624.131.522 ~"k~o main types of nonlinearity are important in calculations of underground structures: physical (nonlinearity of the stress--strain relation) and morphological (nonlinearity of the structure of the calculation schemes).The first nonlinearity is a consequence of the known manifestation of the physical and mechanical properties of the material: The rock mass is practically always deformed nonlinearly when driving workings owing to the development of decompression.The more specific type, the second nonlinearity, is determined by the conSiderable effect on the formation of the stress field in the finished structure of technological construction factors and especially the stepwise opening of the section of the workings and sequence of driving them. The latter necessitates examining structurally nonlinear mathematical models, i.e., those models which are transformed during calculation, reflecting the most characteristic stages of development of the structure during its construction.We will examine certain problems related to the construction and realization of geomechanicalmodels of underground structures incorporating the two indicated types of nonlinearity. Construction of Discrete Models of Structures.The development of a discrete model is the most essential stage of the calculation process when using the finite-element method (FEM). Unfortunately, in the majority of cases the given procedure is presently difficult to formalize [i]. Its realization requires from the calculator, apart from a good understanding of the statics of the structure, skill in constructing approximating meshes. Discretization of nonlinear models has a number of characteristic features.When performing this procedure the approximRting mesh is condensed at places of presumed oscillation of the sought functions in order to provide the necessary accuracy, condensing being accomplished in proportion to the increase of their gradient. In the elastic model oscillation is expressed as pronounced concentrations near sources of disturbances of the field of the function --concentrators --and therefore condensation of the approximating mesh is usually performed according to the law of geometric progression (Fig. la). In the nonlinear model the character of oscillation is somewhat more complex --the site of the extremum is generally not known beforehand and the size of the zone of disturbance of the field of the function can be estimated only approximately.Therefore, when solving nonlinear problems it is better to perform discretization of the models within the indicated zones by uniform partition into finite elements of the minimum necessary size (Fig. ib). Thus the character of the approximating meshes in the elastic and nonelastic models is substantially different. .... Translated from Gidr0tekhnicheskoe Stroitel 'stvo, No. 12, pp. 13-i9, December, 1983.
Among the current trends determining progress in the area of designing supports of chamber working, we can distinguish two main ones: the maximum use of the load-bearing capacity of the earth mass and the creation of designs having an increased deformability (yielding), satisfying at the same time the requirements of the calculated limit state imposed on them.Among the most complicated with respect to designing reliable supports are the workings of the machine halls and transformer rooms of the powerhouses of hydroelectric and pumped-storage stations. As a consequence of the construction, technological, and operating advantages, the workings of such structures, as a rule, are designed with an inverted U-shape. In such workings two main elements of the supports --support of the arch and bolting scheme of supporting the walls --are clearly distinguished in the design and construction plans.Considerable experience in solving the problems in question with consideration of the above-indicated trend was gained during the design and construction of the unique Rogun hydroelectric station. The need to make economical and reliable decisions required the conduction of considerable surveys, design studies, and scientific investigations, effected in many cases by the occurrence of new problems owing to the impossibility of realizing traditional approaches. An analysis of the experience of the Rogun hydrostation unconditionally will be useful in the design of other future hydraulic structures.1. In addition to the large dimensions of the workings of the powerhouse complex (PHC) of the Rogun hydrostation, to a considerable extent the complexity of the problems of designing their support was determined by the characteristics of the engineering-geological situation. The PHC is located in the upper pool of the hydro development at a depth of about 40 m in a stratum of hard siltstones and sandstones, the uniaxial compressive strength (Rco) of which is respectively 80 and 100 MPa. One of the most essential factors which predetermined the need to find unconventional solutions was the pronounced prevalence of contemporary tectonic processes in the formation of the field of natural stresses of the mass. As a result, the components of the tensor of the principal natural stresses were substantially different from the values caused just by gravitational forces. Directly in the stretch of the powerhouse workings the vertical stresses exceed the weight of the overlying rocks by almost 1.5 times and are equal to 14 MPa and the horizontal stresses are equal to 17 MPa. With consideration of the relationship of the values of the natural stresses and strength of the rocks Rco the latter should be classified as strong [1]. Thus fracture of the mass in the vicinity of the workings is possible only along natural joint systems.Sandstones and Siltstones Are Bedded Rocks. The thickness of the beds is 0.5-0.7 m, they occur monoclinally and dip toward the lower pool at an angle of 65-70 ~ The long axis of the powerhouse workings is oriented almost acros...
It is known that calculating structures for their own dead loads in which the gravitational forces are applied to a design model of the completed structure, instantaneous loading (IL) scheme, leads to errors in many cases. In problems of calculating underground structures, for the solution of which models of continuum mechanics are used, this scheme gives divergences so far from the actual picture as to be practically unacceptable.Attention was called to this circumstance in [i] and a general scheme of solution free from the main shortcoming of the IL scheme was proposed. Unfortunately, the fundamental methodological error pointed out in [i] is repeated in many works, theoretical and experimental. The essence of the error is that the IL scheme does not reflect the actual picture of the continuing change in the deformed states of the rock mass and lining: gravitational forces cause initial stresses and strains in the rock undisturbed by tunneling, and only after weakening by a tunnel supported by a lining does the sought deformed state of the mass-lining system occur from the effect of unequalized "removable" stresses applied to the tunnel surface.Let us examine the process of driving an underground tunnel according to [i]. A load P (equal, e.g., to the weight of the overlying rock) is applied using a perfectly stiff crossbar vertical to three bars S M, SC, and S M of the same stiffness (Fig. I). As a result of deformation of the bars the crossbar moves to position I (stage I). The forces in the bars of this case are equal to P/3. Now we remove bar S c and instantaneously replace it by a still undeformed bar* So of the same stiffness and length ~ --AZ. As a result, the unequalized load P/3 with bar S c removed is redistributed over three bars SM, So, and SM, as a consequence of which the crossbar moves to position II (stage If). In this case the force in bar SMwill be equal to (4/9)P and in bar So to (1/9)P. It is obvious that if we simulate the lining by bar SC, stage I will be equivalent to the IL scheme. If we simulate the lining by bar So (actually, this is how it must be done, since it is understood that the lining is being constructed in an already deformed mass), then we will obtain a state of stress corresponding to the proposed [i] scheme for calculating the effect of "removable" stresses. In the given case the IL scheme overestimates the forces in the "lining" (i.e., in bar S C) threefold.For a quantitative evaluation of the indicated error in the IL scheme we investigated a lining supporting a rectangular tunnel (Fig. 2). The calculations were made by the finite element method. As we see from Fig. 2, the maximum forces in the lining calculated according to the scheme in [i] are more than twofold less than according to the IL scheme.Finally, the next problem is an example where the IL scheme cannot yield a solution at all. For example, let it be required to determine the state of stress in the rock mass and a new lining that for some reason replaced the lining installed earlier. It is clear that the stre...
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