6.3.1 Shear tests
In situ shear tests are next in importance to in situ tests on rock deformability. Detailed information on such tests is available either on rock shear strength or on tests of concrete blocks adhered to rock surfaces.
hydraulic jack steel pad steel frame 70 cm
Fig. 6.14 Shear test (Portugese arrange- ment, Rocha). The force, P, has a hori- zontal component, H, causing shear failure.
60 cm Fig. 6.15 French shear test (Electricite de France).
Portuguese tests. Serafim & Lopez at the Fifth International Conference on Soil Mechanics, Paris, July 1961, discussed the technique they used in Portugal (fig. 6.14). They carried out field shear tests on rock blocks of reason- able size, attached to the base rock, and on concrete blocks moulded against the rock surface. Such blocks include some fissures, seams and local altera- tions of the foundation rock (fig. 6.15).
The blocks (70 x 70 cm and 30 cm high) were surrounded by very rigid metallic frames. The blocks and the foundation were kept saturated during the tests. Tangential displacements were measured at two points and the normal ones at four points of the blocks, up to failure. Normal forces were applied first, and only when stabilization of the deformations was reached, were inclined forces applied. These were gradually increased until stabilization of the displacements occurred at each step.
Other in situ tests: shear tests 119 The results were interpreted by tracing Coulomb's lines on a (cr, r) diagram. Two criteria decided the 'tangential stress at failure.' One con- sidered that failure occurred at maximum tangential stress and, the second, that failure occurred when the direction of the vertical displacement of the downstream side of the block was inverted (fig. 6.16).
Forty-four tests were carried out, each parallel and perpendicular to the schistosity planes of analogous rocks, showing approximately the same index of porosity. Shear tests parallel to the schistosity planes gave slightly lower rmax values than other tests. (See also section 12.3 on Morrow Point dam.)
0.4 0.8 1.2 1.6 2.0 2.4 2.8 (+) Vertical displacements (mm)
Fig. 6.16 Vertical displacement curves showing the inversion criteria of failure of field shear tests (after Serafim & Lopez, 1961).
Failure took place in the rock in almost every rupture test on concrete blocks moulded against rock. Some of the results are shown in table 6.1.
U.S. Bureau of Reclamation field tests. A 15 X 15 in by 8 in high block was prepared. The block was made to project above the floor level of a tunnel and was surrounded by a structural steel jacket. Shear and normal loads were applied. The shear load was inclined so that its line of thrust passed through the centre of the shear zone, between the projecting test block and the rock mass, thereby eliminating overturning moments. Instrumentation consisted of dial gauges which measured both vertical and horizontal deformations of the block. The results were correlated with laboratory tests on large blocks (approximately 1 yd3) and with triaxial tests to give a better interpretation of the shearing resistance of the block. Tests were also conducted, utilizing
Table 6.1 Shear strength of rocks tested in situ (after Serafim & Lopez, 1961).
Rock Direction of test / Weathered
granites
f 1
upstream downstream i Weathered r parallel to
schists and j cleavage concrete on] perpendicular schists v to cleavage *
Criteria for failure maximum
stress rmax
inversion of
Index of porosity -
(0
' 3
displacement maximum
7 10
3 7 10 ( stress Tmax | —-
Shearing strength kg/m2
134 3-5 2-2 6-5 2-2 1-5 0 to 4 3-5 to 9
P 62-5
52 46-5 63-5 49 42 59 to 64
60
concrete blocks cast on rock to determine the cohesion and friction resistance at the place of contact. (See also section 12.3 on the tests at Morrow Point dam.)
Similar tests have been conducted by Electricite de France, as well as in Spain, the USSR, and other dam-building countries. Bollo (France) reporting to the 1964 Congress on Large Dams, writes that he found <f>
values as low as 12°-17°, others with <f> = 45°.
6.3.2 Anchorage shear tests
J. A. Banks (1957) carried out some interesting anchorage tests at the power station site of the AUt na Lairige dam in Scotland. The scheme, which in- corporated a gravity section dam, was originally designed for a limited storage (8-3% of the annual run-off). A prestressed concrete design was investigated (83 ft high) and it was estimated that storage could be increased by 10% at practically the same capital expenditure by building a much higher dam. The anchorage method first used at the Cheurfas dam in Algeria was adopted, except that anchorage bars and plates were used instead of cables. The bedrock at Allt na Lairige is granite, a far more compact foundation than that of the Algerian dam.
The method used to test the strength of such an anchorage is clearly shown in fig. 6.17. Rock surface displacements are measured with precision levels.
Rock displacements and concrete displacements relative to the bottom of the pit well are measured with high-tensile steel wires. Figure 6.18 shows the vertical displacement of the rock surface (line A) and of the concrete plug (line B) relative to the rock at base of the pit. Line C gives the absolute displacement of the rock surface, measured by precision level (accuracy ± in). For all practical purposes the test results were reassuring. With a
Other in situ tests: shear tests 121 depth of only 18 ft for the test anchorage as against 26 ft for the anchorage under the dam, a pull of 4400 tons did not damage an anchorage designed for normal P = 1176 tons. The tests were carried out with a bare rock surface, whereas under the dam the full weight of the dam plus the opposite
Fig. 6.17 Detail of test anchorage at Allt na Lairige dam: (A) Freyssinet flat jack;
(B) hand pump; (C) deflectometer; (D) crossbeam; (E) steel tube duct; (F) staffs for vertical displacement measurement (after Banks, 1957).
Applied load (tons)
Fig. 6.18 Deformations recorded at rock anchorage test at Allt na Lairige dam:
(A) vertical displacement of rock surface relative to rock at base of pit under flat jack; (B) vertical displacement of concrete plug relative to rock at base of pit under flat jack; (C) approximate absolute displacement of rock surface measured by precision engineering level; (/)) relaxation periods (after Banks, 1957).
force — P would hold the rock surface. There is no danger to the foundation as long as weights and anchoring forces balance the overturning moment from the horizontal hydrostatic thrust.
The analysis of stress conditions during the test shows that the anchorage forces were transmitted by shear. The weight of the inverted rock cone of 18 ft height and 18 ft radius at the base is about 435 tons. This is quite
inadequate to hold down an uplift thrust of 4400 tons and obviously the uplift force was balanced not by the weight of the rock but mainly by shear stresses. Figure 6.18 shows that deformations were more or less elastic for P = 1000 tons. Beyond that plastic deformations and small ruptures occurred, but the shear strength of the rock was not finally destroyed.
This complexity should be studied in detail by direct mathematical analysis or with photo-elastic methods. It is likely that stresses in the immed- iate vicinity of the application point of the forces are high and that strains will locally reach the domain of plastic deformations, which substantially complicates the theoretical approach. A tentative calculation using Bous- sinesq's formulae is summarized in table 6.2. The maximum shear stress, r,
Table 6.2 Allt na Lairige dam, stresses about the anchorage
Depth above anchorage
plate x = 0-5m
1-0 m 5-5 m 7-95 m
P = 1000 tonnes
&v max Gh max
(kg/cm2) (kg/cm2) 192 10-6
48 2-6 1-6 0-08 0-75 0-04
p = 4400 tonnes
°v max (kg/cm2)
840 210 7
°/i max (kg/cm2)
46-5 11-6 3-8
is less than 30% of avm&x in a direction about <f> = 25° from the vertical.
The most dangerous horizontal stress (tensile stress) occurs for <f> = 0.
The maximum vertical stress <rmax = 840 kg/cm2 for P = 4400 tons as tabulated, is lessened locally because the force P was transmitted to the concrete anchorage through six flat jacks each 870 mm in diameter bringing the stress down to
o w = 4 4 0 0 * 1Q3/(6 x 5 9 0°) = 120 kg/cm2. The flat jacks burst before the rock failed.
6.3.3 Tensile strength of rock masses
Up to now attention has been concentrated on rock crushing strength.
Dam designers are very informative about vertical and shear stresses trans- mitted from the concrete foundation to the rock foundation at the base of gravity, buttress or arch dams, but they rarely give any information on how these stresses are absorbed within the rock mass.
Some investigations going more deeply into this vital aspect have shown that shear stresses parallel to the surface of a half-space cause tensile stresses to develop inside the half-space. Zienkiewicz has calculated the tensile stresses
Creep of rock masses 123 below prestressed dams in the deeper rock mass between the dam heel and the anchorage of the cable. At the Seventh Congress on Large Dams, Rome, 1961, the problems caused by such stresses were examined and it was sug- gested that rock may not be able to stand tensile strains. In the case of rock rupture along the line of highest tensile stresses, the dam may be in danger of overturning or sliding. Zienkiewicz also suggested that a similar area of tensile stresses existed in the rock foundation near the heel of buttresses in a buttress dam. Jimense-Salas & Uriel (1964) and others examined the problem for an ordinary gravity dam and found that the zones under tensile stresses were more extensive than the areas mentioned by Zienkiewicz for anchored dams. This is not improbable, considering how the shape of the dam may influence stress distributions in the rock.
Measurements made inside Straight Creek tunnel (USA) showed that definite areas were under tensile stresses along the soffit which was being excavated in reasonably sound rock. These strained areas could have been investigated with differential rock-bolt extensometers. It is interesting to note that the areas under tension extend beyond those forecast by the theory which assumes sound homogeneous rock and the worst possible case of K = ahjav = 0 (see section 5.4). The area under tension extends even more deeply into the rock masses with increasing density of the rock jointing.
This shows the importance of tensile stresses which develop in rock masses and their obvious danger to the stability of large engineering structures.
There is no known method for the direct measurement of tensile strength of rock in situ. An indirect method is to trace the so-called intrinsic curve (using circles of Mohr) in the area near the point a = 0. Tensile strength is expected to be about the same magnitude as the rock cohesion, but there is no proof that this applies for rock masses.
The whole problem of tensile strength of rock masses will be discussed from another aspect in the sections dealing with tunnel and dam engineering.
Model tests of dam abutment carried out by Fumagalli (19666) at the ISMES Laboratory in Bergamo, show that there is a danger of rock failure by brittle fracture when the dam foundations do not penetrate deep enough into the rock. At greater depths failure occurs by shear fracture of the rock.