NEW

METHODS

AND

DEVICES

INVESTIGATION OF SHEAR STRENGTH BY TORSION TESTING L. Muzhik

METHOD The strength of the rocks in place is the main initial information in the design of mining working of important purpose as well as of other underground structures. Geological investigations often expose the weak spots in rock, for instance rupture cracks, geological breakdowns, stratification, etc. The possibility of the destruction of a scaled rock mass by a cut along one or more attenuation planes grows in this area. It is difficult to measure shear strength in sltu. The main problem here consists in selecting a representative rock specimen which would not be difficult to remove from the earth without damage. Laboratory tests of rock specimens from drill cores yield higher values of the shear strength during shear tests or triaxial tests than do analogous tests in situ. The reason is that the rock specimen prepared for testing under laboratory conditions is selected precisely with a view to the fact that it will endure the test, i.e., a more qualitative specimen is selected in advance. Nevertheless, laboratory shear tests are of importance precisely because they are less difficult. But the results obtained in them should not be utilized directly in practice. They should be an index of the relative strength in correlation with tests at the site. Direct shear testing on large-size specimens (it is now performed in the majority of cases) assumes the difficult separation of a whole block of rocks. This block lies on an attenuation plane and is subjected to both normal and shear loads until it very destruction. Such testing is quite difficult and expensive. Torsional testing is intended for the execution of complex measurements of the shear strength of rocks at the bedding site on specimens of optimal size for which the possibility of destruction is reduced maximally. In general, the shear strength along attenuation domains can be measured in such a manner.

Fig. i IGG Czechoslovak Academy of Sciences, Prague. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 3, pp. 99-106, May-June, 1988. Original article submitted May 20, 1987.

0038-5581/88/2403-0269512.50

9 1989 Plenum Publishing Corporation

269

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Testing

Method

Selection of the Measurement Site. The measurement site is selected so that the hypothesized shear plane will be at 20-40 cm from the wall of the workin S. The surface of 40 x i00 cm of the measurement site should be level and approximately parallel to the measurement plane. Drilling of the Core being Tested. The drillln S rig drifter is installed perpendicularly to the selected plane. DrillinE is performed by a double core barrel with diamond bits of 38- and i12--~ diameter (Fi E. 1). The smaller diameter hole is first drilled under the stay bolt to produce an axial load by means of a simple 38-,-, core drill. The core obtained is used to refine the location of the shear plane. The double-core barrel assures coaxial borinS of the core, where ll2-mm-diameter borin E is performed only at such a hole depth as is needed for Insertion of the barrel. The core is shaped completely only after installation of the 38-w,-diameter stay bolt in the hole and tIEhtenin E the nut to the appropriate stress. In the case of a threat of damage of the rock core by rinsing, air scrubbin S can be used. Fastening of the Stay Bolt to Form an Axial Force. The bolt is installed in a 38-mm-diameter hole. The bolt anchor is terminated by an expandable wedge. A sprin S is situated between the tishtenin S nut and the gasket. It compensates for possible changes in bolt stress durin E the tests. The gasket under the sprin S can be lubricated by a solution or gypsum to smooth

270

Fig. 4

Fig. 5 out the roughness. Such leveling by using a rapidly solidifying solution or gypsum assures perpendicularity of the plane of the fit to the stay bolt axis. The bolt is tightened to the appropriate axial stress by using the nut and a couple-stress wrench (Fig. 2). When initial stresses had been determined earlier at the measurement site by some method, a normal load is given on the shear plane as a function of the stress Up which had actually been determined in this direction. Assembly of the Torsion Cylinder. Three holes are drilled according to a template (Fig. 3) near the prepared core, wherein foundation screws are cemented for fastening the bearing (Fig. 4). The bearing is to prevent bending stresses in the coreduring its torsion test. Soft rubber inserts are installed in the ring formed by the ll2-mm-diameter barrel to hinder the flow of epoxy resin to the outside of the cylinder. The torsion cylinder is pressed to the gasket by using the bearing by means of tightening the foundation screws. Afterwards the slot between the core and the cylinder is sealed at the forward side of the core (best by impressing a rubber spiral separator), keeping the gap at its upper edge here for the insertion of the priming tube. The core is attached to the cylinder by epoxy resin. The resin is forced in the gap between the core and the cylinder from a plastic bottle, as is shown in Fig. 5. After the slot is filled completely, the gap is also covered (best by an appropri271

Fig. 6 700-

dOO~ Relativedeformation /

400" 10

/ 30

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70

,90

Fig. 7 ate mastic). During solidification of the resin, the tightness of the gasket is followed. After solidification of the resin the upper nut of the bearing foundation screws is released. The lower nuts are tightened to the point where the bearing would n o t bind the cylinder at the axis. Assembly of the Handle and the Support Pin. A 42-mm-diameter hole is drilled in conformity with the template and a support pin is cemented therein. This operation is performed during drilling and cementing of the bearing foundation bolts. The handle transmits a torque to the cylinder by means of a tetrahedron. The main arm of the handle has a slot in its end, in which ball roundoff of the pressure bolt enters. By rotating the bolt, an appropriate force is transmitted to the handle (Fig. 6). The angle of rotation is measured by the display located on the support pin. Measurement of the Torque. The torque is measured either by using two wire straingauges glued to the handle near the attachment site or by the deflection of the arm by the display. The torque is determined by the callbration curve (Fig. 7). The apparatus was calibrated on a special calibrating machine by using a KVS-75 precision dynamometer of the firm GHttinger Baldwin Messtechnik (FRG).

1.2.

Order of t h e T e s t i n S

Loading o f t h e core being t e s t e d i s accomplished by t i g h t e n i n g t h e p r e s s u r e b o l t by using t h e s p e c i a l c o u p l e - s t r e s s wrench. The a p p a r a t u s was c a l i b r a t e d f o r p r e c i s e l y t h i s couplestress wrench and pressure bolt. The torque is gradually increased by rotation of the pressure bolt by simultaneously taking down readings of the angle of rotation end the time. The testing can be executed in two modes. First, the shear stresses can be followed for a constant rate of cylinder torsion. Second, a different axial load can be given at individual loading cycles. It is also possible to proceed similarly for the plane already cut

out.

272

Fig. 8

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Fig. 9 As soon as the test is terminated, the cylinder is removed together with the cutout core) the plane of the slice is subjected to investigation, the unevenness is measured, and photographs are taken (Fig. 8). The core is removed from the cylinder by heating until the resin is melted. The hole is shown in Fig. 9 after the test has been performed. 1.3.

Estimation of the Results

In elastic rocks, in the extreme (outer) points of the core in which fracture is initlated) the stress is determined by the expression ~ .~/.~I,

where M K is the torque, r = D/2 is the core radius, and I is the moment of inertia. a plastic material is concerned, the appropriate critical stress will be ~ 0,73M~/I

(1)

When

(2)

under the assumption of constant tangential stresses over all the areas of the plane of breakdown.

273

Evaluating the shear modulus it is impossible to omit the contribution of the steel cylinder in the resistance against the torsion direction. For an annular section with wall thickness t - I/2(D - d) it has the form

,~,.--MJW,=I6MJg/(D'-d').

(3)

where Wp in (4) is the polar modulus of the section (the magnitude of the slice), cm, and d is the inner diameter of the core. The polar moment of inertia Ip and the relative torque @ - alL (~ is the angle of rotation and L is the length of the torsion) are determined by the relations ~=n/32(D'-e) v - 32SdnU

(D' -

(5)

e).

The elastic shear modulus G of the rock is the quantity desired. G - 323~dnv(~

-- e ) =

(6)

Then

(7)

Mdl, v.

The torque for both annular sections of the cylinder (rock and steel) is ~,

= v (U,&, +

(8)

G,~,),

For the steel where the subscript 1 refers to the rock and the subscript 2 to the steel. cylinder G 2 ffi 85,000 MPa. The shear modulus of the rock is determined from the formula

G, -- ~dv~,

--

G, (~dZ,~).

(9)

It is evident that in the formation of a conical shear surface (slice) shape only the rock itself is deformed at the clamped end of the cone. -On the other hand, there is a definite section of length L on the facial part on which just the steel cylinder is subjected to torsion. This means that three sections yield a contribution to the total angle of rotation, namely: Li, the steel cylinder; L 2, the steel cylinder and the rock core; L3, the rock core. Each section has its torsion angle ~i and, therefore, the total sum of these angles yields the measured angle of rotation a = a , + a, +a,.

(I0)

Since the angle =2 has identical values on section L 2 for both the steel and the rock, then

M,--M, + M,,

(ii)

MJGJ,,--M, IGj,.

(12)

and, further,

We can write for the partial angles of rotation

a,--M.L,IG,I,, ~--M,L~G,[,,, a,--M, LJGJ,,.

(13)

Substituting (13) into (i0), we obtain

sj.,jc.,,A, + S ' . L d U , & , + S.LdU,&, -- a.

(14)

We substitute G i from (12) into (14) and we calculate MK2. In conformity with (13) we calculate ~i, ~3 successively and, finally, the desired elastic shear modulus G of the rock also. 2.

EXAMPLES OF APPLICATION

2..I. Measurameut on a Concrete Block. The first tests were performed on a concrete block of i00 x 100 • I00 cm in order to verify the method. Three tests were performed on the block for different axial forces in the stay bolt. Selected as normal stress were on =

276,

O, i0, 15 MPa. Fracture by torsion occurred when T = 1.7 MPa (a n = 0), T = 3.2 (O n = I0), = 3.3 MPa (o n = MPa). The shear modulus is G = 50,000 MPa (o n = 0, G = 60,000 (o n = i0), G = 62,000 MPa (o n = 15). The tests showed the possibility also of application of this method to check out large concrete blocks when breakdown by a blasthole does not threaten the function or stability of the structure. 2.2. Anna Mine in Prshibrami. In this mine the measurement was performed in the chamber between the Prokop shaft and the drift in the direction of the main vein Voitekh. Outcrops of sufficiently open "Sudet" layers from the major part of this section. This is dark gray quartz-saturated graywacke. The initial stress state that had been found by using straingauge measurements was characterized by the quantities a I = 56.2, a 2 = 34.5, 03 = 18.6 MPa while the maximal tangential stresses were ~z = 7.9, T 2 = 10.9, and Ts = 18.8 MPa, respectively. The normal stresses on the areas of the maximal tangential stresses were On3 = 37.4, anz = 26.5, On2 m 45.3 MPa. The normal stress on the shear surface of the torsion test, o n = 37 MPa, was determined from the shear tensor mentioned. Since such a high stress could not successfully be produced by using the stay bolt, the actual axial stress was 20 MPa. Three tests were performed in all: two on graywacke and one on diabase. The first trial was directed so that the shear surface would pass perpendicularly to the stratification. The maximum stress at which fracture was achieved was Tmax = 31.3 MPa. The residual shear strength after fracture was ~p = 27.8 MPa and a n ~ 20 MPa. Under rapid loading a maximal stress T d = 45.1 MPa and a n = 20 MPa was achieved. The plastic shear modulus is G = 8319 MPa. Another trial was constructed so that the shear surface to be assumed was parallel to the layers. The maximal stress here was Tmax = 14.1 MPa. The residual strength after fracture was Tp = 3.8 MPa for a n = 18 MPa. By rapid loading ~d " 9.6 MPa, G = 6.7 MPa was achieved. The above-mentioned "Sudet" graywacke was pierced by diabase dikes in places. The first trial was conducted here so that the shear surface would be oriented perpendicularly to the direction of a dlabase dike. In this case it was a matter of fine-grained homogeneous and isotropic material. Therefore, the orientation Of the shear plane did not exert sufficient influence on the result. Fracture was arrived at in two phases. In Tz = 33.8 MPa, and final fracture in the shear plane at Tma x = 36.6 MPa. The elastic shear modulus was G = 14,700 MPa. It is seen from a comparison with the magnitudes of the initial stress tensor that the level ~max = 18.8 MPa is not achieved only by values in graywacke when the shear plane is parallel to the layers. However, the normal stress at the time of this trial was almost half that calculated by means of the initial stresses. And although the shear strength grows as a n does, an equally critical situation would evidently be formulated when the plane of maximal tangential stresses would agree with the plane of stratification of the sedimentary rocks. 2.3. Mikov Mine. A complex verification was also performed at the Mikov mine of the Slovak magnesite factories in Lubenic, entirely between two worked-out chambers. Here the total stress tensor was also determinedflrst by using the method of complete unloading: anz = 7.2 MPa, an2 = 21.6, an3 = 15.4 MPa. The dynamics of the stress level was observed during working on adjacent chambers. The rock mass here is comprised of coarse-grained magnesite, grading to dolomite in some places. The axial stress in the core was given at 15 MPa. Two trials were made, namely in undisturbed magnesite and in the plane of attenuation. A maximal shear strength of Zma x = 6.3 MPa was achieved in the undisturbed magnesite. After the time of fracture the stress was reduced insignificantly and later kept at about a 6-MPa level. Under rapid loading ~d = 12.7 MPa was reached, from which the stress was again reduced to 6 MPa after a certain time, and G " 8057 MPa. During the trial, when the shear plane agreed with the attenuation surface ~max = 3.7 MPa, while under rapid loading Td = 6.1 MPa, which was again reduced to the initial level after cessation of rotation of the handle arm. 2.4. UD Leshetice. Tests were performed in the 25th stage on adamellite. For a n = 24 MPa a shear strength of Tma x = 19.6 MPa was reached. After shearing off, the tangential stress on the breakdown plane was Tr = 7.2 MPa under constant normal 3tress.

275