Pillar Design With Failure Mechanism And Strength Characteristics Of St. Peter Sandstone

The St. Peter sandstone has a very unique mechanical property: an unusually high friction angle(average 60°), and extremely low or zero cohesion. At present, there is no pillar design methods and thoery which is available for this kind of rock. In order to achieve the balance of maximum economic benifit and safety mining, focus on the unique mechanic properties, this paper studies the strength characteristics and failure mode with uniaxial compressive test and triaxial compressive test, studies the failure criteria for St. Peter sandstone, and learns the stress distribution in the pillar, gives the reasonable pillar size. New understandings and conclusions in this research are as follows:1) Strength characteristics and failure mode under uniaxial compressive testThe objective of this study is to establish a scientific understanding of the uniaxial compressive strength associated with the St. Peter sandstone for reliably determining and using this data.During the course of this investigation a total of 85 uncemented specimens were prepared and tested for the uniaxial compressive strength for the St. Peter sandstone, the largest research effort dedicated to this special topic. A comprehensive and in-depth study was carried out on the test, including, sampling techniques, failure mode, size effect of specimens, shape effect, influence of sand particle structures, elastic properties.A particular problem encountered in the St. Peter sandstone research is the incompatibility of the material property of the St. Peter sandstone and the standard sample preparing practice can easily disintegrate the specimen being processed. Because of this, the first principle for preparing St. Peter sandstone specimens is to minimize the disturbance caused by the sampling techniques. The suggestions were made on the measures to minimize the disturbance based on our extensive experience.This paper revealed the mechanics of two dominated failure formation, vertical splitting and steeply dipped shearing, and linked these mechanics to the basic mechanical properties of the St. Peter sandstone: Vertical splitting is caused by cohessionless property of the St. Peter sandstone and steeply dipped shearing is the result of high friction angle of the St. Peter sandstone. The irregularity of failure locations observed from the sandstone specimens reflects the sensitivity of the failure process to local anomalies, which is also a result of the cohesionless property of the St. Peter sandstone. The sensitivity to local anomalies as manifested by vertical splitting and irregularity of failure locations is one of main reasons that responsible for the large variance of the uniaxial compressive strength associated with the St. Peter sandstone.The size effect of specimens for the St. Peter sandstone is very different from the one that is typically exhibited for most geological materials. The size effect for the St. Peter sandstone is the result two factors: scaling and disturbance by sampling techniques. The factor of disturbance is unique for the St. Peter sandstone and its impact can significantly overweight that of scaling, especially for small specimens. This is why the strength of small St. Peter sandstone specimens is significantly lower than the strength for other specimen sizes. The optimum size of 50 mm determined in this investigation is based on several factors. In addition to the theoretical considerations, scaling and disturbance, as illustrated by the laboratory results, the other two factors are the field investigation and practical considerations. We have conducted a field investigation to back calculate the uniaxial compressive strength for existing pillars. It appears that the strength of 50 mm specimens matches well with the result from this field investigation. Practical considerations are also an important factor for determining the optimum size. Based on the extensive sampling experiences of this paper, 50 mm specimens are the size that can be economically attainableThe shape effect for St. Peter sandstone specimens has not been discussed in any previous researches. A practical implication is that the height/width ratio should not be too low, at least not less than 1.2) Strength characteristics and failure mode under triaxial compressive testThe study carried out by this investigation on the triaxial test for St. Peter sandstone is pioneering in several fronts and has revealed many important information for understand the basic mechanical and strength properties of St. Peter sandstone.Stress-axial strain curves for St. Peter sandstone under triaxial test is studied. The axial stress-axial strain curves obtained from triaxial tests are the record of the failure process, the basic information that allows one to analyze rock properties perspectively. In this regard, this study fills an important gap for St. Peter sandstone study. The axial stress-axial strain curves obtained from this study clearly shows the effect of confining pressure: the rapid increase of the axial stress at failure with the increase of confining pressure. It also clearly shows the change of the material behavior from brittle to ductal because of the increase of confining pressures. The most interesting feature of the axial stress-strain curves obtained from this study is the remarkable similarity for the same group specimens, which is an illustration that these specimens experience a very similar failure process. The similarity is also a strong indication of the stability of the test result. The following example is a further demonstration of the stability associated with triaxial test. For 1S group, two specimens, 1S-4 and 1S-5, were tested under the same confining pressure of 6.88 MPa and the axial stresses at failure obtained for these two specimens are 41.5 and 42.1 MPa, respectively. The difference is only 0.6 MPa, 1.4% of their average strength. From the similarity of their stress-strain curves, it is known that this small difference is by no means an accidental match.Another important contribution by this research is revealing and analysing the failure formation of specimens after failure, which is the first effort for St. Peter sandstone. The failure formation of triaxial test is the result of the failure process recorded under the axial stress-axial strain. After tests, physical samples are preserved for further exploring the failure process. The failure pattern for the triaxial compression test is very different from that exhibited for the uniaxial compression test. For the uniaxial compression test, there are two dominated failure formations, vertical splitting and steeply dipped shearing. However, the pattern of failure is totally random, which is largely controlled by local anomalies. Failures can occur either locally or crossing specimens with unpredicTab. Combinations of two failure formations. The failure pattern for the triaxial is almost identical: a pyramid shape corn is formed at the each end of the specimen. This uniform appearance indicates that the failure process under the triaxial test condition is no longer heavily affected by local anomalies. Rather, it is primarily governed by its inherent mechanical properties. In this regard, the strength assessed from the triaxial test is a much more reliable indication of the strength of St. Peter sandstone than the strength obtained from the uniaxial compression test. A very important feature of the failure pattern observed from the triaxial test is the steep failure angles in the range of 70?-80? degrees, which is a further confirmation of the extremely high friction angles associated with St. Peter sandstone.One of the most important contributions of this investigation is the demonstration that the strength of St. Peter sandstone is primarily governed by its particle structure. This is done by comparing the mechanical response of specimens from two sample groups, 6AR and 1S. The porosities for these two sample groups are 24.5% and 30.5%, which define the porosity range for St. Peter sandstone. The study shows that the strength for 6AR group, the group with the low porosity, is much higher than that for 1S group, the group with the high porosity. At the confining pressure of 6.87 MPa, the strength for 6AR group is 89 MPa which is more than twice of the strength for 1S group, which is 42 MPa, at this confining pressure. The friction angle is also much higher for 6AR group, which ranges from 68? to 73? with an average of 71? while it ranges from 56? to 69? with an average of 63? for 1S group. Because of the critical influence of the particle structure on the strength of St. Peter sandstone, it is important to identify the specimen structure before the test so that the strength data can be analyzed perspectively.In order to measure the effect of confining pressures on the stress at failure for different materials, an index of rate increase of the axial stress at failure, RAS, was defined. RAS provides a quantitative measurement of the increase of the axial stress at failure for each confining pressure unit. A study of RAS for both St. Peter sandstone and conventional geological materials shows that the RAS for St. Peter sandstone is much higher than that for conventional geological materials. This study provides a theoretical base for rock reinforcement and pillar design under St. Peter sandstone condition.3) Failure Criteria of St. Peter SandstoneBased on experimental data of uniaxial and triaxial compressive tests, Mohr-Coulomb strength criterion, Griffith strength criterion and Hoek-Brown empirical strength criterion were further researched under different stress conditions.The Uniaxial compressive strength of St. Peter sandstone samples with equivalent width of 51 mm was measured to be 4.27 MPa. Uniaxial tensile strength of samples were 0.53-0.61 MPa when Griffith strength criterion was applied. Taking fracture closure into consideration the uniaxial tensile strength was tested to be 0.61 MPa.The internal friction angle of St. Peter sandstone samples was determined to be 63? conservatively. Then the formula of Diagonal-lined Mohr-Coulomb strength criterion could be showed as follows:Diagonal-lined Mohr-Coulomb strength criterion could also be showed with principle stress 1s and 3s as follows:With advancement of rock pressure, the strength grown rate of St. Peter sandstone decreased sharply, it showed that its strength was unreasonable exaggerated under highly rock pressure when Mohr-Coulomb strength criterion was applied.The derivations of equations about Two-parameter parabolic Mohr-Coulomb strength criterion were made in this paper. Simply Tensile and compression tests were here to analyse the connection and failure mode between main principle stress and third principal stress, and Two-parameter parabolic Mohr-Coulomb strength criterion could been shown below:This paper analysed Narrowed Hoek-Brown empirical strength criterion and generalized Hoek-Brown empirical strength criterion diacritically with consideration of tested data. Results show that the correlation coefficients were 0.995 and 0.927 separately fot m and s. However, their correlation coefficient was 0.316 when use results together, which means the average m and s could not reflect the strength characteristics of the St. Peter sandstone.4) Pillar design with stress distributionDuring the failure of St. Peter sandstone, the failure mode changes from brittle fracture to ductile fracture. The principle stresses in this progress are not linear. So, the failure criteria of St. Peter sandstone should be considered as parabolic Mohr-Coulomb criteria or Hoek-Brown empirical criteria. As the average m and s in Hoek-Brown empirical criteria could not reflect the strength characteristics of the St. Peter sandstone, parabolic Mohr-Coulomb criteria is applied.Two-parameter parabolic Mohr-Coulomb strength criterion could be shown below:Analysized the equilibrium condition of yield zone, got the width of yield zone and the stress distribution in the yield zone, which are as follows:Based on the parameters of Pattison mine, calculated the pillar load with Tributary Area Theory, designed the pillar size with safety factor of 3, the size of pillars in Pattison mine is 16 m.According to the design, the designed pillar size for Pattison mine is 16 m. Combined with this pillar size, anchor net and shotcrete were used to reinforce the rib of pillar, achieved the purpose of control of small scale roof caving and pillar spalling. At the same time, explained to the Mine Safety and Health Administration(MSHA) of the United States that to solve ground control problems such as roof caving and pillar spalling, not only by increasing the pillar size, for some materials with special properties, such as St. Peter sandstone in this research, the support often much more effective than increasing the pillar size.