COMPARISON ANALYSIS AMONG DIFFERENT CALCULATION METHODS FOR THE STATIC STABILITY EVALUATION OF TAILING DAM

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1 Blucher Mechancal Engneerng Proceedngs May 2014, vol. 1, num. 1 COMPARISON ANALYSIS AMONG DIFFERENT CALCULATION METHODS FOR THE STATIC STABILITY EVALUATION OF TAILING DAM M. L 1, L. Lang 1, X. L 1 1 Research Insttute of Cvl Engneerng, College of Resources and Cvl Engneerng at the Northeastern Unversty (lmng-neu@163.com) Abstract. The statc stablty evaluaton of talng dam s one of the most mportant tasks n the mne envronmental protecton project. The methods for the statc stablty calculaton were dscussed n ths paper, whch were Swedsh Crcle Method, Janbu Method, Bshop Method, Fnte Element Method and Strength Reducton Fnte Element Method (SRFEM) wth fve dfferent falure crterons consdered. The analyss results show that the falure surface smulated by SRFEM was closed to the result of classcal method, and the safety factor by SRFEM wth D-P3 falure crteron was much more closed to the one got from the Fellenus Method. So, t s feasble to evaluate the statc stablty of talng dam through SRFEM. Also, t ndcates that the fnte element method and SRFEM are sutable to smulate practcal engneerng wth the complcated cross secton and non-lnear materals. Keywords: Talng dam, SRFEM, Statc stablty evaluaton. 1. INTRODUCTION The statc stablty analyss for talng dam was started from 1930s usng the lmt equlbrum method orgnated from sol mechancs. After the fnte element method was put forward n 1966, Clongh and other researchers started the stran and deformaton analyss for earth dam. Then the Fnte Element Method (FEM) was used for the evaluaton of talng dam. Tll now the lmt equlbrum method and stran stress analyss method are wdely used n the statc analyss of talng dam and those methods were theoretcally mproved. There were many factors whch nfluenced the stablty of talng dam, such as materal strength, ground water condtons and pore water pressure. However, there s no ndependent analyss system for talng dam. All of the methods were from sol mechancs, such as Swedsh Crcle Method (1936), Janbu Method (1957), Bshop Method (1955), Morgenstern- Prce Method (1965), Spencer Method (1967) and Sarma Method (1973). The man dfferences between those methods were the shape of falure surface and treatment for unknown varables. Another mportant method for the statc stablty analyss s the fnte element method. By ths method, the stress dstrbuton, the force n weak structure surface and falure could be got. Based on the fnte element method, there were two dfferent methods whch were elastc-

2 plastc fnte element method and strength reducton fnte element method (SRFEM). The latter one s more popular now. Zheng Y. R. and Zhao S. Y. (n Chna) make great contrbutons to ths method n theoretcal research and ts engneerng applcatons [1-5]. In ths paper, the comparatve analyss for the statc stablty analyss of talng dam was carred out by the Swedsh Crcle Method, Janbu Method, Bshop Method, Fnte Element Method and SRFEM. 2. METHODS FOR STATIC STABILITY EVALUATION OF TAILING DAM 2.1. Tradtonal Method The lmt equlbrum method was based on the theory of Mohr-Coulomb. The functon was f ' σ u tan ' ' ' ' c σ tan c (1) ' Where f s the shear stress on the slde surface, c s the effectve coheson, s the ' total stress, s effectve normal stress, and ' s the effectve nternal frcton. The safety factor was defned by the rato of / f whch stands for the strength reserve coeffcent for materals. Only the statc stablty condtons and Mohr-Coulomb falure crteron were consdered n ths method. There were many advantages for ths method such as smplfed calculaton and easly used n practcal engneerng. But the relatonshp between stress and stran of sol cannot be got from ths method. The three man methods based on the lmt equlbrum method were Swedsh Crcle Method, Janbu Method and Bshop Method. For the statc stablty analyss of ths project the lmt equlbrum methods were used through the Cvl FEM module n ANSYS. The safety factors and slde surface can be got easly by ths module Fnte Element Method (1) Fnte Element Method The stress and stran dstrbuton of the whole talng dam can be smulated by FEM. The frst step was to get the value of each element. Then the stress dstrbuton n each potental slde surface can be calculated through the transform of stress tensor. Accordng to the concept of lmt equlbrum method, the safety factor of each potental slde surface can be got [6-7]. (2) Strength Reducton Fnte Element Method The secondary development language APDL n ANSYS was used for the programmng of SRFEM, because there s no exstng module for ths method. Ths program contans fve man parts. (1) Create the fnte element model and nput materal parameters. (2) Apply the loads and boundary condtons. (3) Set soluton settngs and nput ntal condton for rou-

3 tne. (4) Get the reducton factors and the dsplacement curve on the top of dam. (5) Accordng to the curve of dsplacement and reducton factors, obtan the safety factor of talng dam. There are two nstablty crterons for SRFEM. One s when the FEM calculaton s non-convergence. The other s when generalzed plastc stran or equvalent plastc stran areas were connected from the toe to the top of the slope. Accordng to the reference [8-9], the former one was thought to be much more reasonable for slope stablty and t was used n ths paper as the talng dam nstablty crteron. There are three parameters for Drucker-Prager (D-P) crteron n ANSYS. They are nternal frcton angle, coheson c and dlatancy angle ψ. If ψ=, the rule s assocated flow rule. If ψ<, the rule s non-assocated flow rule. In the ANSYS, the crteron s D-P1 crteron [10-11]. It means that the safety factors got from ANSYS was under D-P1 crteron. However, there are totally fve dfferent D-P crterons whch can be converted usng equaton (2). By nput dfferent and k, the equvalent c, can be got and used for the smulaton wthout extra secondary development for new materal model. c arcsn 2 3 (1 2 3k 3 )(1 3 ) ( 1 2, 3, 4, 5, ) (2) Where and k are separately related wth nternal frcton angle and coheson. For dfferent D-P crterons, and k represented dfferent crcle n plane [11]. 3 BACKGROUND OF PRACTICAL ENGINEERING The heght, wdth and length of talng dam were separately 19m, 14m and 113m. The ntal dam was constructed by sand stone mxtures. The sub dam was constructed by talngs and sol. The sol thckness covered n the dam surface was from 300mm to 500mm. There were 11 sub dams wth 2m heght each. The dam scene photo and secton selected for calculatons of ths dam were shown n Fg. 1. Accordng to the mechancal model shown n Fg. 1, the fnte element model was created and meshed shown n Fg. 2. The boundary condtons were added ncludng horzontal constrants n both two sdes, and full constrants n the bottom of the model. The load appled n ths model was only gravty. The materal parameters for calculaton were lsted n table 1.

4 Fg. 1 The scene photo and secton for calculatons Fg.2 Fnte element model of talng dam Materal Number Materal name Table 1 Mechancal propertes of materal Gravty densty (kn/m) Compresson modulus Posson rato Coheson (kpa) (MPa) Internal frcton angle ( ) 1 Slt sand of talng Slt sol of talng Ice layer Natural sol RESULTS FROM DIFFERENT METHODS The statc stablty factors were drectly calculated by lmt equlbrum method and fnte element method usng Cvl FEM module n ANSYS software. The strength reducton fnte element method was realzed through the secondary development language APDL of ANSYS. The slde surfaces got from tradton lmt equlbrum method and falure areas calculated by SRFEM were separately shown n Fg. 3 and Fg. 4. The safety factors were lsted n table 2 and table 3.

5 Fg. 3 Typcal slde surface from tradtonal method

6 Fg. 4 The falure surface calculated by SRFEM wth dfferent D-P crterons Table 2 Safety factors calculated by tradton lmt equlbrum of talngs dam Swedsh Bshop Fnte element Method Janbu Method Crcle Method Method method Safety factors Table 3 Safety factors calculated by SRFEM wth dfferent D-P crterons D-P crterons D-P1 D-P2 D-P3 D-P4 D-P5 Safety factors

7 5 RESULTS COMPARISONS The potental slde surfaces calculated by the tradtonal method were almost the same whch were all n the ntal dam. The smallest safety factor was the one got from Swedsh Crcle Method. From the study of strength reducton fnte element method, the deal elastc-plastc model was selected for the statc stablty calculaton of talng dam. The results show that t was feasble and superor to calculate safety factor by SRFEM. Wth the dfferent D-P crterons, the slde surfaces were bascally dentcal and they were closed to the tradtonal method. The factor smulated by D-P1 crteron was the bggest. The other four factors were much closed to those by tradtonal method and fnte element method. The plastc stran areas calculated wth D-P3 and D-P5 crteron were connected from the toe to the top of the ntal dam. The potental slde surface calculated wth D-P3 crteron was much more closed to the one by lmt equlbrum method, shown n the Fg.3. So the safety factor wth D-P3 crteron was recommended for the statc stablty evaluaton of talng dam. 6 CONCLUSIONS The tradtonal lmt equlbrum method, fnte element method and strength reducton fnte element method were ntroduced n ths paper. From the results comparson analyss among dfferent methods, the followng conclusons can be got. (1) The SRFEM was feasble for the statc stablty evaluaton for talng dam. (2) From the safety factors and slde surface comparson among dfferent calculatons methods, the D-P3 crteron was more prorty f the SRFEM was used for the statc stablty evaluaton of talng dam. Acknowledgements Ths study s supported by Safety Dagnose Technque and Control Countermeasures of Talng Dam, Research Insttute of Cvl Engneerng, Northern Unversty, Chna. 7. REFERENCES [1] Zheng Y. R., Zhao S. Y., Song Y. K., Advance of study on the strength reducton fnte element method. Journal of Logstcal Engneerng Unversty. 3, 1-6, [2] Zheng Y. R., Zhao S. Y., Applcaton of strength reducton fem n sol and rock slope. Chnese Journal of Rock Mechancs and Engneerng. 19, , [3] Dawson E. M, Roth W. H., Drescher A. Slope stablty analyss by strength reducton.

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