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The material properties used for the simulations were found in previously published studies and general rules of geological materials. Two materials were used in simulating the effects of bolts on the back stability: potash, and disseminated clay. Potash is a commonly mined mineral and therefore has been extensively tested for strength properties. Potash is known to be a elasto-viscoplastic material indicating, in addition to normal elastic and plastic material properties, potash exhibits time dependent behaviours as well [17]. Over the time ranges of interest, however, the creep strain makes a very minimal difference in the total room closure, on the order of 3 mm per day [37]. Mining a short length of an entry may occur over one or two hours, and therefore allow

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approximately 0.25 mm of creep closure in the entry. A similar material model was used for clay.

A Mohr-Coulomb plastic material model was therefore used for the purposes of finding the immediate deformation of the tunnel and creep was not considered.

5.2.1 Material Properties of Potash

The unconfined compressive strength of the potash material has been found to be 28.1 MPa with a standard deviation of the mean of 1.6 MPa from Lanigan potash samples [7]. The Young’s modulus can also be obtained from the same paper, 5.3 GPa and standard deviation of the mean of 1.10 GPa. Additionally, as per PotashCorp internal data, the friction angle of the ore material in standard ground conditions is approximately 35^o. The final displacements that result can then be compared to the actual displacements recorded in PotashCorp mine sites of between 30 and 40 mm closure in first pass and between 40 and 50 mm displacement in second pass [37].

The material model used in the commercially available Rocscience® programs RS³ and RS² is based on the isotropic Mohr-Coulomb plastic material criterion using tensile strength, friction angle, cohesion, and Young’s modulus. Although potash is known to be anisotropic, an isotropic material model was used for this study. Due to a lack of data, some of these values are based on standard assumptions [38]. From the unconfined compressive strength value, the standard tensile strength and cohesion values can be calculated via the following relations:

𝜎_𝑡 = 1

10𝜎_𝑐 (5.3)

𝜏_𝑐 =1

4𝜎_𝑐 (5.4)

where 𝜎_𝑐 is the unconfined compressive strength 𝜎_𝑡 is the tensile strength, and

𝜏_𝑐 is the cohesion strength.

The after yield, or plastic, parameters for friction angle are assumed to be unchanged from the original values. The Young’s modulus is reduced to zero upon failure. The after-yield values for strength for both the tensile and cohesion strengths however, will be less than the original, before failure, values and were estimated to be reduced by 50%. This ratio of before to after failure values were adjusted to create a model that fits the closure data presented by PotashCorp [37]. The final values used are shown in Table 5.1.

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Table 5.1 - The final properties of potash used for the FEA simulation of the potash tunnel. The values for the friction angle, 𝜽_𝒇, the Young’s modulus, 𝑬, the tensile strength, 𝝈_𝒕, and the cohesion strength, 𝝉_𝒄, are defined previously. The plastic material values, denoted by ‘After Yield Value’, were found by tuning the ratio between original and residual values from the original 50% to 86%

to match experimental results.

Potash Parameters Before Yield Value After Yield Value

𝜎_𝑡 2.8 MPa 2.4 MPa

𝜃_𝑓 35^o 35^o

𝜏_𝑐 7 MPa 6 MPa

𝐸 5.3 GPa 0 GPa

𝜎_𝑈𝐶𝑆 28 MPa 24 MPa

5.2.2 Clay Zone Material Properties

The material properties of the clay seam are not easily determined because the thickness of the seams in the potash ore zone are not thick enough to properly test mechanically. The disseminated clay zone in the area of interest is actually several seams of clay interspersed with halite, where none of the layers are thick enough to properly test by themselves. For this reason, effective material properties for this zone were determined by tuning the material properties to match the expected amounts of tunnel closure. Equations 5.3 and 5.4 can once again be used leaving only the compressive strength and the Young’s modulus to be determined. Young’s modulus here is assumed to be the equal to that of the potash ore. Based on information from PotashCorp, the displacement was graphed for a wide range of values for UCS and the value closest to the expected value (while still resulting in plausible displacement) of 8 MPa was used [37].

The modelled room displacement is affected by the strength of the disseminated clay zone material via what appears to be an inverse power relation. The room closure amounts shown with very low clay zone material strength become very large compared to the actual values expected, as shown in Figure 5.4. A final UCS value of 20 MPa was chosen because this was the lowest value where the displacement trend line still seemed to follow the known room displacement values. The lowest value was used as an attempt to represent the known weakening effect of the disseminated clay while still modelling realistic deformation.

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Figure 5.4 - A comparison of the room displacement with varying effective clay seam strength values. The vertical green and blue lines represent the expected or known values of clay and potash strengths respectively. The upper trendline represents the displacement of a two-pass width room while the lower represents a single pass width. The points at 6, 20, and 30 MPa appear to have been affected by numerical errors. Further, the shaded areas represent the expected values of room displacement for a 1^st pass and 2^nd pass room respectively. A final UCS value of 20 MPa was used for modelling purposes because it represents the strength value closest to the expected value of clay strength while still following the expected values of room displacement.

Table 5.2 - The final back analyzed clay zone material properties used for the FEA simulation of the potash tunnel. The values for the friction angle, 𝜽𝒇, the Young’s modulus, 𝑬, the tensile strength, 𝝈_𝒕, and the cohesion strength, 𝝉𝒄, are defined previously. The plastic material values, denoted by a ‘Residual Values’, found by assuming a 50% decrease from the original before failure values.

Clay Parameters Before Failure Value After Failure Value

𝜎_𝑡 2.0 MPa 1.0 MPa

The models used for simulating the displacement of the potash tunnels allow for sequenced material removal in three dimensions. This allows for simulation of the tunnel behaviour as the tunnel is mined without calculating any time dependent effects. One of the main differences between the currently used bolting procedure and the proposed procedure centers around the

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