ENG  Vol.3 No.4 , April 2011
Probability Analysis for the Damage of Gravity Dam
Abstract: Damage reliability analysis is an emerging field of structural engineering which is very significant in structures of great importance like arch dams, large concrete gravity dams etc. The research objective is to design and construct an improved method for damage reliability analysis for concrete gravity dam. Firstly, pseudo excitation method and Mazar damage model were used to analyze how to calculate damage expected value excited by random seismic loading and deterministic static load on the condition that initial elastic modulus was deterministic. Moreover, response surface method was improved from the aspects of the regression of sample points, the selection of experimental points, the determined method of weight matrix and the calculation method of checking point respectively. Then, the above method was used to analyze guarantee rate of damage expected value excited by random seismic loading and deterministic static load on the condition that initial elastic modulus was random. Finally, a test example was given to verify and analyze the convergence and stability of this method. Compared with other conventional algorithm, this method has some strong points: this algorithm has good convergence and stability and greatly enhances calculation efficiency and the storage efficiency. From what has been analyzed, we find that damage expected value is insensitive to the randomness of initial elastic modulus so we can neglect the randomness of initial elastic modulus in some extent when we calculate damage expected value.
Cite this paper: nullQ. Xu, J. Li and J. Chen, "Probability Analysis for the Damage of Gravity Dam," Engineering, Vol. 3 No. 4, 2011, pp. 312-321. doi: 10.4236/eng.2011.34036.

[1]   Z. Kotulski and K. Sobczyk, “Effects of Parameter Uncertainty on the Response of Vibratory Systems to Random Excitation,” Sound Vibrator, Vol. 119, No. 1, 1986, pp. 159-171.

[2]   H. Benaroya and M. Rehak, “Finite Element Methods in Probabil-istic Structural Analysis: A Selective Review,” Applied Me-chanics Reviews, Vol. 41, No. 5, 1987, pp. 201-213.

[3]   P. D. Spanos and R. G. Ghanem, “Stochastic finite element expansion for random media,” Journal of engineering mechanics, Vol. 115, No. 5, 1989, pp. 1035-1053.

[4]   P. Leger, R. Lariviere, F. Palavicini and R. Tinawi, “Performance of Gated Spillways during the 1996 Sanguinity Flood (Que’bec, Canada) and Evolution of Related Design Criteria,” Proceeding of ICOLD20th Congress, Beijing, Vol. 26, No. 1, 2000, pp. 417-438.

[5]   F.-Y. Wang, Z. S. Xu and L. J. Dong, “Stability Model of Tailing Dams Based on Fuzzy Random Reliability,” Chinese Journal of Geotechnical Engineering, Vol. 30, No. 11, 2008, pp. 1600-1605.

[6]   R. Viertl, “On Reliability Estimation Based on Fuzzy Lifetime Data,” Journal of Statistical Planning and Inference, Vol. 48, No. 5, 2008, pp. 1-6

[7]   E. Castillo, R. Minguez and C. Castillo, “Sensitivity Analysis in Optimization and Reliability Problems,” Reliability Engineering and System Safety, Vol. 93, No. 12, 2008, pp. 1788-1800. doi:10.1016/j.ress.2008.03.010

[8]   J. H. Song and W. H. Kang, “System Reliability and Sensitivity under Statistical Dependence by Matrix-Based System Reliability Method,” Structural Safety, Vol. 31, No. 2, 2009, pp. 148-156. doi:10.1016/j.strusafe.2008.06.012

[9]   K. S. Chin, Y. M. Wang, G. K. K. Poon and J.-B. Yang, “Failure Mode and Ef-fects Analysis Using a Group- Based Evidential Reasoning Approach,” Computers & Operations Research, Vol. 36, No. 6, 2009, pp. 1768- 1799. doi:10.1016/j.cor.2008.05.002

[10]   Y. W. Liu and F. Moses, “A Sequential Response Surface Method and Its Application in the Reliability Analysis of Aircraft Structural System,” Structural Safety, Vol. 16, No. 1-2, 1994, pp. 39-46. doi:10.1016/0167-4730(94)00023-J

[11]   G. E. P. Box and K. B. Wilson, “The Exploration and Exploitation of Response Surfaces: Some General Considerations and Examples,” Bio-metrics, Vol. 10, No. 1, March 1954, pp. 16-60. doi:10.2307/3001663

[12]   A. I. Khuri and J. A. Cornell, “Re-sponse Surfaces: Design and Analyses,” Marcel and Dekker, New York, 1997.

[13]   R. H. Myers and D. C. Montgomery, “Response Surface Methodology: Process and Product Opti-mization Using Designed Experiments,” John Wiley and Sons, Hoboken, 1995.

[14]   F. S. Wong, “Uncertainties in Dynamic Soil-Structure Interaction,” Journal of Engineering Mechanics, Vol. 110, No. 2, February 1984, pp. 308-24. doi:10.1061/(ASCE)0733-9399(1984)110:2(308)

[15]   F. S. Wong, “Slope Reliability and Response Surface Method,” Journal of Geotechnical Engineering, Vol. 111, No. 1, January 1985, pp. 32-53. doi:10.1061/(ASCE)0733-9410(1985)111:1(32)

[16]   L. Fara-velli, “Response Surface Approach for Reliability Analysis,” Journal of Engineering Mechanics, Vol. 115, No. 12, 1989, pp. 2763-2781. doi:10.1061/(ASCE)0733-9399(1989)115:12(2763)

[17]   L. Faravelli, “Structural reliability via response surface,” In: N. Bellomo, F. Casciati, Eds., Proceedings of IUTAM Symposium on Nonlinear Stochastic Mechanics, Springer Verlag, Berlin, 1992, pp. 213-223.

[18]   J. Q. Jiang, C. G. Wu, C. Y. Song, et al., “Adaptive and Iterative Gene Selection Based on Least Squares Support Vector Regression,” Journal of Information & Computational Science, Vol. 3, No. 3, 2006, pp. 443-451.

[19]   C. G. Bucher and U. Bourgund, “A Fast and Efficient Response Surface Approach for Structural Reliability Problems,” Structural Safety, Vol. 7, No. 1, 1990, pp. 57- 66. doi:10.1016/0167-4730(90)90012-E

[20]   M. R. Rajashekhar and B. R. Ellingwood, “A New Look at the Response Surface Approach for Reliability Analysis,” Structural Safety, Vol. 12, No. 3, 1993, pp. 205-220. doi:10.1016/0167-4730(93)90003-J

[21]   X. L. Guan and R. E. Melchers, “Effect of Response Surface Parameter Variation on Structural Reliability Estimates,” Structural Safety, Vol. 23, No. 4, 2001, pp. 429- 444. doi:10.1016/S0167-4730(02)00013-9

[22]   S. Gupta and C. S. Manohar, “Improved Response Surface Method for Time Va-riant Reliability Analysis of Nonlinear Random Structures under no Stationary Excitations,” Nonlinear Dynamics, Vol. 36, No. 2-4, 2004, pp. 267-280. doi:10.1023/B:NODY.0000045519.49715.93

[23]   P. Bjerager, “Methods for Structural Reliability Computation,” In: F. Casciati, Ed., Reliability Problems: General Principles and Applications in Mechanics of Solid and Structures, Springer Verlag Wien, New York, 1991, pp. 89-136.

[24]   B. Fiessler, H.-J. Neumann and R. Rackwitz, “Quadratic Limit States in Structural Reliability,” Journal of the Engineering Mechanics Division, Vol. 105, No. 4, 1979, pp. 661-676.

[25]   K. Breitung, “Asymptotic Approximation for Multi-Nor- mal Integrals,” Journal of Engineering Mechanics, Vol. 10, No. 3, 1984, pp. 357-366. doi:10.1061/(ASCE)0733-9399(1984)110:3(357)

[26]   H. U. Koyluoglu and S. R. K. Nielsen, “New Approximations for SORM Integrals,” Structural Safety, Vol. 13, No. 4, 1994, pp. 235-246. doi:10.1016/0167-4730(94)90031-0

[27]   A. D. Ki-ureghian, H. Z. Lin and S. J. Hwang, “Second-Order Reliability Approximations,” Journal of Engineering Mechanics, Vol. 113, No. 8, 1987, pp. 1208- 1225. doi:10.1061/(ASCE)0733-9399(1987)113:8(1208)

[28]   J. Zhao and Z. Z. Lu, “Response Surface Method for Reliability Analysis of Implicit Limit State Equation Based on Weighted Regression,” Journal of Mechanical Strength, Vol. 28, No. 4, 2006, pp. 512-516.