Reliability analysis of steel lined reinforced concrete pressure pipeline of Three Gorges Power Station Liu Xing, Fang Mei, Chen Zhen, Wang Yun, Gao Rui (School of Civil Engineering and Architecture, Wuhan University of Hydraulic and Electric Engineering, Wuhan 430072, Hubei) Reliability indicators under various steel bar configurations and the reliability of the pipeline were analyzed. : Steel lining; Reinforced concrete; Pressure pipeline; Reliability 1: A Three Gorges power station dam-type powerhouse diversion system uses shallow grooved steel-lined reinforced concrete pipeline, the inner edge of the pipeline is laid with steel plate lining, and it is wrapped with ordinary concrete Three layers of ring-shaped main ribs and several longitudinal structural ribs are arranged along the radial direction of the pipeline. At present, there is no mature formula for calculating the bearing capacity of steel-lined reinforced concrete pressure pipes, and there is no reliability analysis method suitable for designers. The design unit of the Three Gorges Power Station, the Yangtze River Water Conservancy Commission, has summarized the design practice of steel-lined reinforced concrete pipes at home and abroad. On the basis, the boiler formula is used to express the limit state bearing capacity, and the reliability of the structure is described by the safety factor. The design method of the design unit is first introduced, and then the reinforced concrete nonlinear stochastic finite element method is used to calculate the steel lined reinforced concrete pipeline of the Three Gorges Power Station Analyze and directly describe its reliability with reliability indicators, and the conclusions obtained are available to the relevant units.
1 The current design method of the pressure pipeline of the Three Gorges Power Station 1.1 The design principles and assumptions are to adopt the boiler formula, and the following principles and assumptions are proposed: the steel lined reinforced concrete as a whole bears the load. In the hoop stress generated by each load combination, the steel liner only bears the internal water Circumferential stress caused by pressure; in addition to sharing part of the internal water pressure, the outsourcing reinforced concrete also bears the circumferential stress generated by the dam body load. The longitudinal stress on the pipeline when the dam pipe works together (along the axial direction of the pipe) is made of steel-lined reinforced concrete Jointly undertake.
Steel-lined reinforced concrete pipes shall be designed to meet two limit states.
1.2 Design calculation formula Under the limit of bearing capacity, steel lining and reinforced concrete are jointly loaded, and there are finite radial cracks in the encased concrete. It is assumed that on the cracked section, the steel lining and the circumferential reinforcement of each layer reach their yield strength. The configuration area is calculated by the following formula: safety factor at force; Rg, es are the design strength of steel bar and steel lining; 0 is the welding coefficient of steel lining, take d95; Fg, Fs are the cross-sectional area of ​​steel bar and steel lining, respectively.
1.3 The value of safety factor When the steel lined reinforced concrete pipeline is designed according to the bearing capacity limit state, the method of safety factor is used to describe the reliability, and the total safety factor K is used to describe the situation where the steel liner and the reinforced concrete jointly bear the internal water pressure and Using Ks and Kg to describe the situation where the steel lining and the steel bars respectively bear the internal water pressure, the Three Gorges Dam Expert Group, on the basis of summarizing the engineering experience at home and abroad, proposed that the steel lining and reinforced concrete of the steel lined reinforced concrete pressure pipes of the Three Gorges Power Station should be requested The safety factor of each of the internal water pressure alone is greater than 1.0. Some experts hope that the safety factor of the steel lining when it is subjected to the internal water pressure alone is greater than 1.0. After analysis and determination, under the premise of taking the total safety factor K = 2.0, the following two combinations are considered for the safety factor when the steel lining and the steel bar respectively bear internal water pressure: Ks = Kg = 0.81.4 The design results are based on the total safety The coefficient K = 20, and the separate safety factor is the principle of two combinations. The Yangtze River Water Resources Commission divides the axis direction of the steel-lined reinforced concrete pressure pipeline into an upper curved section, an oblique straight section I, an oblique straight section, and a lower curved section. The results are shown in the table below.
Table 1 Design pressure value of each pipe section Table Design working conditions Upper inclined straight section I section Oblique straight section I Lower bend section Upstream design water level Upstream check water level table 2 Steel design strength Steel plate Reinforcement level (new hi level) Note: (1) The design strength of the steel plate in the upper and lower bending sections is reduced by 10%. (2) The steel liner weld coefficient 0195. After considering the temperature stress and crack width and other influencing factors, the design unit recommends the steel configuration with core = 1.2 and Kg = 0.8. The recommended steel configuration is now listed in Table 3 Table 3 Recommended Steel Configuration Scheme Pipe Section Steel Plate Model Steel Plate Thickness / mm Reinforcement Configuration Upper Bend Section Straight Straight Section I Lower Bend Section Note: Rebars are U1 grade steel bars.
5 Discussions on the current design method 1.5.1 Value of safety factor The current design method of the pressure pipeline behind the dam of the Three Gorges Power Station uses the safety factor K (or Kg, Ks) to describe the structural safety. Regardless of the total safety factor or the individual safety factor, as the designer's practical experience accumulates, its value will be appropriately reduced. Although the individual safety factor can be considered to be less than 1.0, the total safety factor is always greater than 1.0. Unified standards for hydraulic structures. The reliability of a structure refers to the probability that a structure will perform a predetermined function within a specified time under specified conditions. In other words, if the structure is highly reliable, its reliability probability is high (the probability of failure is small), otherwise The reliability probability is small (the failure probability is large). Therefore, it can be considered that the reliability of the structure can be correctly judged only by finding the reliability probability (or failure probability) of the structure under actual conditions. 1.5.2 Bearing capacity limit state Three Gorges power station steel lined reinforced concrete The pressure pipeline mainly bears the internal finite element calculation results to show that: under the design internal water pressure, neither the steel lining nor the steel bars have reached their respective yield strengths. Only when the design internal water pressure reached about 3 times, the radial crack at the pipeline Only steel lining and steel can achieve the yield strength, which shows that: steel lining and reinforced concrete jointly bear the internal water pressure; steel lining The assumption that the steel bars are solely responsible for the internal water pressure is inconsistent with the actual working behavior of the pipeline structure; under the effect of the design internal water pressure, the true safety factor of the structure is greater than the corresponding design value. Based on the above discussion, how to correctly evaluate the steel lining of the Three Gorges Power Station The actual reliability of reinforced concrete pressure pipes is a problem worthy of study. 2 The combination of nonlinear stochastic finite element reliability analysis elements, the establishment of reinforced concrete nonlinear stochastic finite element theory and corresponding calculation methods, the compilation of computer software and its before and after Processing software. This method will be used to evaluate the reliability of the current design of the steel-lined reinforced concrete pressure pipeline of the Three Gorges Power Station, and directly obtain its reliability index under various steel configurations, and use the probability of failure to evaluate the reliability of the pipeline. The basic theory and calculation method of linear stochastic finite element can be referred to, due to space limitations, this article will not repeat it. 2.1 Calculation model selection Because the pipeline structure mainly bears internal water pressure, according to the original design, take the upper straight section oblique straight section I, The inclined straight section and the lower curved section are used as the control section. According to the plane strain problem, the pipeline concrete grade is No. 250, and the remaining concrete is No. 150. 2.2 Calculated load The main calculation load is the internal water pressure. The design value and calibration of the internal water pressure of the control section of each pipe section The nuclear value is shown in Table 12.3 The limit state equation According to the conclusion of the simulation model test research, it can be considered that the damage sign of the steel lined reinforced concrete pressure pipe is that the tensile stress of the steel liner and the steel bar reaches their respective yield strengths, therefore, the corresponding bearing capacity limit state It can be expressed by the following limit state equation: top: fc, fs are steel lining and steel bar respectively Yield strength; e, es were calculated steel steel liner and stress.
4 Statistical parameters of random variables When performing nonlinear stochastic finite element analysis and calculation of reinforced concrete, the steel lining, the elastic modulus cross-sectional area of ​​the reinforcement, the hydraulic deformation of the concrete are used for a large number of simulation models, 2D and 3D nonlinear hemp modulus ! Coagulation. The degree of spread, the thickness of the concrete element, and the external load c-steel yield strength are all considered as random variables. In this paper, based on the collected data and the statistical data of the hydraulic standard compilation group, the statistical values ​​of the above random variables and the corresponding probabilistic distribution are now listed in Table 4 3. Calculation Results and Analysis 3.1 Calculation Results Arrangement According to the aforementioned principles, the Three Gorges The calculation results of the reliable index of the bearing capacity of the steel-lined reinforced concrete pressure pipeline behind the dam are listed in Table 53.2. Analysis of the calculation results According to the probability statistical theory, the failure probability P / has the following relationship with the reliability index U: Table 6 gives the failure probability P / and reliability The corresponding relationship of the index U is now discussed in the calculation results listed in Table 5. 21 The general rule of the reliability index The reliability index of the upper bending section is the largest, and the reliability index of the lower bending section is the smallest; under the same steel configuration, the design water level (upstream elevation 175.0m) The reliability index is large, and the guilty index is small when checking the water level (upstream height 180.4m); for any steel configuration, the reliability index of the steel lining is less than the reliability index of the steel bar, indicating that the tensile stress of the steel lining is close to its yield strength (Or probability) is greater than the degree or probability that the tensile stress of the steel bar is close to its yield strength; the steel corresponding to the minimum value of the reliable index The unit is located at the top of the pressure pipe, and the steel element corresponding to the minimum value of the reliable index is located at the top of the pressure pipe and is the innermost steel bar; Outline) Probability distribution steel lined normal mode steel bar normal volume concrete normal steel normal intercept line normal surface normal area normal steel normal bar normal heavy concrete normal yield strength steel lined normal steel bar normal note : Rebars are U1 grade rebar.
Table 5 Calculation Results of Reliable Indexes for Bearing Capacity of Pressure Pipes behind the Three Gorges Hydropower Station Calculation Location Design Internal Water Pressure Steel Lining Reinforcement Steel Lining Thickness Maximum Reliability Index for Maximum Tensile Stress Maximum Reliability Index for Maximum Tensile Stress Oblique and straight sections at upper bends.
Inclined straight section: Rebar configuration in the lower curved section Note: The rebars are 111 grade rebars.
According to the comparison of P / and U in Table 6, the failure probability of steel linings or steel bars is less than one part per million, and the corresponding reliability index is much greater than the first level of the safety level and is the target reliability index for brittle failure; = 1.0) , Steel configuration 2 (Ks = 1.2, Kg = 0.8) and the recommended steel configuration 3 scenarios. If the safety factor is used to describe the reliability of the pipeline, steel configuration 1 and steel configuration 2 are different, namely steel configuration 2 steel lining The safety factor of steel is increased by 2 (%) than that of steel configuration 1 steel lining; the safety factor of steel configuration 2 steel bar is reduced by 20% than the safety factor of steel configuration 1 steel bar. However, the reliable index obtained in the three configuration cases or failure The rates are almost equal.
3.22 Evaluation of the current design safety According to the reliability index calculated in this paper and the corresponding failure probability, it can be considered that according to the current design, the steel lined reinforced concrete pressure back pipe behind the dam of the Three Gorges Power Station has sufficient bearing capacity, or that the design is partial Conservative, there seems to be room for adjustment. Based on the above discussion, it can indeed be seen that it is difficult to scientifically describe the structural reliability with a single safety factor. It is recommended that the calculation of the bearing capacity of such non-bar structure in the future should refer to the reliability index Or failure probability
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