A Machine for Static and Dynamic Triaxial Testing

A versat i le mach ine has been deve loped to test geo log ica l spec imens

large enough (0.3-m d iameter ) to a l low mode l ing of jo int sys tems and of

tunnels wi th ins t rumented tunne l - re in forcement mode ls

by P.E. Senseny, H.E. Lindberg and T.C. Kennedy

ABSTRACT--A machine has been developed for studying the static and dynamic triaxial constitutive behavior of large specimens of geologic and construction materials. Test speci- mens can also contain a cylindrical tunnel cavity to permit study of tunnel-reinforcement structures and rock-structure interaction. The specimens are 0.3 m in diameter and 0.3 to 0.45 m high; the model tunnels can be up to 50 mm in dia- meter. Static and dynamic triaxial loads can be applied with maximum pressures of 200 MPa in static tests and 100 MPa in dynamic tests. Dynamic loading can also be superimposed on a static preload as large as 20 MPa. To facilitate study of tunnel reinforcement, the tunnel is maintained at ambient pressure, with access at both ends for instrumentation and photography. Example results show the influence on tunnel deformation of loading rate as well as the presence of joints and their orientation. For a given allowable tunnel closure, substantially greater pressures can be sustained under dynamic loading than under static loading, and substantially greater pressures can be sustained by an intact specimen than by a jointed specimen.

Introduction

Several laboratory investigations have been performed to study the influence of rock strength and the presence of joints and bedding planes on the deformation of model deep-buried structures. ,-4 These studies were restricted to static loading and small deformations of the model structure because of limitations on testing-machine capability. For a more complete understanding of the influence of the surrounding rock on the deformation of deep-buried structures, dynamic loading and large structure deformations must be studied. This requires development

P.E. Senseny and [I.E. Lindberg are Research Engineer and Staff Scientist, respectively, Poulter Laboratory, SRI International, Menlo Park, CA 94025. T.C. Kennedy is Assistant Professor, Department of Mechanical Engineering, Oregon State University, Corvallis, OR 97331. Original manuscript submitted: June 7, "1978. Revised version received: November 2, 1978.

of a testing machine having greater load capability, as well as a dynamic-loading mode.

The triaxial-testing machine shown in Fig. 1 was designed and fabricated to test 0.3-m-diam cylindrical specimens that contain scale-model tunnels and tunnel- reinforcing structures up to 50 mm in diameter.' Standard cylindrical triaxial specimens can also be tested. The machine can impose a general triaxial loading on a speci- men either statically or dynamically (the difference in loading rates is more than five orders of magnitude). It can also superimpose a dynamic loading on a static pre- load. Vertical pressures can be applied up to 200 MPa statically and up to 100 MPa dynamically. Lateral con- fining pressures up to 150 MPa can be applied either statically or dynamically, and static preload pressures can be as large as 20 MPa. Figure 2 shows schematically several standard load paths that can be applied statically or dynamically. These load paths include isotropic compression, uniaxial compression, uniaxial strain, and triaxial load paths for determining the influence of pressure on the strength geological materials.

The testing machine consists of a series of stacked rings and plates held together by 12 studs spanning the height of the machine. Use of a number of rings and plates, rather than a single chamber, gives the machine maximum versatility; addition or removal of a few parts can trans- form the machine into several static and dynamic con- figurations within the same basic frame. The interfaces between the plates and rings are sealed with face-seal O- rings. Hydraulic nuts at the bottom of each stud apply tensions of 1.25 MN so that the total force holding the machine together is 15 MN. This force reacts the force generated by the vertical and lateral loading pressures. Static loading pressures are supplied by hydraulic pumps outside the machine; dynamic pressures are supplied by explosive gas sources within the machine.

This large testing machine is patterned after a smaller prototype 6,7 used to test 0.1-m-diam rock specimens geo- metrically similar to the 0.3-m-diam specimens. The small

Experimental Mechanics 9 63

PraneethaHighlight

Fig. 3--Cross section of the testing machine in the dynamic triaxial configuration

Fig. 1--Large-scale testing machine located at the SRI Corral Hollow Experimental Site, Tracy, CA

machine was developed to test scale-model tunnels and simple tunnel-reinforcing structures in the laboratory.

ISOTROFIC Pv~ / UNIAXIAL

i ~ / . STRAIN

~ ~l/" ,/../'" TRIAXIAL

.o~ UNIAXIAL STRESS

Pv

Fig. 2--Schematic showing several standard load paths

However, realistic modeling in more complex scale-model tests required larger specimens. Testing at the larger, 0.3- m-diam size allows more detailed modeling of joints in the rock specimen and reduces the effects of grain size com- pared with joint spacing and tunnel diameter. The tunnel- reinforcing structures can be modeled in more detail, with more comprehensive instrumentation for tunnel closure and reinforcing-structure strain and deformation.

The remainder of this paper discusses the operation of the machine in its dynamic and static configurations and then concludes with test results that show how tunnel deformation is influenced by loading rate as well as by the presence of joints and their orientation.

Dynamic Testing For dynamic testing, the machine can be stacked in

either of two ways. In the dynamic triaxial configuration, the lateral and vertical pressures are applied separately. A cross section of the testing machine in this configuration is shown in Fig. 3. Two explosive charge chambers provide the loading pressures, a vertical loading chamber at the top of the machine and a lateral loading chamber at the bottom. The specimen is located approximately midway between the two charge chambers. The explosive gases from the top charge chamber load the top of the specimen directly to provide the vertical loading. The reaction load under the specimen is supported by a plate with a thin oil chamber above it that allows monitoring of the reaction pressure. The explosive gases from the bottom charge chamber pressurize a second oil chamber that surrounds the specimen to provide lateral loading. The interface between the explosive gas and the oil chamber is a Bello- fram located under the vertical reaction plate.

64 9 February 1979

Fig. 4 - -Cross sect ion of the test ing machine in the dynamic isotropic conf igurat ion

~_ 60

40 ~ 3o ~ 20

~ o

-5 5 10 15 2 25 30 T IME - - ms

(a) P1-GAS PRESSURE ABOVE SPECIMEN

5 0 ~ -

I 301 - 2 o ~

-5

(d)

0 5 10 15 20 25 30 T IME - - ms

P3-OIL PRESSURE IN LATERAL CHAMBER (UPPER)

70

60

5O

I 40 w 30 oc

20 Q3 w 10

-5 0 5 10 15 20 25 30 T IME - - ms

(b) P2-GAS PRESSURE ABOVE SPECIMEN

60~ 50~

I 4o~ ~ ~c 301

20F 10F

~- 0

-5 0 5 10 15 20 25 30 T IME - - ms

(e) P4-OIL PRESSURE IN LATERAL CHAMBER (CENTER)

7O 6O 5O

q 40 ~: 3O

2O 10 I 0!

5 0 5 10 15 20 25 30 5 T IME - - ms

(c) P6-OIL PRESSURE BELOW (f) SPECIMEN

7O

60

50

L 40 ~: 30

20 10 o

0 5 10 15 20 25 30 T IME - - ms

PS-OIL PRESSURE IN LATERAL CHAMBER (LOWER)

Fig. 5 - -P ressure data from a uniaxial strain test

The pressure in the oil surrounding the specimen is measured at three axial locations by pressure gages at stations 3, 4 and 5. The pressure in the gas above the specimen is measured at two opposing locations by pressure gages at stations 1 and 2. The reaction pressure in the oil under the specimen is measured by the gage at station 6. In dynamic testing, it is crucial to measure the vertical reaction pressure under the specimen to ensure that small misalignments have not introduced impact and oscillations.

The second dynamic configuration, for isotropic loading, is shown in Fig. 4. In this configuration, only the charge chamber at the top of the machine is used and the speci- men is completely surrounded by oil. Again, the oil is pressurized by explosive gases acting across the Bellofram, but with the Bellofram now located above the specimen.

Figure 5 shows typical pressure pulses from a uniaxial- strain-loading test. Records of the vertical pressure in the gas above the specimen (stations 1 and 2) and in the oil under the specimen (station 6) are shown in Fig. 5(a), (b) and (c). With the exception of a small blip at the beginning of the pressure pulse in the oil under the specimen, the two vertical pressure records are identical. This indicates that the loading on the specimen is uniform, i.e., there is no evidence of wave-propagation effects along the axis of the specimen caused by specimen misalignment or a pressure-risetime too short compared with the wave-transit time down the specimen. Figures 5(d), (e) and (f) show the records of the pressure pulse in the lateral chamber at

stations 3, 4 and 5. These pressure records are also identical, indicating that the lateral pressure loading is uniform, with no wave propagation effects in the oil surrounding the specimen.

The risetime of the pressure pulses (about 13 ms for the pulses shown in Fig. 5) is controlled by adjusting the open area of the holes through the orifice and baffle plates. Opening the holes reduces the risetime and closing the holes increases it. Minimum risetime is approximately 0.3 ms, but it is usually increased to reduce axial-stress waves and, hence, produce uniform equilibrium loading through- out the length of the specimen. The pressure pulse decay is controlled by increasing or decreasing the area of the holes in the vent rings that allow the explosive gases to escape from the charge chambers. Increasing the area of the holes shortens the decay time and reducing the area lengthens it. The magnitude of the pressure pulse is con- trolled mainly by the size of the explosive charge. Peak pressure increases linearly with the mass of explosive. A 2-kg charge gives a peak pressure of about 70 MPa.

The explosive used is a low-density mixture of PETN and microspheres in the ratio 9 : 1 by weight. Microspheres are tiny inert plastic spheres that slow the detonation rate in the PETN and therefore reduce the detonation pressure from over 20 GPa to about 0.7 GPa. The PETN/micro- sphere mixture is loaded into cylindrical paper canisters whose aspect ratio is roughly unity. Both the vertical and lateral charges have 0.91-m-long Primacord leads connected

Experimental Mechanics 9 65

to a common detonator that ensures simultaneous detonation.

For a test in which the loading on the specimen is specified solely in terms of known tractions, the proper load path can be followed by suitably adjusting the rise- time, peak pressure and decay time of both the vertical and lateral pressure pulses. Such tests include isotropic compression, uniaxial compression, and triaxial com- pression. However, for a test in which the load path is determined by specimen response, such as a uniaxial- strain-loading test, it is necessary to guess the proper load path and the appropriate pressure-pulse characteristics.* A good first guess is the corresponding load path from a similar static test in which the kinematic constraint, e.g., uniaxial strain, is satisfied exactly. (How this is done is described in the next section.) The pressure pulses are then adjusted to produce the static-load path. The speci- men response, e.g., lateral strain, is measured during the test so that a second guess can be obtained and the procedure is repeated. Usually, the second guess gives an adequate approximation to the desired load path.

The maximum vertical pressure that can be applied in a dynamic test is about 100 MPa. This value is based on an estimated low-cycle fatigue limit for the 12 studs that hold the testing machine together, using measured dynamic strains and assuming a desired machine life of about 500 tests. The 150-MPa upper bound on the lateral confining pressure is calculated to be the pressure needed to overcome the 15-MN force provided by the studs that hold the machine together. The measured transient strains in the studs during several tests indicate that the size of the lateral confining pressure explosive charge does not significantly affect the fatigue life of the machine.

Static Testing

Figure 6 shows the testing machine in its static con- figuration. Only one additional plate is needed to convert to this configuration from the dynamic triaxial con- figuration. The new plate is located immediately above the specimen and contains the vertical loading port.

Loading on the specimen in the static configuration is provided by two hydraulic pumps outside the testing machine. One pump supplies the vertical pressure and the other supplies the lateral confining pressure. For iso- tropic compression, either or both of the pumps can be used to provide a single pressure source analogous to the single explosive charge in the dynamic isotropic con- figuration. The pumps have a maximum pressure capability of 210 MPa. Typically, loading takes about 20 rain (more than five orders of magnitude slower than in the dynamic tests), although the loading time could be reduced to about 5 min if the pumps were permitted to operate at their rated capability.

For tests in which loading on the specimen is specified solely in terms of known tractions, the hydraulic pumps are controlled manually to produce the desired load path. However, for a test in which the load path is determined by specimen response, the loading pressures are controlled automatically by a microprocessor. The uniaxial-strain- loading test is used as a specific example to present the details of automatic load control.

For a uniaxial-strain-loading test, the desired constraint is no radial motion of the lateral surface (equivalent to zero circumferential strain). The outputs of two circum- ferential strain gages on the specimen are fed into the microprocessor in digital form at 0.3-s intervals. The microprocessor averages these two strain values and compares the average with specified deviations from zero, typically + 10 -5. If, for example, the lower limit, -10 -5, is exceeded, then the pump that supplies the lateral confining pressure is stopped until the specimen expands enough under the increasing vertical pressure that the average lateral strain is between _+ 10 -s. The microprocessor then allows the lateral pump to operate again.

The limits on pressure capability in the static mode are based on the pressures that overcome the 15-MN force holding the machine stack together. The calculated vertical and lateral confining pressure limits are 200 MPa and 150 MPa, respectively.

Example Test Results

Tests were performed to study the influence on tunnel deformation of loading rate, as well as of the presence of joints and their orientation. The loading in .these tests was uniaxial-strain loading, which is imposed in the field by a plane P-wave.

To study the influence of loading rate, we performed tests in which the loading rates were 6 10 -5 MPa s-' and 5 103 MPa s-', a difference of five orders of magnitude. The specimens were made from a rock simulant, SRI

* Achieving uniaxiaLstrain loading by passive constraint in a close-fitting steel container was rejected because it would introduce wall friction and because, in many rocks of interest, the rock modulus is comparable to that o f steel, so the lateral constraint would be incomplete.

Fig. 6--Cross section of the testing machine in the static triaxial configuration

66 9 February 1979

RMG 2C2, representative of tuff found at the Nevade Test Site and characterized by the following parameters :8.9

Young's Modulus, E = 7.9 GPa Poisson's ratio, u = 0.23 Compressive strength, ~, = 25.4 MPa Friction angle, q~ = 0.04 tad

The specimens contained 50-mm-diam tunnels reinforced with simple 6061-T0 aluminum tubes having a mean- radius-to-wall-thickness ratio of 11.5.

In sequence, the static-loading capability was developed after the dynamic capability. Hence, instrumentation of

m T ~ I i

Static

9 Dynamic

I m s Ld

q

z z

~"~ SPRING LINES J J 9

_ _ _ _ I [ _ _~_ [ . _ _ . J~ _ _ 10 20 30 40 50 60

VERTICAL PRESSURE PV " - M9~

Fig. 7--l-unnel closure vs. vertical pressure for static and dynamic uniaxial-strain loading of saturated SRI RMG 2C2

tunnel closure and reinforcing-structure deformation is more sophisticated in the static test than in the dynamic test. Figure 7 shows both crown-invert (vertical) and springline (lateral) tunnel closures as functions of vertical pressure. The static data, plotted with the solid lines, show that the crown-invert dimension closes with in- creasing vertical pressure at an increasing rate; the curve becomes steeper as the vertical pressure increases. The springline dimension, on the other hand, opens with increasing vertical pressure (plotted as negative closure) but at a decreasing rate and levels off at about 35 MPa. Tests on similar specimens in the smaller testing machine ~ show that, as the pressure increases above 35 MPa, the springline motion eventually results in positive closure. Dynamic-test results, shown as solid circles, are simply posttest tunnel closures as a function of peak vertical pressure. (Results obtained previously with the small specimens loaded statically" show that posttest tunnel closures are virtually the same as the maximum closure measured at peak load; springback is less than AD/D = 0.2 percent.)

Results in Fig. 7 show that, for a given vertical tunnel closure, substantially higher pressure can be sustained in a dynamic test than in a static test. More extensive tests on both dry and fully saturated 0.1-m-diam SRI RMG 2C2 specimens show that the increased vertical pressure required in dynamic tests is due to both the greater strain rate in the rock skeleton and the greater induced pore- water pressure."

To study the influence on tunnel deformation of the presence of joints and their orientation, we performed static-loading tests (/iv --- 6 x 10 -2 MPa s ~) on an intact and two jointed specimens of a hard-rock simulant whose intact constitutive parameters are :9

Young's modulus, E = 21.2 GPa

Fig. 8- -Posttest cross section of jointed rock and deformed tunnel after static uniaxial-strain loading to Pv = 80 MPa

Experimental Mechanics 9 67

6

5

4

O :~ 2

,z o

-I

-2 I -3

0

I [ I r I

- / ~ -- cROWN-

8 = rr/4

- o=~ \

_ INTACT

__ e = /r/4 ~ .~SPRINGLIN[

k ~ J I J I

20 4O 6O 8O 100 VERTICAL PRESSURE, PV - - MPa

Fig. 9--Tunnel closure vs. vertical pressure for static uniaxial-strain loading of jointed and intact hard-rock simulant

I 120

Poisson's ratio, ~ = 0.23 Compressive strength, a, = 25.8 MPa Friction angle, 4) = 0.51 rad

The tunnel-diameter-to-joint-spacing ratio was six; so, the joint spacing was small compared to the 50-mm-diam tunnel, but large compared to grain size. In one jointed specimen, the joint normal was vertical (in the direction of loading, 0 = 0) and in the other specimen the joint normal was ~r/4 rad from the loading direction (0 = 7r/4). Figure 8 shows the posttest cross section of the 0 = ~r/4 specimen. No block motion occurred in either jointed specimen; so, tunnel deformation is the result of plastic deformation and fracture of the intact material between the joints plus localized slipping along the joints.

In both jointed and intact specimens, the circular tunnel ovals with the minor axis at the crown-invert diameter (in the loading direction). Figure 9 plots tunnel closure at the crown-invert and springline diameters as a function of vertical pressure. Crown-invert closure increases with increasing vertical pressure in all three specimens.

The presence of joints reduces the load a specimen can sustain at a specific crown-invert closure, and joint orientation strongly influences the reduction in load capacity. Load capacity decreases as the angle 0 between the joint normal and the loading direction increases. For example, at a crown-invert closure of 5 percent, the load carried by the intact specimen is about 100 MPa. The load carried by the jointed specimen for which 0 = 0 is 90 MPa, a reduction of ten percent. However the load carried by the 0 = 7r/4 specimen is reduced by 45 percent, to 55 MPa.

Joints also influence springline closure. In the intact specimen, the springline diameter first increased (negative closure), then it started to decrease and the closure actually became positive. This trend is the same as that found in the intact SRI RMG 2C2 specimens. Springline closure in the 0 = 0 specimen is always positive, but small, roughly 0.25 percent until late in the test when it approaches

0.5 percent. In the 0 = r /4 specimen, however, the springline motion is large. Closure decreases at an increasing rate as the vertical pressure increases, and at the end of the test the springline diameter increased 2.75 percent while the crown-invert diameter decreased nearly 6 percent.

These test results show that loading rate and joints are important parameters in the design of deep-buried structures.

Conc lus ions

A large triaxial machine for static and dynamic testing has been designed, constructed and developed into a working laboratory tool. The machine tests specimens 0.3 m in diameter and can be used to study rock-cavity re- inforcement as well as rock constitutive behavior. The machine has been used to study rock-cavity reinforcement in intact and jointed rock. Results of dynamic and static uniaxial-strain-loading tests on specimens of tuff simulant that contain reinforced 50-mm-diam tunnels show that, at a specified crown-invert tunnel closure, a substantially greater pressure can be sustained in dynamic tests than in static tests. Results from previous tests on similar 0.1- m-diam specimens indicate that both greater strain rate in the rock skeleton and greater induced porewater pressure contribute to greater specimen strength in dynamic tests. Results of tests on jointed and intact specimens show that joints can significantly weaken a reinforced rock cavity.

Acknowledgments Machine design, fabrication, and development was

sponsored by the Defense Nuclear Agency under Contract DNA0001-75-C-0245. The authors are indebted to Eugene Sevin, Kent Goering, and LTC Danny N. Burgess of DNA for their technical support and encouragement. At SRI, George R0 Abrahamson, Carl Blahnik, John Busma, George Cartwright, William Wilkinson, Dex Witherly and James Zaccor made essential contributions to the machine design and development, which are gratefully acknowledged.

References 1. Daniel, 1.M., Rowlands, R.E. and Singh, M.M., "'Experimental

Investigation of Small-Scale Lined and Unlined Cylindrical Cavities in Rock," AFWL-TR-70-55, Illinois Institute of Technology Research Institute, Chicago, 1L (Nov. 1970).

2. Hendron, A.J. and Engeling, P., "'Model Tests of Lined Tunnels in a Jointed Rock Mass," M-41, Construction Engineering Research Laboratory, Champagne, IL (May 1973).

4. Hendron, A.J., Engeling, P. and Aiyer, A.K., "Tests on Lined Openings in Jointed and Intact Rock, "' DACA 39-67-0009, Department of Civil Engineering, University of Illinois, Urbana, 1L (Jun. 1972).

4. Heuer, R.E. and Hendron, A.J., "'Tests on Unlined Openings in lntact Rock," DACA 39-67-C-0009, Department o f Civil Engineering, University of lllinois, Urbana, IL (Feb. 1971),

5. Senseny, P.E. and Lindberg, H.E., "'Theoretical and Laboratory Study of Deep-Based Structures, Volume 1." Triaxial Machine for Static and Dynamic Testing of 12-inch-Diameter Rocks, '" DNA 4425F-1, SRI International Final Report, Project 4121, Menlo Park, CA (Jul. 1977).

6. Kennedy, T.C, and Lindberg, H.E., "Laboratory Investigation of Rock Cavity Reinforcement, '" DNA 4023F, SRI International Final Report, Project 3743, Menlo Park, CA (Apr. 1976).

7. Kennedy, T.C. and Lindberg, H.E., "'Model Tests for Plastic Response of Lined Tunnels, "" J. of the Eng. Mech. Div., ASCE, 104, 339-420 (Apr. 1978).

8. Senseny, P.E. and Lindberg, H.E,, "'Theoretical and Laboratory Study of Deep-Based Structures, Volume H: Model Tests and Analysis of Mighty Epic Structures, "' DNA 4425F-2, SR1 International Final Report, Project 4121, Menlo Park, CA (Dec. 1977).

9. Senseny, P.E. and Lindberg, H.E,, "Laboratory Study of Deep- Based Structures in Support of Diablo Hawk, "" DNA O000Z, SR1 Inter- national lnterim Report, Project 5762, Menlo Park, CA (Feb. 1978).

68 9 February 1979