-table caused by water percolating in the rock masses. The horizontal component of the forces
216 Rock slopes and rock slides
is usually small. Greater forces may be exerted when the level of the water in storage reservoirs varies rapidly by — A/Ji. or + A/72 as shown in figs.
9A\a,b. This theory from soil mechanics is well known. Figure 9.11c is a method for calculating the forces transmitted by a flow of water to the rock using the approach developed in section 8.2.
A / /2
(c)
ground water 1 ^ level
Fig. 9.11 kx and k2 — perviousness of primary and secondary joint; bx and b2
distances between joint systems.