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102 fourth /nternational Symposium on Salt-Northern Ohio Oeologica/ Society loads, other input variables are environmental and con- struction factors. The output variables for most problems in rock mechanics are stress, strain, and displacement. Physical description of the system The description of the system consists of the following: (a) the size and shape of the opening; (b) its location below the surface; (c) the profile and the distribution of geologi- cal discontinuities (e.g., fissures, 'faults, joints, cleavages and bedding planes) of the surrounding rock; (d) mechan- ical properties of the surrounding rock, and (e) support schemes used to maintain stability. Determination of the response of the system This requires (a) the development of a model for the system and (b) the use of analytical and experimental techniques [o determine [hr response of the model to the prescribed inputs. Two eeneral approaches may be em- ployed to determine the response of the system from the defined input and the described system. They are the test- ing approach and the macroanalytical approach. The lat- ter invoh~es [he development of a mathematical model for the system. !t is the macroanal}'tical approach that forms the basis for the majority oC the existing design methods in engineering practice and was used in the study reported herein. Decision on acceptability of subsidence Based on field experience, if the predicted results ap- pear reasonable, the output o(the system should be com- pared with performance criteria to see i( surface subsidence and horizontal strain are within allowable lim- its to prevent damage to structures situated in the vicinity of the mined area. Improvement of prediction techniques This consists of monitoring the performance of the s}'stem and comparing it with predictions. Such compari- sons are essential to the development of improved predic- tive techniques. The scope of this paper invokes Sleps Z through 4. In addition, a number of case history studies where field subsidence information is available were studied for the purpose oC establishing the feasibility of using the tech- niques developed in this investigation for predicting sub- sidence. Many of the variables influencing the subsidence were studies by Nair and Chang (1969x). They were the size, the depth of the caviq•, the initial stress state, and the variation in modulus within bedded deposits. It has been shown that most of these variables may be accounted for uhrn the finite clement technique is utilized to compute the subsidence due to underground cavities. Qualitative comparison of analytic results ssith obsdnrd subsidence phenomena indicated, however, [hat the computed sub- sidence was generally much smaller than the observed subsidence, and that the subsidence extended over a larger area than the actual subsidence in the field. The major cause of the discrepancy was a result of the assumption made in the previous analytical studies that the rock sur- rounding an opening is, and acts as, a continuous mass. It is known that in the presence of a stress field, the existence of geologic (eatures in a rock mass such as fissures, faults, joints, cleavages and bedding planes can cause large defor- mations and failures. Furthermore, the geologic features mentioned above rend to localize the deformation to the area above the opening, by limiting the continuum action of the surrounding rock mass. Consequently, the deforma- tion pattern obtained from the analytical study treating the rock mass as a true continuum swill underestimate the deflection near the opening and the influence of the open- ing will extend to a greater distance. Therefore, it was considered logical that techniques be developed for com- puting the increased subsidence that may result from fail- ure in the surrounding rock mass in the form of (1} rock failure in the immediate vicinity of the opening due to critical stress conditions, or (2) failure along certain geo• logical discontinuities such as faults, joints or bedding planes, or due to the presence of fissures in the rock mass. It is the development and utilization of anal}'[ical tech- niques to include these (actors that is the primary concern of this paper. FAILURE CRITERIA As discussed previously, this study is concerned with the subsidence above mined areas due to failure in the surrounding rock mass. It is, therefore, appropriate to review briefly the types of rock (allure that are pertinent to the prediction of subsidence from solution mining oper- ations. Four possible types of rock failure are discussed in the (ollouing paragraphs. Compressive yielding A rock mass when subjected to a certain stress state in the field may reach a point where y'ielding' may occur without change of external loads. For purely cohesive isotropic materials, the yield criterion is defined by the (ollosving stress state: (mot -P>)2 + (~z -c*3)'' + (tea -Pt)2 - kt in which vt, Q,, o-y are the principal stresses and k a limiting value deduced from uniaxial tests. A plasticity criterion which includes friction effects, 'f'ielding ^ considered under faiWre (or the sake n( smplicity. It is rcwgnind chat }Melding does not imply failure in the usual sense.