It is a well-known fact that the economic design of linings for hydraulic delivery tunnels calls for maximum utilization of the load-carrying capacity of the enclosing hard rocks. In present design practice, such rocks are taken to be elastic, instantaneously deformed media, and stresses in the lining are determined by the theory of elasticity. At the same time, investigations of deformation properties of hard rocks in situ show that most of such rocks, under continuous load, are capable of different degrees of continued deformation, i.e., of creep. For this reason, the actual state of stress in the lining may substantially differ from that computed from the theory of elasticity.This article integrates the results of special fietd studies of creep in hard rocks at the V. V. Kuibyshev MISI (Moscow Civil Engineering Institute) * and presents a method of stress state calculation for delivery tunnels in creepprone rocks.To determine slow deformations in various types of hard rocks, special experiments with rectangular concrete plates 1 m z in area were carried out in galleries at the sites of the Kirovsk and Andizhan dams of the Uzbek SSR (Fig. 1).Rock creep was studied at increasing and decreasing pressures on the plates. Analysis of the experimental data shows no substantial qualitative difference in the reaction of the rock surfaces in question (chlorite-sericite schists, black shales, stratified and massive sandstones) to the local static load. This makes it possible to consider the investigation results as valid for the total rock mass. We now turn to the principal deformations in these rocks upon initial loading. Figure 2 shows typical mean deformation (S) --mean pressure (p) graphs reflecting the rock surface behavior as the pressure is applied to the plate in increments. These graphs show that the enveloping function S = f(p), represented by the dashed line in Fig. 2, is generally nonlinear, at both increasing and decreasing pressures. For the rocks under study this function is substantially nonlinear as a rule in a relatively narrow range of increasing pressures, fluctuating from 2.5 to 10 kg/cm 2, depending on the rocks. At higher pressures, up to Pmax = 40 kg/cm z used in the experiments, the enveloping function can be taken as linear. The deviations from linearity are slight and irregular; they may be due to scatter of the experimental data.
Calculation of the linings of pressure mnneIs for internal pressure with consideration of the resistance of the rock is usually done on the basis of solutions obtained by methods of elastic theory, i.e., the rocks and concrete are regarded as instantaneously deformable media, which does not always correspond to their actual properties [1][2][3][4]. The effect of concrete creep was studied in [5,6] and of rock creep on the stress of linings was investigated in [4]. However, under real conditions both these factors must be taken into account. A theoretical investigation of the effect of rock and concrete creep on the stress of a single-layer lining in a pressure tunnel under the effect of an internal uniformly distributed pressure is presented below. The characteristics established from the results of field investigations published earlier [3,4] are used for describing rock creep.
A dependable and economic planning of the linings of hydraulic pressure tunnels requires a maximum utilization of the mechanical properties of the surrounding formation. The widespread belief of purely elastic behavior of a rock formation does not correspond to fact because the majority are capable of deformation to some extent with time when pressure is applied to them, i.e., they have the property of creep. When the lining of a pressure tunnel acts together with the surrounding formation, creep may have a substantial effect on the stressed state of the lining. It is therefore necessary to investigate the theological properties of rock formations [1].Creep is usuaUy studied on specimens and the results of the investigation are applied to the massif [2]; it is assumed that the specimens represent sufficiently accurately the behavior of the rock massif. However, the deformation properties of fissured heterogeneous rock massifs which serve as foundations of hydraulic structures can be determined only by methods of large-scale field investigations. This paper discusses a method of determining the regularities of creep of fissured rock formations,* using as an example investigations with trial static loading of stratified sandstone which is one of the investigated types at the site of construction of a dam in the Kirgiz SSR.The course of the experiment is shown in Fig. 1.The pressure at each stage was kept constant until the deformation of the surface of the rock was stabilized; after that, the pressure was reduced to zero and the reversal of the creep phenomena was investigated.The dependence of conditional-momentary deformations on the average pressure (Fig. 2) was obtained by plotting deformations corresponding to each step. Since the loading in each case was done from zero, the abscissa of the graph corresponds to full conditional-momentary deformation of the surface of the rock as a function of the applied pressure (the proceeding unloading in each case was not considered). In Fig. 2 is shown also the relationship (curve 3) plotted with the results of unloading at each step. An analysis of the curves shows that the condkionalmomentary deformation in loading and in unloading are similar.Curve I is clearly non-linear, but it can be represented by two linear intervals, 0-10 and10-40 kg/cm 2. The deviation from a linear relationship in the fkst interval is small, in the second it does not exceed 10 percent. Curve 2 practically coincides with the relationship constructed with all loading cycles. This shows that the formation does not change its state in the course of the test. mm o,z Uo:E p.q5 IC' s j! [ IJi t 1 ! I _I_A i , : I f I I I "!Litl 5 I0 ~5 ZO ~ 30 ~ ~ ~5 50 ~'~ CO S5 7Oh Fig. 1. Deformation of the surface of the formation with time as a function of the applied pressure (punch No. % stratified sandstone). Conditional-momentary flexures at different stages of loading are shown in F ig. 3. A comparison of the experimental curves with the theoretical ones shows that they are close in position. The theorerical...
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