Pillar strength equation

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Pillar strength equation

Sign up Log in Extending empirical evidence through numerical modelling in rock engineering design 3. The failed pillars were typically surrounded by pillars that appeared to be stable, showing minimal signs of disturbance. The observations led to the conclusion that the failed pillars represent the low end of the distribution of possible pillar strengths, and not the average pillar strength.

Pillar strength equation particular concern was that the failed pillars were impacted by large angular discontinuities. Discontinuities are not always readily visible to production staff when developing a pillar, but become apparent only when the pillar becomes fully loaded or when bench mining is carried out around the pillars.

Particularly hazardous conditions can result if large angular discontinuities cause unstable blocks to slide or topple from the pillar ribs. Of the eighteen failed pillars identified in the above studies, seven were associated with large angular discontinuities.

It was also observed that widely spaced angular discontinuities were present in the majority of limestone mines.

Pillar strength equation

Clearly, the effect of large discontinuities has to be taken into account in the design of pillar systems in limestone mines. Empirical design approach The empirically developed design approach of Roberts et al. Using this approach, the strength of a pillar that is square in plan can be expressed as follows: The value of k can be expressed in terms of the uniaxial compressive strength UCS as follows: The concern was that a collapse can occur if angular discontinuities weaken a large proportion of the pillars in a panel.

Therefore, it was decided to introduce an adjustment to the pillar strength equation that accounts for the weakening effect of angular discontinuities. However, the lack of sufficient field cases made it impossible to conduct a statistical analysis of the failed cases to estimate the impact of the angular discontinuities.

Numerical models were therefore used to investigate the likely effect of discontinuities on pillar strength. Modelling analysis The numerical models were designed specifically to determine how the inclination and frequency of large, roof-to-floor discontinuities would affect the strength of the slender pillars found in limestone mines.

Model calibration and validation was carried out against the empirically developed pillar design method of Roberts et al. Models were created to simulate pillars with width-toheight ratios of 0.

These models did not contain any explicitly modelled angular discontinuities. The rock mass properties were selected to simulate a good quality rock mass representative of the rock found in limestone mines.

Figure 3 shows the comparison between empirical and model results. It was concluded that the modelling method provides a realistic representation of pillar strength over the range of width-to-height ratios shown. Further modelling was conducted by introducing large angular discontinuities into the pillar models.

Figure 4 shows one of the models, indicating the location of the angular discontinuity and associated rock Figure 3—Validation of numerical model of a pillar against the empirically derived pillar strength equation of Roberts et al.equation, pillar stability curves can be generated.

The pillar stability curves generated using this procedure do not resemble the empirïcd curves derived by other authors. Further Figure 1: Strength factor contours of a pillar using ni = , s = and oc = PARAMETRIC STABILITY ANALYSIS OF ROOM AND PILLAR METHOD IN DEEP COAL MINES (∆S) to the span of the pillar as given in Equation (5) [3]: (5) Where: is the original span of the pillar and ∆S: is the roof sag.

is the ratio of the pillar strength to the average stress in the pillar. Strength is usually determined by means of test cylinders made of fresh concrete on the job and tested in compression at various ages. The requirement is a certain strength at .

adequately determined using the power formula s p ‹K W a Hb; –1ƒ where s p (MPa) is the pillar strength, K (MPa) is the strength of a unit volume of coal, and W and H are the pillar width and height in metres, respectively.

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We are different in many terms but still, an unseen force attracts us and we are indeed the pillar of strength for each other. He fills my shortcomings and I conceal his and we work together on our strength.

Beam Bearing on Concrete. Last Revised: In this case P p is the nominal bearing strength of the concrete surface is computed using SCM equations J and J In actuality, equation J is a special case of equation J (when A 1 = A 2), so equation J can be used at all times.

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