eRocks

The HPB consists of a steel bar (1.2m length) which has a rock sample attached to it. A second bar (6.4m length) is then used to impact the sample. An optical sensor is then used to calculate the speed of the impact bar at the moment of impact. Two strain gauges at either end of the two bars are used to record the longitudinal strain wave that propagates through the bars after impact. The force on that sample can be resolved and a force / time signal can be calculated. Integration of the force / time history to breakage can be used to calculate the total energy imputed into the system.

Although there are a number of methods of administering an impact the underlying principals are similar, namely that by varying the input energy of the impacting body and the size of the test sample it is possible to build a complex input energy to product size relationship. The results of the test allow the calculation of the t10 value, which is the percentage passing 1/10th of the initial mean size. From the t10 value it is possible to obtain the rock mechanic parameters A (theoretical limiting value of t10) and b (slope of the t10 versus specific comminution energy) which are material related.

A variety of tests exist that utilise some form of impact to quantify the strength of a given material or individual particle. Depending on the test specifics the impact is generally administered by one of three main processes, free falling, pendulum or impacting object.

The ring-loaded disc strength test method was developed for the ceramics industry as a means of testing the strength of a range of brittle ceramic materials such as alumina and zirconia. Godfrey [1987] used the test as an alternative to the traditional flexural three point bend test as it required less time and skill to produce test specimens and the need for a good edge surface finish was eliminated. In addition to these sample preparation advantages is the convenience of the test procedure itself, which consists of placing a disc (19mm in diameter and 3mm thick) in a brittle flexure test rig on a load frame and applying a steady load until the sample fractures. In the test the disc sample is supported on a ring of ball bearings accurately seated in a platten. A smaller diameter ring of ball bearings is then used to apply a load to the sample from above at a fixed rate. A theoretical relationship was derived between the stress and the geometric properties of the specimen based on the use of toroidal rings to support the test piece and apply the load. The simpler ring support system was shown to give the same results as a toroidal design and has been adapted in the current work. Using this arrangement, the load at fracture is recorded and the values are substituted into equation 1 below in order to calculate the stress:-

Where :
ï?³r = Stress in Radial Direction Mpa
W = Load Newtons
T = Thickness Metres
ï?µ = Poisson Ratio
Rl = Radius of load circle Metres
Rs = Radius of circle support Metres
Rd = Radius of disc Meters

The method was first applied to mineral systems by Kingman et al [1996] as a means of determining the effect of dielectric heat treatments on the strength of Norwegian ilmenite and showed that the strength of the mineral decreased with increasing exposure time to microwave radiation. Work by Young [1998] showed a positive correlation between data from the ring-loaded disc test and the Bond Work Index for different materials that were tested.

The test resembles a three-point bend test with a V shape or notch cut perpendicular to the axis of the specimen. The notch is positioned directly below the loading point. The test can be Level I consisting of just the yield load, and Level II which requires continuous load and displacement results. Care is taken to observe any anisotropic characteristics and hence any planes of weakness are positioned parallel or perpendicular to the loading axis. Mode I fracture toughness (KIC) can be estimated using the relationships given in Equations (1) and (2) below:-

(1)

(2)

Where :

KIC = Mode I fracture toughness. MN/M^1.5
Amin = Dimensionless factor.
Fmax = Maximum Load KN
D = Core diameter cm
a0 = Chevron tip distance from specimen (0.15D)
S = Distance between support points (0.33D)

The ASTM has standards laid down for similar tests that are conducted on concrete samples.

A test based on a similar principle is also given by the ISRM and this ‘short rod test’ comprises the same notch, but the use of smaller lengths of sample is possible. Ouchterlony and Zongqi [1983] investigated the short rod test and its accuracy of determining the KIC of rock samples. It was concluded that loading rate played no significant role in the results and that the method gives good results.

Bearman et al [1989] investigated the comminution potential or rock using the chevron bend test and worked towards a ‘comminution index’. The standards set down by the ISRM were adhered to. It was concluded that the only loading test to come close to the performance of the CB test was the UCS test.

A uniaxial compressive test is one where a disc sample is axially loaded and is unconfined in all other orientations. A cylinder-loading test can be both point and line loading of a core sample under diametric conditions.

Kotte et al [1968] compared UCS, cylinder and triaxial tests. He observed that cracks formed parallel to the loading force and concluded that these tests gave good indications for the prediction of strength of rock materials.

Broch [1972] investigated the UCS method and pointed out the extensive sample preparation required to perform this test. The relationships he used depending on point or line loading, are given below:-

Where k is a constant, P is the applied load, D is the distance between loading points and T is the maximum tensile strength. The constant k was found to be from 0.5 – 1 and was a function of sample geometry. A correction factor was used to relate core sizes to a ‘standard’ 50mm diameter core. This sample correction is annotated as Is(50) and when k=1 the following relationship can be assumed:-

Work by Chau and Wong [1996] investigated the relationship between UCS, point load and Brazilian test methods. They concluded that a constant (k) relating UCS to strength index is not to be taken as universal and therefore it is not always safe to use the following equation:

This was further confirmed by Bowden et al [1998].

Gunsallus and Kulhawy [1984] and Bearman [1999] investigated the relationship between UCS and cylinder tests to KIC as they considered the Mode I fracture toughness a good indication of rock comminution behaviour. They concluded that if the ISRM standards were adhered to then the UCS and cylinder methods were accurate in their results.

The ring test is similar in form to that of the Brazilian test, but differs by having an axial hole. This hole means that when the disc is compressed it fails in a tensile manner. The hole removes the stress concentrations at the loading surface. Hobbs [1963] suggested that a relationship between tensile and compressive strengths was present for massive laminated rocks. However, Hudson [1968] concluded that the tensile strength of the material increased as the diameter of the hole decreased. This suggests that results achieved are a factor of the experiment and not a property of the material.

The Brazilian test is one that compresses a sample diametrically inducing a stress that causes the sample to yield in tension. The standard procedure can be found in the ISRM [Brown (Ed), 1981] and a similar method is recommended by the ASTM. The relationship between applied forces and yield loads is given by:-

Where P is the yield load in Newtons, D is the disc diameter in mm and t is the thickness of the disc in mm.

Authors have investigated the method both practically and theoretically and have found the two to be comparable. The method of breakage is well documented and has had the term ‘hourglass’ associated with it. Figure 3.3.2.2 shows the typical fracture patterns that are observed in samples.

Figure 3.3.2.2 Typical Brazilian Test Fracture Pattern

Clark [1993] found that the crack initiates in the centre of the specimen and that stress concentrations built up around the loading platens effectively hindering crack propagation in that area.

Fairhurst [1964] and Wijk [1978] looked at the validity of the method from a theoretical perspective and favoured this method to that of the point-load test.

Gunsallus and Kulhawy [1984] conducted an extensive study into the test and compared it to other methods including the UCS, the point load test and KIC. It was concluded that the Brazilian method was more variable in its results than that of the KIC test, was similar in variation to the UCS, but had less variation than the point-load test.

Berry et al [1984] also compared the Brazilian to the UCS method for a range of materials to investigate the effect of rock morphology on comminution behaviour. They found the Brazilian test to give higher positive correlation values (r = 0.93) than that of the point load test

Numerous authors have investigated the loading of irregular lump samples to measure their strengths. The method involves testing a sample between two loading implements, which can be in the form of points or flat surfaces. The sample is then subjected to an increasing load until breakage occurs.

Work conducted by Hiramatsu and Oka [1966] compared the point loading of spherical specimens to irregular lump samples using a range of materials. They concluded that the tensile strength could be approximated to 0.9 times the critical load and can be represented by the following equation:-

Where F0 is the critical load and 2a is the distance between the loading surfaces.

Broch [1972] gives a detailed review of the work previously carried out and compared the point load test to that of the uniaxial compression test (UCS). He concluded that the point test could be considered a suitable replacement to the UCS method. Other benefits to the point load of irregular lump samples was the need for little sample preparation and the possible portability of the method due to the reduced forces required to induce failure.

Bieniawski [1974] compared the results of irregular lump loading to that of axially and diametral loading of core samples and concluded that the axial type test was the most suitable and that to avoid confusion this type of test be used in preference to other tests.

A rock sample is pulled axially until it yields. This is performed in a similar way to that of well established metallurgical tests. The main problem encountered is the method used for gripping the sample. Ramana and Sarma [1987] proposed a method of using split-collar grips as a means of applying the force to the sample. The grips themselves require a lining of cork to reduce stress build-up, which needs to be renewed every thirty tests. It was concluded that this method was comparable to the indirect Brazilian test.

The International Standard of Rock Mechanics [Brown (Ed) 1981] discusses problems associated with bending and subsequent stress concentrations which can affect results. These factors have to be considered. One problem related to this type of test is the need for sample lengths, which are long enough to be gripped adequately.