Apparatus for Testing Concrete under Multiaxial Compression

This paper describes a new test facility for 12 determining material mechanical properties of struc-13 tural concrete. The novel facility subjects 100 mm 14 cubic concrete specimens to true multiaxial compres-15 sion ( (cid:1) 1 6¼ (cid:1) 2 6¼ (cid:1) 3 ) up to 400 MPa at temperatures of 16 up to 300 o C. Forces are delivered through three 17 independent loading frames equipped with servo-18 controlled hydraulic actuators creating uniform dis-19 placement boundary conditions via rigid platens. 20 Specimen deformation is calculated from displace-21 ments measured to an accuracy of 10 (cid:1) 6 m using a 22 system of six laser interferometers. The combination of 23 stiff loading frames, rigid platens, an accurate and 24 reliable strain measurement system and a fast control 25 system enables investigation of the material response 26 in the post-peak range. The in-house developed con-27 trol software allows complex multi-stage experiments


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The lack of a comprehensive database of stress and F compression and extension tests [8], carried out in a specially designed apparatus operating at higher pressures, revealed the dramatic effect of confinement on the stress-strain nonlinearity of concrete.The strains he measured at peak stress were over 57 times larger than those seen under uniaxial compression.The triaxial cell tests performed by Jamet et al. [9] showed that with the increase of confinement the post-peak behaviour of micro-concrete gradually changed from brittle to ductile.Similar change in behaviour was observed in tests on concretes with three different strengths carried out in the Colorado triaxial cell [10].These tests indicated that for higher strength concretes the transition from brittle to ductile behaviour occurred at higher levels of confinement.In 1999 Lee and Ansari [11] calibrated their constitutive model using data from tests on highstrength concrete in a cell allowing up to 83 MPa confinement and 574 MPa axial stress.In 2002 Sfer et al. [12] tested larger (150 mm diameter, 300 mm long) cylinders in a triaxial cell with a capacity of 4.5 MN axial load and 140 MPa confinement pressure.These tests confirmed the transition from brittle to ductile behaviour and suggested that with the increase of confinement the rupture mode changed from a diffuse distribution of microcracks to a mechanism involving fewer macrocracks separating the specimen into two or three blocks.This was in contrast to the earlier findings of Newman, which suggests that a particular care is needed in interpreting the effects of the boundary conditions at the specimen-platen interface.Other triaxial cells introducing improvements of the original Hoek Cell design include the facilities in Milan and Bergamo [13] and the recently developed GIGA triaxial cell in Grenoble, a rig capable of delivering up to 2500 MPa axial stress on 70 mm diameter, 140 mm long cylindrical specimen, at confinements of up to 850 MPa [14].
While providing important information on the effect of confinement, the triaxial cells are constrained to operate on the compression and extension meridians (that is, the Lode angle is either þ%=6 or À%=6).The first efforts in true multiaxial compression testing of concrete were made over thirty-five years ago by researchers at the University of New Mexico [15].
They developed an apparatus comprising three independent frames with rigid platens, using polyethylene pads and grease to reduce the platen constraint.This was achieved by a custom built system for data acquisition and control with dedicated control software specially developed to meet this requirement.
Other important design requirements were: (v) to minimise the friction on the platen-specimen interface, and (vi) to ensure that the three stresses are delivered centrally on the six faces of the specimen.

Loading and Load Measurement
The load in mac 2T is delivered by three 4 MN hydraulic actuators installed in independent, diagonally interlaced loading frames (Fig. 2).This design was chosen to minimise the snap-back potential of the loading frames without increasing the demand on the unloading speed of the servo-hydraulic control system.The high stiffness of the frames was achieved by keeping the tensile bars and the crossheads as short as possible, while allowing sufficient room for the specimen to be installed and removed.Each frame comprises two 200 mm Cachan [22].

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The load to the specimen is delivered by 200 mm 266 diameter rams, through a system of cooling, heating A nominally uniform stress field in a (homogenous) specimen can only be achieved by (i) eliminating the friction on the platen-specimen interface, (ii) ensuring that the central axes of the loading platens always cross at the centroid of the specimen and (iii) using precisely machined, right regular cubic specimens.In previous rigid-platen rigs the friction has been reduced by using either greased polyethylene pads (New Mexico [15]) or brush platens (Eindhoven [17]).Polyethylene pads cannot sustain the high temperature levels required in mac 2T and, although brush platens have been successfully applied in high-temperature testing (in the biaxial Braunschweig rig [19]), they would not be suitable for post-peak testing where large postpeak deformations may lead to bending and buckling   reaches a pre-defined level.
2. 1DC is a procedure in which one axis (' 1 ) is under displacement control with a prescribed displacement rate (R D ), whereas the other two axes are in load control, following ' 1 at preset ratios 2 and 3 .
The change of ' 1 is monitored at regular time intervals (t c ), and, assuming that the stress rate remains unchanged during two successive intervals ), the loading rates for the other two directions (k ¼ 2; 3 ) are calculated as: R k ¼ where A is the loading area.This procedure is used for experiments in which one stress (' 1 ) is close to the peak, such as triaxial compression (' 1 > ' 2 ¼ ' 3 ), or tests in which the three stresses are different (' 1 > ' 2 > ' 3 ).
3. 2DC is similar to the 1DC procedure, but with two leader axes in displacement control (with prescribed rates R D1 and R D2 ) and one in load control.The loading rate in the third axis is calculated in the same way as that in the 1DC procedure, but with the stress rate taken as an average of the stress increments measured in the two leader axes.
This procedure is used for close-to-peak testing near the extension meridian, where the stresses in two directions are similar while the stress in the third direction decreases or remains constant (' 1 % ' 2 > '3).
The two DC procedures are used for testing close to peak and in the post-peak region.They are not suitable for lower stress levels where the specimen is still relatively stiff and even low displacement rates in the leader axes can produce high loading rates in the load-controlled axes, possibly resulting in serious over/under shooting of the PID controllers and, ultimately, to loss of control.The execution of the DC sequences is controlled by setting limits to the values of (i) the loading stiffness S ¼ $ ' 1 =$ " 1 and (ii) ratio between the current stress and the maximum stress recorded during the sequence ¼ ' 1 = '1 ; calculated for the leader axis (or average of the two leader axes in 2DC) at the end of intervals with a predefined duration t c .The limit of the stress ratio is always set between 0 and 1.If S lim > 0, then the sequence is terminated when S < S lim , before the specimen starts softening (pre-peak tests).If S lim < 0, then the sequence is terminated when the stress ' 1 drops below lim '1 (post-peak tests).
Stress probing procedures are test sequences in which the specimen is loaded/unloaded by a small stress (typically $ ' P ¼ 2 À 3MPa )in each of the three directions, while the strains in the other two directions are kept constant.The results are used to determine the values of the tangent stiffness and elastic unloading stiffness matrices of the material for a given stress state (at the start of the probing procedure).
4. P3LC is a stress probing procedure in which the three stress probes are performed in load control.
When the stress in the probing direction i increases by $ ' Pi i ; the strain in this direction changes to this matrix, a measure of impending material instability can be determined [24].This measure (the determinant of the acoustic tensor) has both direction and magnitude, thus it may be represented graphically (Fig. 11) by a surface which starts out as being spherical and evolves (collapses) into a form where the radius becomes zero in the direction normal to the orientation of a newly formed discontinuity surface.Such results give a detailed picture of the material behaviour under multiaxial compression needed for construction of advanced constitutive models.

Conclusions
The new mac 2T facility was developed to overcome the lack of high quality experimental data on the behav- Manually operated, pressure controlled actuators with a load capacity of 270 kN were used to test 57 mm cubic specimens under stresses of up to 105 MPa.These findings were valuable, although comparisons with conventional triaxial results suggested that the New Mexico rig did not adequately remove platen friction.In the most comprehensive study of concrete under true 130 multiaxial compression, Scavuzzo [16] performed 67 131 tests in a fluid platen rig at the University of Colorado.132 In addition to simple triaxial compression, triaxial 133 extension and multiaxial compression with three differ-134 ent principal stresses, the cubic specimens were tested 135 under cyclic, staircase, piecewise-uniaxial and circular 136 loading paths.However, the Colorado stress-controlled 137 rig was unable to capture any possible strain softening 138 in the material.The stress range of this impressive 139 apparatus was further limited by the use of leather pads 140 inserted between the fluid cushions and the concrete 141 specimens, which led to stress concentration and de-142 velopment of diagonal cracks near the corners of the 143 specimens at relatively low stress levels.It was at the crete at Elevated Temperature (maccet !mac 2T ; pro-Multiaxial compression of 100 mm cubic speci-183 mens up to 400 MPa at any Lode angle 184 (' 1 6 ¼ ' 2 6 ¼ ' 3 ).Delivery of stresses up to 400 185 MPa was required to allow structural concretes 186 of the type used in existing nuclear power plant 187 reactor and containment vessels (typical uniaxial 188 compressive strength f c = 50 -60 MPa) to be 189 loaded to peak under high levels of hydrostatic 190 confinement (over 100 MPa).The specimen size 191 was fixed at 100 mm to ensure that a represen-192 tative volume was tested when using 20 mm 193 coarse aggregate.These constraints led to a 194 design solution incorporating three independent 195 loading frames each of 4 MN load capacity.196 (ii) Ability to test in the post-peak range.Valuable 197 information on the effective ductility and frac-198 ture energy can be obtained by monitoring the 199 post-peak response.However, once the maxi-200 mum stress is attained, there can be a sudden 201 release of energy stored in the loading frames 202 and the specimen.This can lead to an uncontrol-203 lable disintegration of the specimen, with loss of 204 load and displacement measurements.In mac 2T 205 this effect was minimised by using a combination 206 of compact, stiff loading frames (reducing the 207 elongation of the tensile bars and bending of the crossheads) and a fast, displacement-controlled servo-hydraulic system that is able to unload the actuators rapidly as the specimen fragments.A disadvantage of rigs where displacements are measured using strain gages bonded to the specimen surface (typical for triaxial cells) is that the large cracks that develop in the post-peak range can fracture the gauges, or local spalling occurs leaving the gauge intact but useless in terms of capturing the global response.This is avoided in mac 2T by using un-interruptible laser interferometers that allow an accurate, continuous displacement signal throughout the test.(iii) Multiaxial compression at temperatures up to 300 o C .The high temperature practically eliminates the fluid platen option and introduces additional requirements on the data acquisition system, such as minimising the effects of temperature variations on strain measurement.In mac 2T the loading platens are made of temperature resistant steel (Durehete 1055, 20CrMoVTiB4-10), whereas the thermal effects on the strain measurements are minimised by using a contactless, laser interferometer system.(iv) Complex multi-stage experiments following arbitrary pre-programmed loading paths with simultaneous temperature cycling.This requirement reflects the desire to generate experimental data for calibrating generalised 3D models able to simulate the response of the material to any combination of loading paths and temperature histories.

Fig. 1 .
Fig. 1. mac 2T apparatus for multiaxial compression of concrete at elevated temperature

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and loading platens.In each test, a set of six new 1 mm thick steel tiles with 0.25 mm PTFE pads are placed between the loading platens and the concrete specimen to reduce friction-induced shear stresses at the interface.The loading platens have a spherical seat arrangement to accommodate minor departures in the specimen from a right-regular cube.The 95 mm square loading surface is smaller than the surface of the specimen to prevent contact between adjacent loading platens.One of the actuators (X) has a 180 mm stroke which, when fully retracted, leaves enough space for installing and removing the specimen.The stroke of the other two actuators is 60 mm.The pressure in the system is provided by a 30 MPa hydraulic power unit, which can generate loads up to 3.61 MN (or ' ¼ 400 MPa over a 95 Â 95mm 2 area).

Fig. 5
Fig. 5 System for strain measurement and displacement control: (a) platens with installed vacuum tubes, (b) mounting of lasers and (c) schematic diagram of laser interferometer system