case 2: Tunnel bore stable, tunnel heading not stable
11.3 Percolating water through dam rock foundations;
11.3.3 Casagrande's critical opinions; present approach to
(1) Casagrande's opinions. In January 1961, A. Casagrande, delivering the First Rankine lecture to the Institution of Civil Engineers, London, syste- matically questioned grouting procedures and endeavoured to prove that they
338 Rock mechanics and dam foundations
are useless for reducing the uplift pressures under dams. He started with an earth dam on loose, pervious alluvium (fig. 11.14a), and related his remarks to concrete dams built on solid competent rock (fig. 11.146). In this diagram it is assumed that the depth to the impervious soil under the dam is d, and B the width of the dam base.
l y " p i e z o m e t r i c line
pervious d impervious
! / = 0 A-,
\ . —r^-^-—-^^ .piezometric line
' A j ' * *' r i soil)
<^*"£> pervious A'2 / fc impervious
(b)
Fig. 11.14 Casagrande's theory on grouting.
M (pervious soil) (c)
Assuming the grout curtain to be a nearly impervious, very thin curtain (e^d 0), then Dachler's well-known theory (1936) shows that it causes only negligible pressure losses. Measurements carried out under earth dams showed that the pressure line is nearly linear, the pressure loss, A/?, caused by the grout curtain being negligible, thus confirming the Dachler-Casagrande theory. The immediate reaction to this theory was to observe that the thick- ness, e, of a grout curtain should never be negligible. Those under the Serre- Poncon rock-fill dam and the High Aswan dam are quite substantial. In particular, the width e of the grout curtain under a concrete dam with width B is definitely not negligible. As soon as the ratio e\B becomes significant then the pressure losses through the curtain are proportionately greater.
Casagrande's thesis would have been easier to demonstrate if it had been assumed that the soil foundations of the earth dam were pervious at great depth (fig. 11.14c). He published several diagrams similar to fig. 11.15
junction curtain
piezometric line
;allery
>grouted foundation .drain
-main grout curtain
Fig. 11.15 Piezometric line under concrete dam.
showing that the piezometric line, measured under a concrete dam, depends on the position of the drainage system and not on the position of the grout curtain. His conclusions were that expensive grouting is useless and that a much cheaper drainage system is the only efficient method of controlling the piezometric line along the dam foundations.
In fact, the whole theory of uplift pressures and pressure lines had been developed long before Casagrande and it was accepted that they do not depend on the absolute value of the perviousness of the medium, k, but only on the relative perviousness of the grouted to ungrouted medium, k/k2. But the discharge seeping under a dam is directly proportional to the absolute value of k. It was argued that the purpose of grouting was not really to decrease the uplift pressures (an uplift factor of A = 0-80 to X = 1-0 being accepted by all dam designers) but to check possible water seepage and losses under or round a dam (Jaeger, 19496, 1956,19616).
It was additionally observed (fig. 11.15) that interstitial water pressure is measured along the foundation line between concrete and rock, which is grouted, so that the k value along the foundation is about the same from heel to toe of the dam. This explains why the pressure line of uplift is linear along the foundations.
(2) Further research on grouting and draining, Casagrande's lecture was delivered one year after the rupture of the Malpasset dam. It was a time when many designers were deeply concerned with basic concepts in dam design and they realized that the main problem to be analysed was the bulk stability of the concrete dam plus rock masses modified by the grouting and drainage systems (Jaeger, 19616, 1964a; Londe & Sabarly, 1966). It was becoming clear that many problems were so intimately linked that none could be discussed without full consideration of the others (fig. 11.16).
possible line of rupture possible line of rupture section A.A
grout curtain tc\
Fig. 11.16 Schematic representation of the bulk stability of a dam, depending on the position of the grout curtain (after Jaeger, 19616).
340 Rock mechanics and dam foundations
Pacher and Miiller had been studying the rock abutments of the Kurobe IV arch dam (Japan). (The methods used by Miiller and John to determine the density and main directions of the fissures have already been dealt with.) In 1962 (Salzburg), Pacher & Yokota reported on their investigations into seepage problems. Yokota (1963) assumes that water seepage through highly fissured rock is similar to that through a homogeneous porous medium (laminar flow) and that the law of Darcy applies. Comparison of results obtained in nature, by reading piezometric levels in boreholes, with those obtained in the laboratory will show whether this assumption is correct.
(All theories developed by Casagrande are implicitly based on the same assumption.) If the law of Darcy is accepted then the use of electrical ana- logues for rapid research is justified.
Yokota describes how he tested the efficiency of grout curtains using an electric analogue and then made drainage tests on two- and three-dimen- sional models. For three-dimensional models an agar gel was used. The efficiency of a grout curtain is defined by
rj = (Kx - K2)IKl9
where K± — the permeability coefficient of the rock mass before grouting and K2 = the permeability after grouting. The porosity P of the curtain is given by 1 — rj = K2\KX. A better definition would be to introduce the dischargesqx and#2 before and after grouting: rj = (q± — q2)lqi> The porosity factor then becomes P = q2lqi- The final purpose of the research was to establish a design for the grout curtain and associated drainage system, for Kurobe IV dam. It was decided that drainage holes with 56 mm diameter and 10 m apart were an acceptable solution.
Tests were carried out on a three-dimensional model:
(a) without curtain grouting and without drainage, (b) with curtain grouting only,
(c) with grouting and drainage curtain,
(d) with so-called direct drainage in addition to (c).
The results showed that the reduction of flow due to the grouting curtain was only 10%, while with drain holes added the total flow was increased by 27%; but the level along the downstream rock surface (which is a measure of the pressure) was decreased to 65 % of the original flow. Comparisons were made on the prototype by measuring water levels in twenty-four piezometers, when the reservoir was partly full at elevation 1376 m. Yokota summarizes his views as follows: 'Curtain grouting is necessary to plug rather wide openings or cavities in the rock, but it seems very difficult to form a so-called watertight screen.' He found, on the other hand, that drains were very effective in reducing hydrostatic pressure. His conclusions confirm the opinion that grouting curtains and drainage sytems should be used simultaneously (fig. 11.16c) (Jaeger, 19616,1964a).
Pacher investigated the general stability of the rock abutments of Kurobe IV dam. Some of his research about the flow lines in grouted, homogeneous rock and the pressure gradients are shown in figs. 11.17 and 11.18. He con- cluded that the shape of the grout curtain had to be inclined and adapted
P in percentage of//
100
pressure /;
60 40 20
y j
**•
I 1
a 1 w | JI,"
r^ IT
ằ- -perviousgrout curtain
20 40 60 80 100 %/>
Fig. 11.17 Pressure diagram for a pervious grout curtain, p = pressure as indicated on the diagram (after Pacher, 1963).
Fig. 11.18 Grout curtain at Kurobe IV dam. Estimated flow and equipotential lines. Symbols: , grout curtain; , equipotential lines; •, flow lines (after Pacher, 1963).
in plan view to local conditions. In fig. 11.18 it can be clearly seen how the curtain is curved in plan view in order to increase the efficient mass of rock forming anchorage for the dam on the downstream side of the curtain.
Research into the same problems was also carried out in France by Londe
& Sabarly (1966) and by Sabarly (1968) who arrived at very similar con- clusions. To make his point clear, Sabarly published two sketches showing the
342 Rock mechanics and dam foundations
forces F and F' acting on the rock foundations; one where there is a grout curtain and the other where drainage was used under the dam (fig. 11.19). A simplified calculation shows that F' = F sin a/a. Additionally the direction
impervious grout screen
F= yH(R - r)
drainage system F = YH(R - r) 5UL2
Fig. 11.19 Simplified sketch comparing the force, F, on a grout screen with the force, F\ on a drainage system (after Sabarly, 1968).
of F' is far more favourable than the direction of F. A more detailed calcula- tion could be developed using Pacher's approach. Sabarly also confirms the thesis of Casagrande, by showing that there is a far greater reduction in uplift forces under a dam when drainage is used instead of a grout curtain.
His general conclusions concerning dam foundations are: in the case of an impervious rock mass, a grout curtain is not very efficient. To check uplift pressures he suggests building a drainage system rather than a grout curtain.
A theory of drainage system has been developed elsewhere (C. Jaeger, 1956).
In very pervious rock, grouting may be required to reduce the discharge of water seeping through the fractures and fissures. Too high a discharge may saturate the drainage system and make it inoperative or may erode the fissures. Grouting is supposed to check the discharge of percolating water.
A very large grout curtain was required to stop leakage under the Camarasa dam (Spain) as the water losses under pressure could be higher than the average yearly inflow to the reservoir (approx. Il/m3/s). A large grout curtain was also required for the Dokan dam (Iraq) (Jones et aL, 1958) to stop leakage through very pervious rock. In other cases, stopping the water loss was imperative for economic reasons.
Sabarly recommends inclined grout curtains, similar to those proposed by others (Jaeger, 19616). He mentions the possibility that arch dams might rotate around their foundations. This rotation, in addition to a radial dis- placement may cause an open fissure under the heel of the dam (fig. 11.20), and a rupture of the impervious grout curtain. (This rupture is not likely to occur on the foundations of double curvature arch dams and of gravity dams where the rotation of the dam base is smaller.)
Sabarly describes the case of an arch dam with a vertical cylindrical upstream face. The vertical upstream grouting curtain followed the heel of
upstream dam face reservoir
empty
1^ dam face
| reservoir full
compressed area
Fig. 11.20 Rotation of the base of an arch dam (after Sabarly, 1968).
the dam. This was reinforced by a short inclined secondary curtain drilled from the gallery (fig. 11.21). The dam functioned well for several years.
During a period when the reservoir was empty, piezometric boreholes were drilled from the gallery. When the reservoir was filling up, a few metres
reservoir^
empty cylindrical
upstream face — • secondary <
curtain main front • curtain
r reservoir full
open * I fissure^
piezometers drains
Fig. 11.21 Arch dam with cylindrical upstream face (after Sabarly, 1968).
before reaching its top level the piezometers suddenly began to discharge.
Rising water levels made the discharge increase to 1200 litres/min per piezometer, which is quite considerable for small boreholes. Drains were drilled on the toe of the dam (see fig. 11.21) but they discharged very little.
It was assumed that rotation of the dam had opened a fissure, probably near the concrete-rock line, and water had penetrated direct into the piezometers, the discharge being
q = Ahxe39
where e is the width of the fissure, which increases with reservoir levels, and fix the available head. Discharge under the dam is increased proportionally to the third power of e and increases with the dam rotation. To stop the water
344 Rock mechanics and dam foundations
losses and additional uplift pressures, Sabarly suggested that a grout curtain and drainhole should be located as indicated in fig. 11.22. This would stop water losses progressing towards the toe of the dam but would not decrease
upstream face
grout curtain
/ drainage j* system
I I
Fig. 11.22 Suggested location of grout curtain.
the uplift pressures, or solve the more important problem of bulk stability of the rock foundations.
It is suggested that the correct choice of the dam profile (double curvature arch dams) would avoid excessive rotation of the foundation and so avoid fissuring of the rock. The Italian 'pulvino' design would be most efficient in such a case. A 'pulvino' is a pressure distribution slab following the periphery of the dam foundations (the dam shell rests on the pulvino). A peripheral joint is provided which is usually grouted after settlement of the rock founda- tions and before raising the water level in the reservoir (fig. 11.23). But the
~grout curtain
Fig. 11.23 Arch dam with peripheral 'pulvino' (after Semenza).
joint can be left open and provided with an elastic seal. Such a design, strongly advocated in many papers (Jaeger, 1950, 1964a, b), spreads the com- pression forces on the rock over a wider field, equalizes them and avoids any major rotation of the foundations, the elastic seal being able to absorb small
rotations of the dam shell. A somewhat similar design has been used by Gicot for the Schiffenen dam to compensate for the difference of the elastic modulus of the rock in the river bed and on the natural lateral abutments.
(3) Rock grouting for consolidation of rock masses. In considering the prob- lem of drainage-grouting primarily on uplifts, Casagrande has neglected some other very important aspects. The case just mentioned shows the danger of excessive water losses. There are other aspects of the problem requiring close investigation.
Rock grouting can be used for consolidating fissured rock masses. Semenza successfully used it on the rock abutments of the high Vajont arch dam. At the same time the grout pressure increased the rock stiffness and brought the Young's modulus of the rock masses, Er, to the required high uniform values to be introduced in the elastic analysis of the dam shell.
Several years before Semenza, Coyne (France) used systematic grouting for consolidation of the rock abutments of the Castillon arch dam and the Chaudanne arch dam. More recently, similar techniques were used for the Kariba dam (Rhodesia) and the Dokan arch dam (Iraq). In all these cases rock grouting was vital to the final success of the design.
More information on this will be given in the next chapter.