GRD Journals- Global Research and Development Journal for Engineering | Volume 4 | Issue 10 | September 2019 ISSN: 2455-5703
Factor of Safety and Reliability Analysis of Rock Slope using GEO5 Software Md. Khaja Moniuddin Assistant Professor Department of Civil Engineering BKIT Bhalki, India
Sharankumar Mathada Assistant Professor Department of Civil Engineering BKIT Bhalki, India
Dr. Vageesha S. Mathada Assistant Professor Department of Civil Engineering BKIT Bhalki, India
Abhijith H T PG Student Department of Civil Engineering BKIT Bhalki, India
Abstract The entire earth consist of so many varieties of rock minerals which compositely for an entire rock mass which may be natural or artificial rock slopes which are at the level of the ground itself or it may be a deepest cuts or the hill slopes above the ground level. The factor of safety plays a major role in rock slope analysis. Due to the uncertainty involved in the calculation of rock parameters the application of factor of safety is widely used in analysis. Theses factor of safety are determined here by using Geo5 demo version software based on the uncertainty involved in the various rock parameters. The simple reliability analysis will provides the means of combined effect of uncertainty involved in calculations. The additional parameters such as standard deviation, mean, reliability index are used to determine the probability of failure of the rock slope. This probability of failure will helps to determine the reliability of the rock slope which in turn gives the idea of the stability of rock slope for any future recommendations regarding the actions for their stability. Keywords- Standard Deviation, Mean, Reliability Index, Probability of Failure
I. INTRODUCTION Here we use the Geo5 software for the analysis of the analysis of the factor of safety of the rock slope. The software uses the Mohr’s coulombs criterion for calculation of the FS of the slope, the mode of failure considered is the plane slip surface. The input parameters such as the unit weight, cohesion, angle of internal friction are used to determine the FS of rock slope. The reliability analysis mainly refers the percentage of probability of failure of the rock slope from results provided by the software. They take into account the various uncertainty in the input parameters and helps in selecting the correct factor of safety. The reliability analysis is carried by using the three sigma rule, in which the variance the each parameters are taken into account and then the varied values as been used in determination of factor of safety. The variation which provides the minimum factor of safety is considered as critical. If this factor of safety is well within the required factor of safety then the rock slope is considered as stable. If not then the anchors as used to strengthen the rock (any other method of strengthening can also be used). A. Geo5 Software – Both Analytical methods and Finite Element method are available in the software – A large number of problems such as stability of slopes, reinforced soil structures, rock slope stability, spread footings, plates, beams, cantilever walls, gravity walls, abutments, gabions, pile foundations, sheeting design and analysis, earth pressure, settlement analysis, etc. can be solved using this software. – It empowers design and analysis of rock stability with plane, polygonal slip surface and stepped slip surface. – Any method of failure criterion such as Mohr’s Coulomb , Barton Bandis and Hoek –Brown can be used for analysis
II. METHODOLOGY A. Factor of Safety The factor of safety is the constant which is imposed by standard laws, such that the slope should confirm or exceed this number for the stable of the slope for a long period of life. Resisting force Factor of safety = Driving force
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Factor of Safety and Reliability Analysis of Rock Slope using GEO5 Software (GRDJE/ Volume 4 / Issue 10 / 009)
B. Mohr’s Coulomb Model
Fig. 1: Mohr’s Coulomb Model
– –
The software makes use of the Mohr’s Coulomb Model for determining the factor of safety. Mohr’s coulomb model describe the shear strength of rocks and soils at different effective stress
C. – – – –
Uncertainties of the Variables It is the measure depression of frequency distribution or probability distribution. These Coefficient of variation are given by Harr and Kulhaway based on three sigma rule Three sigma rule is given by Dia and wang(1992). According 3-σ rule 99.73% of the values of the normally distributed parameters fall within standard deviation average. Table 1: Coefficient of variance chosen for analysis
Parameters Unit weight(kN/m3 ) Angle of Internal friction(ϕ)degree Cohesion(C) in kPa
COV 10 10 20
D. – – –
Reliability Analysis Level I method: Modelled by single habitual value. Level II method: Modelled by the mean value, standard deviation and the coefficients of correlation between variables. Level III method: Modelled by their combined distribution function and the probability of failure is determined to estimate of reliability. – Level IV method: Outcome (cost) of collapse are also taken in to consideration. The probabilistic strategies of reliability analysis include the following 1) Monte Carlo Simulation Method (MCS) 2) First-Order Second-Moment Method (FOSM) 3) First and Second Order Reliability Method (FORM, SORM) 4) Point Estimation Methods 1) Monte Carlo Simulation Method (MCS) One of the mean to evaluate the probability of failure of slopes is the utilization of Monte Carlo Simulation method. In this regard distinct values of the constituent random uncertainties are generated according to their probability distribution, and the productivity is calculated, then, for each produced set. The procedure is iterated several times to derive a rough, distinct probability density function of the performance function. This method is simple but time consuming. 2) First-Order Second-Moment Method (FOSM) The First Order Second-Moment Method is a notable option to Monte Corlo Simulation method, developed by Cornel (1971). It comprises on a primary sequence Taylor series estimation of the average (mean) and deviation (variance) of the performance function. Fractional by-products of this later calculated at the average values are so required An. easy way of this technique called as the Mean value First Order Second Moment method (MFOSM) was advocated and employed by Hassen et. al. (1999), to find the risky slip circle with minimum reliability index in a probabilistic analysis of slope stability. The approximation of the derivatives is a numerical difficulty of the FOSM method; additionally it is known to loose precision as FOS winds up non-linear and as the variance coefficient of the component expands, which is unluckily a frequent occurrence in the field of geotechnical engineering. All rights reserved by www.grdjournals.com
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Factor of Safety and Reliability Analysis of Rock Slope using GEO5 Software (GRDJE/ Volume 4 / Issue 10 / 009)
3) First and Second Order Reliability Method (FORM, SORM) The most regularly used methods in geotechnical engineering field are the First and Second Order Reliability Methods; the HasoferLind reliability index yielding is the base for these methods, therefore an invariant type of the reliability method. The First Order Reliability method (FORM) involves fitting a tangent hyper plane to the surface of the limit state at the design point, as illustrated in Fig. Hence the notable step in this method is the search for the design point p*. Several algorithms are suggested for the resolution of this issue. The Second-Order reliability method (SORM) involves fitting of a hyper-paraboloid to the surface of the limit state at the design point permitting the consideration of its curvature. As shown in Fig. 3a. The hyper-paraboloid is identical to the hyper plane distant of βs from the source (origin) of the normalized space. The SORM have the same drawback as in the previous method regarding the difficulty in approximation of partial derivatives. 4) Point Estimation Methods This category of techniques involves approximation of integrals which describe the moments relating to the use of statistics of the performance function through a collection of well-defined rules and regulations.
Fig. 2 (a): Cornel
Fig. 2 (b): Hasofer-Lind Reliability Index
III. PROBLEM The problem taken from the manual provided by the Geo 5 software has been used as an example for the reliability analysis .The geotechnical parameters of the rock mass were determined on the basis geological and archival investigations Unit weight of rock = 26 KN/m3 Effective angle of friction Ď•' = 430 Effective cohesion C' = 423 KPa
Fig. 3: Cross section of side rock hill cutting
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Factor of Safety and Reliability Analysis of Rock Slope using GEO5 Software (GRDJE/ Volume 4 / Issue 10 / 009)
The average unconfined compressive strength (determined by Schmidt hammer) = 60 MPa. The active height suggested by the geologist is 10.57 in hydrological survey no underground water flows were observed. A. Results After analysing the above mentioned problem, the following are the results obtained.
Chart 1: FOS Distribution Chart
Fig. 4: Slip surface minimum FOS
Fig. 5: Most probable slip surface zone
The various factor of safety given by the software for various uncertainties applied for the rock parameters a number of slip surface has been obtained for each variations. The slip surface for the minimum FOS is obtained for the combination of unit weight varied by 3σ times and cohesion and internal friction varied -3σ times. The min FOS this combination is 9.65. Similarly for the maximum FOS is obtained when γ varied 3σ and c varied -3σ and varied 3σ with a FOS of 124.51. All rights reserved by www.grdjournals.com
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Factor of Safety and Reliability Analysis of Rock Slope using GEO5 Software (GRDJE/ Volume 4 / Issue 10 / 009)
IV. CONCLUSIONS 1) From the reliability analysis carried out using the Geo5 software for various variances of the parameters such as cohesion, unit weight and angle of internal friction, we obtain a various number of results for various combinations. 2) From the results it has been clear that the lowest factor of safety occurs when the parameters γ varied 3σ times, ϕ varied -3σ, and C-varied -3σ, and provides FS=9.65>>>1.5. 3) The most probable slip surface zone will occurs in the ordinates of (0,5), (5.54,6.84), (8.34,8.94), (0,5). 4) Hence it shows that the rock is stable for long time and does not need any further action to increase its stability. 5) The probability of failure of for the given rock slope is 0.0090956 and it lies between the 0.003 and 0.01 and the reliability is 99.090% it indicates rock slope is reliable and good in performance no need for the further actions to increase its stability.
REFERENCES [1] [2] [3] [4] [5] [6]
Michael Duncan et all (April 2000): “Factor of safety and reliability in Geotechnical Engineering” Harr and Kulhaway, et all (2000): “Probabilistic Back Analysis of Geotechnical Systems” Vageesha Salkani Mathada (2014): “Spacial Distribution of Risk and Reliability in Slopes” C.Huang and X.P.Zhou et all (2017):“Two-Dimensional Stability Assessment to Rock Slopes Based on Random Field D K Baidya and A. GuhaRay (2017): “Geotechnical Engineering Reliability Aspects” R.K.Sharma, Vishal Kumar, N. Sharma, (2012): “Slope stability analysis using software GEO5 and C programming”.(International Conference on Chemical, Ecology and Environmental Sciences’ march 2012 Bangkok)
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