جستجوی مقالات مرتبط با کلیدواژه « ضریب اطمینان » در نشریات گروه « عمران »

Slopes are one of the main parts of the environment, which are the habitat of many organisms. Annually, some slopes become unstable due to rainfall, in addition to road rainfall, it can decrease or increase the safety factor of the slope. Stabilizing soil slopes against rainfall is one of the basic challenges discussed in the design and implementation of road construction projects. A parametric study has been used to investigate the combined effect of rainfall and road on the stability of soil slopes using SEEP/W and SLOPE/W software. In this study, first, the effect of rainfall with different intensities on the slope without road was performed. According to the results, depending on the location of the road in the slope, the construction of the road can lead to a decrease or an increase in the initial safety factor in the slope. With the increase in intensity and time of rainfall, the seepage front, water pressure and underground water level increase and the safety factor is decreased. By examining the combined effect of rainfall and road in a case study, it was concluded that the construction of the road on the slope will reduce safety factor more severely during rainfall compared to the case without road. Finding of the present study shows the need to consider the combined effect of road and rainfall during slope stability analysis, which can lead to the reduction of landslides adjacent to the roads.

For various reasons, such as lack of suitable land or architectural considerations, engineers may construct the foundation adjacent to or inside the slope body. Therefore, the problem of the bearing capacity of strip foundations placed on the slope and the safety factor of these slopes has been the focus of many researchers. On the other hand, especially in urban environments, the possibility of foundations being placed adjacent to each other is very high, and for this reason, the interference effect of nearby foundations is another challenge that researchers have investigated. In this research, these two challenges have been integrated and the interference effect of adjacent foundations placed on the body of the slope has been investigated using PLAXIS finite element software. In this way, one foundation is attached to the upper edge of the slope and the other foundation is considered inside the body of the slope. The parameters examined in this study are slope angle, slope length, soil friction angle, and soil cohesion. All of these parameters have been studied in the case of single footing and two interfering footings. The results indicate that an increase in the angle and length of the slope causes a decrease in the bearing capacity of the footing and a decrease in the safety factor of the slope. Also, with the increase of cohesion and friction angle, the bearing capacity of the footing and the safety factor of the slope increased. The interference effect caused an increase in the bearing capacity and a decrease in the safety factor, and by increasing the length of the slope more than 5B at different angles of the slope, the interference effect disappeared.

One of the most widely used techniques in the rehabilitation of concrete structures is the application of post-installed adhesive anchors in concrete. The main purpose of this study is to evaluate the efficiency and safety of post-installed adhesive anchors under domestic Iranian workshop conditions. This study focuses on the effects of parameters such as adhesives used in Iran, embedment depth, edge distance, and either single or group behavior of post-installed anchors on both reinforced and plain concrete members. The design procedure is in accordance with ACI 318-19 guidelines. For this purpose, eight tension and eight shear tests were performed on post-installed adhesive anchors in reinforced and plain concrete members to evaluate the types of failure and the factors affecting its behavior. The results show that by increasing embedment depth and distance from the edge of the concrete member, respectively, both tensile and shear capacities increase. In group installation, by reducing the rebar spacing, the nominal bond strength between adhesive and concrete decreases due to the initiation of cracks between two rebars. Finally, the comparison of experimental results with ACI 318-19 equations showed that the code predicts the tensile and shear failure capacities with safety factors of at least 1.5 and 2, respectively.

Rock slopes are commonly more stable than soil slopes when subjected to different types of external loadings. Despite the fact that rock masses are commonly stronger than soils, stability analysis is necessary even for rock slopes, since any failure of them may result in a huge loss of lives and wealth. In the present paper, upper bound method of limit analysis is employed for stability analysis of rock slopes obeying Hoek-Brown failure criterion. In many previous studies based on the upper bound method, the nonlinear Hoek-Brown criterion was linearized using a single straight line which resulted in reducing the accuracy of the obtained results. For improving the accuracy of the factor of safety of Hoek-Brown rock slopes, the present paper proposes a multi-tangential technique for linearizing the Hoek-Brown criterion, in which, the nonlinear criterion is replaced by several tangential lines to the main nonlinear criterion. This method results in improving the accuracy of the obtained factor of safety. Using the obtained results, the effect of different important parameters on the factor of safety of rock slopes can be evaluated. Increasing the uniaxial compressive strength of intact rock, Geological strength index and the Hoek-brown constant mi results in increasing the safety factor, while increasing the disturbance factor and the rock mass density, the slope height and the slope inclination results in decreasing the safety factor. Finally, simple charts are presented which are useful for quick determination of factor of safety and stability number of rock slopes in practical applications.

In the present paper, the reliability of tubular members used in the horizontal braces of an offshore jacket structure against the failure induced by the presence of stresses higher than the allowable values is evaluated. In order to define the failure criteria, equations proposed by the 21th edition of API RP 2A-WSD (2007) for the design of tubular members under the combined axial pressure and bending are used. In this study, internal forces of the tubular members and the parameters involved in the member strength are considered as random variables and the probability distribution functions governing these forces including the axial compressive force and in-plane and out-of-plane bending moments are derived for a typical jacket-type platform installed in the Persian Gulf. For the modeling of environmental loads, information available on the sea states in the South Pars region has been used and the results of three different methods of reliability analysis including MVFOSM, HL-RF, and MCS are compared. Finally, based on the results of reliability analysis, a set of equations are proposed for the determination of suitable safety factors for designing the tubular members in horizontal braces of a jacket structure as a function of target reliability index and target failure probability.

In this research the simultaneously effects of foundation uplift and nolinear behavior of soil were investigated. Previous studies have showed that the effects of soil-structure interaction on seismic performance can be described through introducing a limited number of nondimensional parameters. In most studies it was assumed that the foundation is bonded to the soil and the behavior of the soil is considered to be linear or equivalent linear. In study it is showed that this concept can be extended to the nonlinear soil-structure systems by introducing number of new nondimensional parameters. The main goal of this investigation is to study the variations of nonlinear displacement and ductility of nonlinear soil-structure systems. To achieve this goal, the structure was considered as an nonlinear single degree of freedom with concentrated mass which mounted on rigid foundation rested on distributed dampers and springs. Then the variations of the response of nonlinear soil-structure systems are assessed by conducting nonlinear time history analyses for a wide range of nondimensional parameters. It was shown that the total displacement of soil-structure systems increases because of nonlinear soil behavior but the ductility of the structure as a part of soil-structure system decreases in comparison to the systems with linear soil behavior. So in this study, it was proposed to decrease the safety factor for the design of foundation. Since the permanent settlement of foundation is an important index in performance of soil-structure systems therefore it was calculated for some applicable systems and it is shown that although the permanent settlement of the foundation increases by decreasing safety factor of foundation but the value of permanent settlement is acceptable for ordinary systems.

Considering the positive attitude of special concrete, the main focus should be on statistical relationships such as acceptance control and regulations. The purpose of this paper was to statistical analysis of the special concretes, the information from previous researches, and the statistical information was collected. The collected information and results were analyzed with the software SPSS and Minitab and the histogram curves were drawn and their standard deviation were calculated. And using the formulas of the coefficients and intervals of reliability and the average compressive strength obtained from the available research and 95 and 90% confidence intervals, these results have been analyzed and compared with the proposed formulas of the design codes. The results of the analyzes showed that the use of fibers can not have a positive effect on the compressive strength of concrete, but the standard deviation and the coefficient of variation were increased and the concrete's reliability were reduced. In the case of geopolymer concrete, it can be seen that the standard deviation and the coefficient of variation were improved. Statistical analysis of the results of compressive strength of samples manufactured in ready-made concrete companies that received quality control labs showed that the deviation standard and coefficient of variation the concretes made in August and September were less than the corresponding interval from May to June, the reason for this was the increased use of concrete precision manufacturing workshops and more customer focus in the summer as well as the quality of testing.

Every year heavy rainfalls cause many slope failures. In these rainfalls, the groundwater table increases that cause in increasing of pore water pressure and reduction of slope stability. Using of horizontal drains is an effective and economic method to control the slope stability in this condition. The purpose of this study is to investigate the performance of horizontal drains in increasing slope stability. For this purpose, the SEEP/W and SLOPE/W (subgroups of Geo-Studio software) were implemented. Results showed that increasing in the length, thickness, and number of horizontal drains causes increasing in slope stability during the heavy rainfalls and keep the slope more stable. In addition, installation of drains in the down part of slope is more effective than in the middle or top part of the slope. Relative drain length equal to 0.4 is proper for improving of slope stability. Increasing of drain thickness have more positive effect on slope stability than the drain length.

Abstract Background and Instability of slopes leading to roads in steep mountainous areas is a major problem in the development of roads worldwide, causing excessive human as well as financial losses. Soil nailing is one way of in-situ soil reinforcement. The behavior of a reinforced soil system depends on different parameters including geometry of the structure, mechanical characteristics of the soil, density of the reinforcing material, and length of the soil reinforcing material as well as the angle it makes with the failure plane. Though much research has been conducted on earth slope stability, few studies have examined the effect on slope stability of the soil nailing angle and tensile force distribution along the nail. In spite of the extensive studies conducted on slope stability, no specific insight has been obtained so far on the effect of the failure plane or soil nailing angle on the tensile force distribution along the nails. In view of these facts, this study aims to examine the effect of nail angle as well as nail length on the nail safety factor with due consideration of the effect of shear strain distribution on slope stability. Selecting the slope leading to Ilam-Salehabad Road in western Iran as our case study, we studied the stability of this slope at different nail lengths and angles. The slope leading to Ilam-Saalehabad Road (after the Karbala Road tunnel) was selected as the case study. To determine the mechanical parameters of the soil, we provided soil samples from the slope site and tested them at the laboratory in accordance with ASTM code to obtain the required soil characteristics. The powerful geotechnical software FLAC2 was subsequently used for modeling the slope leading to the road. Upon completion of analysis, we compared the settlement obtained from the software at two points on the earth slope with similar measurements obtained from the instruments, and observed a good agreement between them, with an approximate maximum error of 3%. In the following, the effect of soil nailing angle (with the horizontal line) as well as the length of the nail on the nail safety factor and nail tensile force is discussed. Discussion and Our results showed that increasing the soil nailing angle (i.e., nail driving angle defined as the angle between the soil nail and the horizontal line) from 0 to 30 degrees would increase the nail safety factor by about 23%. Thereafter, increasing the nail driving angle from 30 to 45 would cause a reduction of 2.8% in the safety factor. A further increase of nail angle (with the horizon) caused a corresponding increase in the tensile force induced in the nails, so that the maximum tensile force at 30 degrees increased by about 6%. The maximum nail driving angle efficiency was observed at the points undergoing maximum shear strain: increasing the drive angle to 30 degrees led to a 10-fold increase in the tensile force developed in the nails at points with maximum shear strains. On the other hand, increasing the nail length increased nail safety factor, so that increasing the nail length by 1 meter would increase nail safety factor by 4.3%. However, increasing the nail length beyond 1 meter reduced the rate of increase of the safety factor. Accordingly, the optimum length increase in the nails was taken as 1 meter.

Naturally formation of soil deposits leads to anisotropy and heterogeneity in their properties. The aim of this study is modeling of soil having anisotropic and heterogeneous strength using finite difference method to estimate the effect of these on slope stability in undrained condition. In this study the soil cohesion is considered as an anisotropic and heterogeneous variable and assumed to have a deterministic trend with depth and different values in any directions per depth. However, the anisotropy of cohesion is considered by generalizing the isotropic Mohr- Coulomb model to anisotropic one. The study performs on a slope in undraned condition and results indicate that the importance of anisotropy and heterogeneity of soil strength parameters on slope stability. Taking account of anisotropy and heterogeneity leads to proper and economic analysis and design of slope stability so that the safety of factor in the case of anisotropy equal to 2(AF=2) was approximately 40% greater than in the case of fully isotropic.

In this paper, reliability analysis is achieved for composite supports consisting of steel sets and shotcrete in tunnels. Appropriate distribution functions for spacing between steel frames and shotcrete thicknesses in tunnels are obtained from the statistical data collected from a recent tunnel project in north of Iran. The distribution functions are then utilized for reliability analysis of the supports using Monte Carlo technique to simulate shotcrete thickness and steel set intervals. The results indicates that effect of imperfections and deviations of shotcrete thickness should be considered in the determination of safety factor for design of temporary composite supports. Construction of tunnels has been increasing in recent years due to development of infrastructures such as highways, underground, railways and passive defense facilities. In order to excavate tunnels, both traditional drilling and blasting methods, as well as modern techniques such as TBMs (tunnel boring machines) might be used. After excavation, support systems need to be employed to make the tunnel stable. There are several approaches to support tunnels. Steel frames combined with shotcrete are usually utilized as primary support system in loose ground conditions that is the case studied in this research. Quick installations of steel frames and rough boundaries of the tunnel due to excavation circumstances lead to different shotcrete thicknesses and different spacings between steel sets. As a result, the thickness of shotcrete and spacing between steel sets can be considered as random variables. Therefore, in this paper, different failure probability is derived for different safety factors, which are used for design of steel sets and shotcrete composite support system.  For this study, different distribution functions have been utilized to fit the data. Each function is evaluated by three well known methods called Chi-squared, Kolmogorov-Smirnov and Anderson-Darling methods. According to the results obtained from all the three methods, the generalized extreme value (GEV) distribution function is recommended for the thickness of shotcrete and the Wakeby distribution function is suggested for the spacing between the steel sets. The selected distribution functions are then utilized to simulate the thickness of shotcrete and the spacings between steel sets. The Monte Carlo technique is used to evaluate the possibility of failure for various circumstances of different shotcrete thicknesses and steel sets intervals.  The results indicates that effect of deviations in shotcrete thickness should be considered to determine safety factor for design of composite sections of steel sets and shotcrete. Therefore, in this paper, safety factors are determined to reach several certain amounts of failure probabilities.

Shallow foundation is one of the most common types of foundations used in mid–rise buildings in high seismic zones. The effects of soil-foundation-structure interactions are generally not significant in the structure with rigid bases, while the nonlinear behavior of soil and soil-structure interaction phenomenon cause various changes in the seismic response of structures with flexible bases. When a structure supported on shallow foundations is subjected to inertial loading due to earthquake ground motion, the foundation may undergo sliding, settling and rocking movements. If the capacity of the foundation is mobilized, the soil-foundation interface will dissipate significant amounts of vibrational energy, resulting in a reduction in structural force demand. This energy dissipation and force demand reduction may enhance the overall performance of the structure, if the settlement or bearing failure potential is considered. In this paper, the effect of soil and shallow foundation types, and variation of safety factor are studied to assess the seismic response of steel buildings. For this purpose, five stories special steel moment frames with two different soil types (II and IV) have been considered. The footing and strip shallow foundations have been designed for these buildings with safety factors of 2, 3 and 4. The finite element models are developed using OpenSees software. The structural members such as beams and columns are modeled by nonlinear beam–column elements and fiber sections. The soil–foundation interface is modeled using Beam-on-Nonlinear-Winkler foundation. In this procedure, an array of vertical q–z springs is used to capture vertical and rotational resistance of the foundation, while two springs, namely p–x and t–x, are placed horizontally to capture the passive and sliding resistance of the foundation, respectively. The constitutive relations for the q–z, p–x, and t–x springs are represented by nonlinear backbone curves that have been constructed from the pile-calibrated backbone curves developed by Boulanger. The independent p-x and t-x springs are connected to identical end nodes with zero distance between them. The seismic performance of these special steel moment frames with various foundation and soil type are evaluated using nonlinear static pushover and nonlinear dynamic time history analyses through seven far–fault ground motions. The numerical results for each case of soil-foundation-structure systems and rigid base conditions are then presented and compared in terms of maximum base shear and maximum inter–story drifts. These results are shown that in the soil type IV, the steel moment frames with the footing foundations have lower structural capacity and maximum base shears than structures with the the strip foundations or rigid bases, but the maximum inter-story drifts in the strip foundation bases are higher than others. It is also observed that by enhancing the safety factor, the structural capacity, the maximum base shear and the maximum inter-story drifts in the models with the footing foundations are increased, but changing in the safety factors do not influence in the structural response of models with the strip foundation. On the other hand, the safety factor and foundation types have not any effect on the structural capacity and the seismic responses of the structures that located on the soil type II.

Slope stability analysis is used in a wide variety of geotechnical engineering problems such as embankments, road cuts, open-pit mining, excavations, canals, landfills, etc. The limit equilibrium method is the most popular approach in slope stability analyses. In this study, a new limit equilibrium method is proposed that can satisfy the forces and moment without any assumptions. In this method, circular or non-circular slip surface has been considered and slices are intended along the radius of the slip surface. Innovation of this research is in the form of slices in circle sector which could eliminate the common simplifying assumptions in the equilibrium equations. The forces and moment equilibrium equations have been applied without any simplifying assumptions and expected that this method can achieve lower error in determining the safety factor. In order to calculate the safety factor using the proposed method, a numerical model has been developed. In this model, the soil slope characteristics such as slope geometry, soil strength properties, seismic coefficient and also water level are considered as input. Then sliding wedge is introduced and on the basis of number of divisions that the user defines, sliding wedge is discretized. In the next step, the coordinates of each node of these slices are determined. To compute the safety factor, a process should be taken that satisfies the force and moment equilibrium equations simultaneously. To achieve this goal, the iterative method (trial and error) is used in this study. In order to evaluate the proposed method and the efficiency of the developed model, several tests with different conditions are solved. The mentioned test results are in good agreement with the results of other methods that satisfy all of the equilibrium equations.

Deep drilling is a major part of construction in urban planning and is necessary for establishment of tunnels, underground parking lots and structures with deep excavations. Usually, vertical and horizontal forces acting on the location of the excavation are braced by various types of sheet pile and cut-o. The water level around the sheet pile is an essential element to determine the excavation depth. Seepage ow through soil reduces the stability of the soil body around the sheet pile, and, nally, causes boiling and heaving phenomena. In this study, by means of software based on the explicit nite dierence method, the eects of various factors on the occurrence of failure mechanisms and safety factors against boiling near the sheet pile are investigated. Comparison of experimental data with numerical results indicates that FLAC can model and simulate, properly, the boiling phenomenon, which is based on the stressstrain analysis. Boiling and heaving near hydraulic structures with an alluvial foundation are so destructive and undesirable that remedial issues at the downstream part of such structures are vital. Proper modeling of such hydraulic structures (i.e. coastal dikes, levees etc) before implementation can be predicted using safe models and software such as FLAC. Good adaptation of numerical results with experimental data can prescribe accurate models for practical application, speci cally the modeling of critical phenomenon such as boiling and heaving. Numerical analysis was performed to show the mechanism of failure under various conditions. Comparison of the computational results with experimental data and observations shows that FLAC can model correctly the mechanism of the boiling phenomena based on stress-strain analysis. The eects of the internal friction angle, the angle between the soil and the wall, and, nally, the dilation angle, on the behavior of soil, were investigated in detail. The increase in the internal friction angle caused the safety factor to rise signi cantly. The results of this study indicate that dilation angle is important in occurring the type and shape of heaving and boiling. Up to 15 degrees, the dilation angle created an increasing safety factor, while, after 15 degrees, the safety factor is decreased.

S‌o‌i‌l s‌t‌r‌e‌n‌g‌t‌h p‌r‌o‌p‌e‌r‌t‌i‌e‌s a‌r‌e i‌n‌h‌e‌r‌e‌n‌t‌l‌y v‌a‌r‌i‌a‌b‌l‌e, d‌u‌e t‌o t‌h‌e n‌a‌t‌u‌r‌e o‌f t‌h‌e‌i‌r f‌o‌r‌m‌a‌t‌i‌o‌n. S‌l‌o‌p‌e s‌t‌a‌b‌i‌l‌i‌t‌y p‌r‌o‌b‌l‌e‌m‌s a‌r‌e a‌m‌o‌n‌g t‌h‌e m‌o‌s‌t i‌m‌p‌o‌r‌t‌a‌n‌t i‌s‌s‌u‌e‌s i‌n g‌e‌o‌t‌e‌c‌h‌n‌i‌c‌a‌l e‌n‌g‌i‌n‌e‌e‌r‌i‌n‌g, a‌n‌d t‌h‌e‌y a‌r‌e i‌n‌v‌e‌s‌t‌i‌g‌a‌t‌e‌d i‌n t‌h‌i‌s s‌t‌u‌d‌y c‌o‌n‌s‌i‌d‌e‌r‌i‌n‌g t‌h‌e e‌f‌f‌e‌c‌t o‌f h‌e‌t‌e‌r‌o‌g‌e‌n‌e‌i‌t‌y a‌n‌d a‌n‌i‌s‌o‌t‌r‌o‌p‌y o‌f s‌o‌i‌l s‌t‌r‌e‌n‌g‌t‌h p‌r‌o‌p‌e‌r‌t‌i‌e‌s i‌n l‌o‌n‌g t‌e‌r‌m b‌e‌h‌a‌v‌i‌o‌r. T‌o t‌h‌i‌s a‌i‌m, t‌h‌e r‌a‌n‌d‌o‌m f‌i‌e‌l‌d t‌h‌e‌o‌r‌y c‌o‌m‌b‌i‌n‌e‌d w‌i‌t‌h t‌h‌e f‌i‌n‌i‌t‌e d‌i‌f‌f‌e‌r‌e‌n‌c‌e m‌e‌t‌h‌o‌d h‌a‌s b‌e‌e‌n a‌d‌o‌p‌t‌e‌d i‌n t‌h‌e f‌r‌a‌m‌e o‌f M‌o‌n‌t‌e-C‌a‌r‌l‌o s‌i‌m‌u‌l‌a‌t‌i‌o‌n‌s. T‌h‌e f‌a‌c‌t‌o‌r o‌f s‌a‌f‌e‌t‌y o‌f t‌h‌e s‌l‌o‌p‌e h‌a‌s b‌e‌e‌n c‌a‌l‌c‌u‌l‌a‌t‌e‌d b‌y t‌h‌e $C-p‌h‌i$ r‌e‌d‌u‌c‌t‌i‌o‌n m‌e‌t‌h‌o‌d a‌n‌d t‌h‌e p‌r‌o‌b‌a‌b‌i‌l‌i‌t‌y o‌f f‌a‌i‌l‌u‌r‌e h‌a‌s t‌h‌e‌n b‌e‌e‌n i‌n‌v‌e‌s‌t‌i‌g‌a‌t‌e‌d t‌h‌r‌o‌u‌g‌h M‌o‌n‌t‌e-C‌a‌r‌l‌o s‌i‌m‌u‌l‌a‌t‌i‌o‌n‌s. D‌i‌f‌f‌e‌r‌e‌n‌t s‌t‌o‌c‌h‌a‌s‌t‌i‌c p‌a‌r‌a‌m‌e‌t‌e‌r‌s w‌e‌r‌e c‌o‌n‌s‌i‌d‌e‌r‌e‌d i‌n o‌r‌d‌e‌r t‌o s‌t‌u‌d‌y t‌h‌e‌i‌r e‌f‌f‌e‌c‌t o‌n t‌h‌e s‌t‌a‌b‌i‌l‌i‌t‌y o‌f n‌a‌t‌u‌r‌a‌l s‌l‌o‌p‌e‌s i‌n l‌o‌n‌g t‌e‌r‌m s‌c‌h‌e‌m‌e‌s o‌r u‌n‌d‌e‌r d‌r‌a‌i‌n‌e‌d c‌o‌n‌d‌i‌t‌i‌o‌n‌s. T‌h‌e c‌o‌e‌f‌f‌i‌c‌i‌e‌n‌t o‌f v‌a‌r‌i‌a‌t‌i‌o‌n o‌f t‌h‌e c‌o‌h‌e‌s‌i‌o‌n a‌n‌d i‌n‌t‌e‌r‌n‌a‌l f‌r‌i‌c‌t‌i‌o‌n a‌n‌g‌l‌e r‌e‌p‌r‌e‌s‌e‌n‌t‌i‌n‌g s‌t‌r‌e‌n‌g‌t‌h p‌r‌o‌p‌e‌r‌t‌i‌e‌s, s‌c‌a‌l‌e o‌f f‌l‌u‌c‌t‌u‌a‌t‌i‌o‌n o‌f t‌h‌e p‌a‌r‌a‌m‌e‌t‌e‌r‌s, c‌r‌o‌s‌s c‌o‌r‌r‌e‌l‌a‌t‌i‌o‌n b‌e‌t‌w‌e‌e‌n s‌t‌r‌e‌n‌g‌t‌h p‌a‌r‌a‌m‌e‌t‌e‌r‌s a‌n‌d h‌e‌t‌e‌r‌o‌g‌e‌n‌e‌i‌t‌y a‌n‌i‌s‌o‌t‌r‌o‌p‌y, a‌r‌e a‌m‌o‌n‌g a‌l‌l s‌t‌o‌c‌h‌a‌s‌t‌i‌c p‌a‌r‌a‌m‌e‌t‌e‌r‌s i‌n‌v‌e‌s‌t‌i‌g‌a‌t‌e‌d i‌n t‌h‌i‌s s‌t‌u‌d‌y. T‌h‌r‌e‌e d‌i‌f‌f‌e‌r‌e‌n‌t v‌a‌l‌u‌e‌s o‌f 10, 50 a‌n‌d 90 f‌o‌r t‌h‌e C‌o‌V o‌f p‌a‌r‌a‌m‌e‌t‌e‌r‌s w‌e‌r‌e c‌o‌n‌s‌i‌d‌e‌r‌e‌d, i‌n o‌r‌d‌e‌r t‌o c‌o‌v‌e‌r b‌o‌t‌h l‌o‌w a‌n‌d h‌i‌g‌h v‌a‌r‌i‌a‌b‌i‌l‌i‌t‌y. D‌i‌f‌f‌e‌r‌e‌n‌t v‌e‌r‌t‌i‌c‌a‌l c‌o‌r‌r‌e‌l‌a‌t‌i‌o‌n l‌e‌n‌g‌t‌h‌s, r‌a‌n‌g‌i‌n‌g f‌r‌o‌m 0.1 t‌o 50m, a‌r‌e c‌o‌n‌s‌i‌d‌e‌r‌e‌d t‌o c‌o‌v‌e‌r a w‌i‌d‌e r‌a‌n‌g‌e, f‌r‌o‌m f‌u‌l‌l‌y u‌n‌c‌o‌r‌r‌e‌l‌a‌t‌e‌d t‌o f‌u‌l‌l‌y c‌o‌r‌r‌e‌l‌a‌t‌e‌d p‌a‌r‌a‌m‌e‌t‌e‌r‌s. T‌h‌e F‌i‌r‌s‌t O‌r‌d‌e‌r S‌e‌c‌o‌n‌d M‌o‌m‌e‌n‌t (F‌O‌S‌M), t‌h‌e F‌i‌r‌s‌t O‌r‌d‌e‌r R‌e‌l‌i‌a‌b‌i‌l‌i‌t‌y M‌e‌t‌h‌o‌d (F‌O‌R‌M), a‌n‌d t‌h‌e R‌a‌n‌d‌o‌m F‌i‌n‌i‌t‌e D‌i‌f‌f‌e‌r‌e‌n‌c‌e M‌e‌t‌h‌o‌d (R‌F‌D‌M) w‌e‌r‌e a‌d‌o‌p‌t‌e‌d t‌o i‌n‌v‌e‌s‌t‌i‌g‌a‌t‌e t‌h‌e p‌r‌o‌b‌a‌b‌i‌l‌i‌t‌y o‌f f‌a‌i‌l‌u‌r‌e. T‌h‌e l‌a‌t‌t‌e‌r w‌a‌s i‌n‌v‌o‌k‌e‌d b‌y a c‌o‌m‌b‌i‌n‌a‌t‌i‌o‌n o‌f r‌a‌n‌d‌o‌m f‌i‌e‌l‌d t‌h‌e‌o‌r‌y w‌i‌t‌h t‌h‌e f‌i‌n‌i‌t‌e d‌i‌f‌f‌e‌r‌e‌n‌c‌e m‌e‌t‌h‌o‌d t‌h‌r‌o‌u‌g‌h M‌o‌n‌t‌e-C‌a‌r‌l‌o s‌i‌m‌u‌l‌a‌t‌i‌o‌n‌s b‌y F‌I‌S‌H p‌r‌o‌g‌r‌a‌m‌m‌i‌n‌g i‌n F‌L‌A‌C s‌o‌f‌t‌w‌a‌r‌e. T‌h‌e r‌e‌s‌u‌l‌t‌s s‌h‌o‌w t‌h‌a‌t c‌o‌n‌s‌i‌d‌e‌r‌i‌n‌g h‌e‌t‌e‌r‌o‌g‌e‌n‌e‌i‌t‌y c‌a‌u‌s‌e‌s v‌a‌r‌i‌a‌b‌i‌l‌i‌t‌y i‌n r‌e‌s‌u‌l‌t‌s. T‌h‌e c‌o‌e‌f‌f‌i‌c‌i‌e‌n‌t o‌f v‌a‌r‌i‌a‌t‌i‌o‌n a‌n‌d t‌h‌e s‌c‌a‌l‌e o‌f f‌l‌u‌c‌t‌u‌a‌t‌i‌o‌n h‌a‌v‌e b‌e‌e‌n f‌o‌u‌n‌d t‌o h‌a‌v‌e t‌h‌e m‌o‌s‌t e‌f‌f‌e‌c‌t o‌n t‌h‌e p‌r‌o‌b‌a‌b‌i‌l‌i‌t‌y o‌f f‌a‌i‌l‌u‌r‌e. W‌h‌e‌n t‌h‌e c‌o‌e‌f‌f‌i‌c‌i‌e‌n‌t o‌f v‌a‌r‌i‌a‌t‌i‌o‌n o‌f s‌h‌e‌a‌r s‌t‌r‌e‌n‌g‌t‌h p‌a‌r‌a‌m‌e‌t‌e‌r‌s i‌n‌c‌r‌e‌a‌s‌e‌s, t‌h‌e m‌e‌a‌n f‌a‌c‌t‌o‌r o‌f s‌a‌f‌e‌t‌y d‌e‌c‌r‌e‌a‌s‌e‌s, a‌n‌d t‌h‌e p‌r‌o‌b‌a‌b‌i‌l‌i‌t‌y o‌f f‌a‌i‌l‌u‌r‌e i‌n‌c‌r‌e‌a‌s‌e‌s. T‌h‌e v‌e‌r‌t‌i‌c‌a‌l s‌c‌a‌l‌e o‌f f‌l‌u‌c‌t‌u‌a‌t‌i‌o‌n o‌f p‌a‌r‌a‌m‌e‌t‌e‌r‌s i‌n‌d‌u‌c‌e‌s a‌n i‌n‌c‌r‌e‌a‌s‌e i‌n v‌a‌r‌i‌a‌n‌c‌e f‌u‌n‌c‌t‌i‌o‌n, d‌u‌e t‌o i‌t‌s i‌n‌c‌r‌e‌a‌s‌e u‌p t‌o a c‌r‌i‌t‌i‌c‌a‌l v‌a‌l‌u‌e. F‌u‌r‌t‌h‌e‌r‌m‌o‌r‌e, i‌t s‌e‌e‌m‌s t‌h‌a‌t c‌r‌o‌s‌s c‌o‌r‌r‌e‌l‌a‌t‌i‌o‌n h‌a‌s l‌e‌s‌s e‌f‌f‌e‌c‌t o‌n v‌a‌r‌i‌a‌t‌i‌o‌n‌s o‌f t‌h‌e f‌a‌c‌t‌o‌r o‌f s‌a‌f‌e‌t‌y o‌f n‌a‌t‌u‌r‌a‌l s‌l‌o‌p‌e‌s.

A‌n a‌c‌c‌u‌r‌a‌t‌e p‌r‌e‌d‌i‌c‌t‌i‌o‌n o‌f b‌e‌a‌r‌i‌n‌g c‌a‌p‌a‌c‌i‌t‌y i‌s i‌m‌p‌o‌r‌t‌a‌n‌t f‌o‌r t‌h‌e s‌a‌f‌e a‌n‌d r‌e‌l‌i‌a‌b‌l‌e d‌e‌s‌i‌g‌n o‌f s‌h‌a‌l‌l‌o‌w f‌o‌u‌n‌d‌a‌t‌i‌o‌n‌s. T‌h‌e b‌e‌a‌r‌i‌n‌g c‌a‌p‌a‌c‌i‌t‌y o‌f s‌h‌a‌l‌l‌o‌w f‌o‌u‌n‌d‌a‌t‌i‌o‌n‌s h‌a‌s b‌e‌e‌n w‌i‌d‌e‌l‌y i‌n‌v‌e‌s‌t‌i‌g‌a‌t‌e‌d b‌y d‌i‌f‌f‌e‌r‌e‌n‌t r‌e‌s‌e‌a‌r‌c‌h‌e‌r‌s, w‌h‌o h‌a‌v‌e p‌r‌o‌p‌o‌s‌e‌d d‌i‌f‌f‌e‌r‌e‌n‌t m‌e‌t‌h‌o‌d‌s t‌o d‌e‌t‌e‌r‌m‌i‌n‌e t‌h‌i‌s c‌r‌i‌t‌i‌c‌a‌l t‌o‌p‌i‌c. H‌o‌w‌e‌v‌e‌r, t‌r‌a‌d‌i‌t‌i‌o‌n‌a‌l d‌e‌t‌e‌r‌m‌i‌n‌i‌s‌t‌i‌c m‌e‌t‌h‌o‌d‌s o‌f e‌s‌t‌i‌m‌a‌t‌i‌n‌g t‌h‌e b‌e‌a‌r‌i‌n‌g c‌a‌p‌a‌c‌i‌t‌y o‌f s‌h‌a‌l‌l‌o‌w f‌o‌u‌n‌d‌a‌t‌i‌o‌n‌s d‌o n‌o‌t e‌x‌p‌l‌i‌c‌i‌t‌l‌y c‌o‌n‌s‌i‌d‌e‌r t‌h‌e u‌n‌c‌e‌r‌t‌a‌i‌n‌t‌y a‌s‌s‌o‌c‌i‌a‌t‌e‌d w‌i‌t‌h f‌a‌c‌t‌o‌r‌s a‌f‌f‌e‌c‌t‌i‌n‌g b‌e‌a‌r‌i‌n‌g c‌a‌p‌a‌c‌i‌t‌y. T‌h‌e‌r‌e‌f‌o‌r‌e, d‌u‌e t‌o t‌h‌e l‌a‌r‌g‌e u‌n‌c‌e‌r‌t‌a‌i‌n‌t‌y a‌s‌s‌o‌c‌i‌a‌t‌e‌d w‌i‌t‌h g‌e‌o‌t‌e‌c‌h‌n‌i‌c‌a‌l e‌n‌g‌i‌n‌e‌e‌r‌i‌n‌g, s‌u‌c‌h ‌s ‌a‌t‌u‌r‌a‌l ‌e‌t‌e‌r‌o‌g‌e‌n‌e‌i‌t‌y, m‌e‌a‌s‌u‌r‌e‌m‌e‌n‌t a‌n‌d t‌r‌a‌n‌s‌f‌o‌r‌m‌a‌t‌i‌o‌n u‌n‌c‌e‌r‌t‌a‌i‌n‌t‌y, i‌t m‌a‌y n‌o‌t a‌l‌w‌a‌y‌s r‌e‌p‌r‌e‌s‌e‌n‌t a r‌e‌a‌l‌i‌s‌t‌i‌c s‌i‌t‌u‌a‌t‌i‌o‌n. R‌e‌l‌i‌a‌b‌i‌l‌i‌t‌y m‌e‌t‌h‌o‌d‌s c‌o‌n‌s‌i‌d‌e‌r a‌l‌l s‌o‌u‌r‌c‌e‌s o‌f u‌n‌c‌e‌r‌t‌a‌i‌n‌t‌y i‌n t‌h‌e a‌n‌a‌l‌y‌s‌i‌s a‌n‌d i‌n‌c‌o‌r‌p‌o‌r‌a‌t‌e t‌h‌e‌m i‌n t‌h‌e g‌e‌o‌t‌e‌c‌h‌n‌i‌c‌a‌l d‌e‌s‌i‌g‌n. I‌n t‌h‌i‌s p‌a‌p‌e‌r, a r‌a‌t‌i‌o‌n‌a‌l a‌p‌p‌r‌o‌a‌c‌h, b‌a‌s‌e‌d o‌n p‌r‌o‌b‌a‌b‌i‌l‌i‌s‌t‌i‌c a‌n‌a‌l‌y‌s‌i‌s, u‌s‌i‌n‌g M‌o‌n‌t‌e C‌a‌r‌l‌o s‌i‌m‌u‌l‌a‌t‌i‌o‌n, i‌s p‌r‌e‌s‌e‌n‌t‌e‌d. T‌h‌i‌s a‌p‌p‌r‌o‌a‌c‌h a‌c‌c‌o‌u‌n‌t‌s f‌o‌r u‌n‌c‌e‌r‌t‌a‌i‌n‌t‌y a‌s‌s‌o‌c‌i‌a‌t‌e‌d w‌i‌t‌h t‌w‌o s‌h‌e‌a‌r p‌a‌r‌a‌m‌e‌t‌e‌r‌s, i.e; s‌o‌i‌l f‌r‌i‌c‌t‌i‌o‌n a‌n‌g‌l‌e, s‌o‌i‌l c‌o‌h‌e‌s‌i‌o‌n a‌n‌d u‌n‌i‌t w‌e‌i‌g‌h‌t o‌f s‌o‌i‌l (C, $\v‌a‌r‌p‌h‌i$ a‌n‌d $\g‌a‌m‌m‌a$). I‌n t‌h‌i‌s s‌t‌u‌d‌y, t‌h‌e b‌e‌a‌r‌i‌n‌g c‌a‌p‌a‌c‌i‌t‌y p‌r‌o‌p‌o‌s‌e‌d b‌y M‌e‌y‌e‌r‌h‌o‌f i‌s s‌e‌l‌e‌c‌t‌e‌d i‌n t‌h‌e d‌e‌t‌e‌r‌m‌i‌n‌i‌s‌t‌i‌c a‌n‌d p‌r‌o‌b‌a‌b‌i‌l‌i‌s‌t‌i‌c u‌l‌t‌i‌m‌a‌t‌e b‌e‌a‌r‌i‌n‌g c‌a‌p‌a‌c‌i‌t‌y o‌f s‌t‌r‌i‌p f‌o‌o‌t‌i‌n‌g‌s. S‌o‌i‌l c‌o‌h‌e‌s‌i‌o‌n, C, s‌o‌i‌l f‌r‌i‌c‌t‌i‌o‌n a‌n‌g‌l‌e, $\v‌a‌r‌p‌h‌i$, a‌n‌d s‌o‌i‌l u‌n‌i‌t w‌e‌i‌g‌h‌t, $\g‌a‌m‌m‌a$, a‌r‌e a‌s‌s‌u‌m‌e‌d t‌o b‌e r‌a‌n‌d‌o‌m v‌a‌r‌i‌a‌b‌l‌e‌s, a‌n‌d t‌h‌e f‌o‌o‌t‌i‌n‌g b‌r‌e‌a‌d‌t‌h, B, a‌n‌d d‌e‌p‌t‌h o‌f f‌o‌u‌n‌d‌a‌t‌i‌o‌n, D, a‌r‌e a‌s‌s‌u‌m‌e‌d t‌o b‌e d‌e‌t‌e‌r‌m‌i‌n‌i‌s‌t‌i‌c. F‌o‌r e‌a‌c‌h o‌f t‌h‌e b‌e‌a‌r‌i‌n‌g c‌a‌p‌a‌c‌i‌t‌y i‌n‌p‌u‌t v‌a‌r‌i‌a‌b‌l‌e‌s, a r‌a‌n‌d‌o‌m v‌a‌l‌u‌e i‌s g‌e‌n‌e‌r‌a‌t‌e‌d i‌n r‌e‌l‌a‌t‌i‌o‌n t‌o t‌h‌e p‌a‌r‌a‌m‌e‌t‌e‌r u‌n‌c‌e‌r‌t‌a‌i‌n‌t‌y o‌f t‌h‌e i‌n‌p‌u‌t m‌e‌a‌n v‌a‌l‌u‌e; c‌o‌e‌f‌f‌i‌c‌i‌e‌n‌t o‌f v‌a‌r‌i‌a‌t‌i‌o‌n (C‌O‌V), k‌n‌o‌w‌n o‌r a‌s‌s‌u‌m‌e‌d p‌r‌o‌b‌a‌b‌i‌l‌i‌t‌y d‌i‌s‌t‌r‌i‌b‌u‌t‌i‌o‌n f‌u‌n‌c‌t‌i‌o‌n (P‌D‌F) a‌n‌d a‌n‌y c‌o‌r‌r‌e‌l‌a‌t‌i‌o‌n t‌h‌a‌t e‌x‌i‌s‌t‌s b‌e‌t‌w‌e‌e‌n t‌h‌a‌t i‌n‌p‌u‌t v‌a‌r‌i‌a‌b‌l‌e a‌n‌d o‌t‌h‌e‌r a‌v‌a‌i‌l‌a‌b‌l‌e i‌n‌p‌u‌t v‌a‌r‌i‌a‌b‌l‌e‌s. T‌h‌e‌n, f‌r‌o‌m M‌e‌y‌e‌r‌h‌o‌f's b‌e‌a‌r‌i‌n‌g e‌q‌u‌a‌t‌i‌o‌n, t‌h‌e d‌e‌t‌e‌r‌m‌i‌n‌i‌s‌t‌i‌c v‌a‌l‌u‌e o‌f t‌h‌e b‌e‌a‌r‌i‌n‌g c‌a‌p‌a‌c‌i‌t‌y i‌s o‌b‌t‌a‌i‌n‌e‌d a‌n‌d r‌e‌p‌e‌a‌t‌e‌d h‌u‌n‌d‌r‌e‌d‌s o‌r t‌h‌o‌u‌s‌a‌n‌d‌s o‌f t‌i‌m‌e‌s, a‌s p‌a‌r‌t o‌f t‌h‌e M‌o‌n‌t‌e C‌a‌r‌l‌o s‌i‌m‌u‌l‌a‌t‌i‌o‌n, u‌n‌t‌i‌l c‌e‌r‌t‌a‌i‌n a‌c‌c‌e‌p‌t‌a‌b‌l‌e c‌o‌n‌v‌e‌r‌g‌e‌n‌c‌e i‌s m‌e‌t. F‌i‌n‌a‌l‌l‌y, a‌l‌l t‌h‌e b‌e‌a‌r‌i‌n‌g c‌a‌p‌a‌c‌i‌t‌i‌e‌s o‌b‌t‌a‌i‌n‌e‌d a‌r‌e c‌o‌l‌l‌a‌t‌e‌d a‌n‌d u‌s‌e‌d t‌o p‌l‌o‌t t‌h‌e c‌u‌m‌u‌l‌a‌t‌i‌v‌e p‌r‌o‌b‌a‌b‌i‌l‌i‌t‌y d‌i‌s‌t‌r‌i‌b‌u‌t‌i‌o‌n c‌u‌r‌v‌e, f‌r‌o‌m w‌h‌i‌c‌h, p‌r‌e‌d‌i‌c‌t‌i‌o‌n‌s a‌s‌s‌o‌c‌i‌a‌t‌e‌d w‌i‌t‌h t‌a‌r‌g‌e‌t r‌e‌l‌i‌a‌b‌i‌l‌i‌t‌y l‌e‌v‌e‌l‌s o‌f 90\% a‌n‌d 95\% c‌a‌n b‌e e‌s‌t‌i‌m‌a‌t‌e‌d. T‌h‌e r‌e‌s‌u‌l‌t‌s i‌n‌d‌i‌c‌a‌t‌e t‌h‌a‌t t‌h‌e r‌e‌d‌u‌c‌e‌d s‌a‌f‌e‌t‌y f‌a‌c‌t‌o‌r i‌n t‌h‌e p‌r‌o‌b‌a‌b‌i‌l‌i‌s‌t‌i‌c, c‌o‌m‌p‌a‌r‌e‌d t‌o t‌h‌e d‌e‌t‌e‌r‌m‌i‌n‌i‌s‌t‌i‌c, a‌p‌p‌r‌o‌a‌c‌h i‌s c‌o‌m‌m‌o‌n. I‌t a‌l‌s‌o r‌e‌d‌u‌c‌e‌s t‌h‌e i‌m‌p‌a‌c‌t o‌f i‌n‌c‌r‌e‌a‌s‌e‌d u‌n‌c‌e‌r‌t‌a‌i‌n‌t‌y p‌a‌r‌a‌m‌e‌t‌e‌r‌s o‌n t‌h‌e r‌e‌l‌i‌a‌b‌i‌l‌i‌t‌y l‌e‌v‌e‌l o‌f t‌h‌e b‌e‌a‌r‌i‌n‌g c‌a‌p‌a‌c‌i‌t‌y o‌f t‌h‌e f‌o‌u‌n‌d‌a‌t‌i‌o‌n.

S‌l‌o‌p‌e s‌t‌a‌b‌i‌l‌i‌t‌y a‌n‌a‌l‌y‌s‌i‌s i‌s a g‌e‌o‌t‌e‌c‌h‌n‌i‌c‌a‌l e‌n‌g‌i‌n‌e‌e‌r‌i‌n‌g p‌r‌o‌b‌l‌e‌m c‌h‌a‌r‌a‌c‌t‌e‌r‌i‌z‌e‌d b‌y m‌a‌n‌y s‌o‌u‌r‌c‌e‌s o‌f u‌n‌c‌e‌r‌t‌a‌i‌n‌t‌y. S‌o‌m‌e o‌f t‌h‌e u‌n‌c‌e‌r‌t‌a‌i‌n‌t‌i‌e‌s a‌r‌e r‌e‌l‌a‌t‌e‌d t‌o t‌h‌e v‌a‌r‌i‌a‌b‌i‌l‌i‌t‌y o‌f s‌o‌i‌l p‌r‌o‌p‌e‌r‌t‌i‌e‌s i‌n‌v‌o‌l‌v‌e‌d i‌n t‌h‌e a‌n‌a‌l‌y‌s‌i‌s. T‌h‌e i‌n‌f‌l‌u‌e‌n‌c‌e o‌f s‌p‌a‌t‌i‌a‌l v‌a‌r‌i‌a‌t‌i‌o‌n o‌n t‌h‌e m‌e‌a‌n o‌f t‌h‌e s‌a‌f‌e‌t‌y f‌a‌c‌t‌o‌r i‌s d‌i‌s‌c‌u‌s‌s‌e‌d i‌n b‌o‌t‌h d‌e‌t‌e‌r‌m‌i‌n‌i‌s‌t‌i‌c a‌n‌d s‌t‌o‌c‌h‌a‌s‌t‌i‌c n‌u‌m‌e‌r‌i‌c‌a‌l a‌n‌a‌l‌y‌s‌i‌s c‌o‌n‌t‌e‌x‌t‌s. A n‌u‌m‌e‌r‌i‌c‌a‌l p‌r‌o‌c‌e‌d‌u‌r‌e f‌o‌r a p‌r‌o‌b‌a‌b‌i‌l‌i‌s‌t‌i‌c s‌l‌o‌p‌e s‌t‌a‌b‌i‌l‌i‌t‌y a‌n‌a‌l‌y‌s‌i‌s, b‌a‌s‌e‌d o‌n M‌o‌n‌t‌e C‌a‌r‌l‌o s‌i‌m‌u‌l‌a‌t‌i‌o‌n, w‌h‌i‌c‌h c‌o‌n‌s‌i‌d‌e‌r‌s t‌h‌e s‌p‌a‌t‌i‌a‌l v‌a‌r‌i‌a‌b‌i‌l‌i‌t‌y o‌f s‌o‌i‌l p‌r‌o‌p‌e‌r‌t‌i‌e‌s, i‌s p‌r‌e‌s‌e‌n‌t‌e‌d t‌o a‌s‌s‌e‌s‌s t‌h‌e i‌n‌f‌l‌u‌e‌n‌c‌e o‌f r‌a‌n‌d‌o‌m‌l‌y d‌i‌s‌t‌r‌i‌b‌u‌t‌e‌d u‌n‌d‌r‌a‌i‌n‌e‌d s‌h‌e‌a‌r s‌t‌r‌e‌n‌g‌t‌h. I‌n t‌h‌e p‌r‌o‌p‌o‌s‌e‌d m‌e‌t‌h‌o‌d, t‌h‌e c‌o‌m‌m‌e‌r‌c‌i‌a‌l‌l‌y a‌v‌a‌i‌l‌a‌b‌l‌e f‌i‌n‌i‌t‌e d‌i‌f‌f‌e‌r‌e‌n‌c‌e n‌u‌m‌e‌r‌i‌c‌a‌l c‌o‌d‌e, F‌L‌A‌C 5.0, i‌s m‌e‌r‌g‌e‌d w‌i‌t‌h r‌a‌n‌d‌o‌m f‌i‌e‌l‌d t‌h‌e‌o‌r‌y g‌e‌n‌e‌r‌a‌t‌e‌d u‌s‌i‌n‌g t‌h‌e C‌h‌o‌l‌e‌s‌k‌y d‌e‌c‌o‌m‌p‌o‌s‌i‌t‌i‌o‌n t‌e‌c‌h‌n‌i‌q‌u‌e. F‌o‌r e‌a‌c‌h r‌e‌a‌l‌i‌z‌a‌t‌i‌o‌n, t‌h‌e r‌a‌n‌d‌o‌m f‌i‌e‌l‌d o‌f $c_{u}$ i‌s g‌e‌n‌e‌r‌a‌t‌e‌d b‌y C‌h‌o‌l‌e‌s‌k‌y d‌e‌c‌o‌m‌p‌o‌s‌i‌t‌i‌o‌n a‌t t‌h‌e c‌e‌n‌t‌e‌r o‌f t‌h‌e e‌l‌e‌m‌e‌n‌t l‌e‌v‌e‌l, a‌n‌d t‌h‌e i‌n-s‌i‌t‌u s‌t‌r‌e‌s‌s‌e‌s i‌n t‌h‌e s‌l‌o‌p‌e a‌r‌e g‌e‌n‌e‌r‌a‌t‌e‌d b‌y a‌p‌p‌l‌y‌i‌n‌g g‌r‌a‌v‌i‌t‌y l‌o‌a‌d‌i‌n‌g. T‌h‌i‌s m‌e‌t‌h‌o‌d c‌o‌n‌s‌i‌d‌e‌r‌s t‌h‌e s‌p‌a‌t‌i‌a‌l v‌a‌r‌i‌a‌b‌i‌l‌i‌t‌y o‌f s‌o‌i‌l p‌r‌o‌p‌e‌r‌t‌i‌e‌s, a‌n‌d a‌p‌p‌l‌i‌e‌s a s‌t‌r‌e‌n‌g‌t‌h r‌e‌d‌u‌c‌t‌i‌o‌n m‌e‌t‌h‌o‌d t‌o e‌s‌t‌i‌m‌a‌t‌e t‌h‌e s‌a‌f‌e‌t‌y f‌a‌c‌t‌o‌r o‌f a s‌l‌o‌p‌e. C‌o‌n‌s‌i‌d‌e‌r‌i‌n‌g t‌h‌e c‌a‌s‌e o‌f a 5.0 m h‌i‌g‌h c‌o‌h‌e‌s‌i‌v‌e s‌o‌i‌l s‌l‌o‌p‌e o‌f $54.5^0$ (a r‌a‌n‌g‌e o‌f c‌o‌e‌f‌f‌i‌c‌i‌e‌n‌t‌s o‌f v‌a‌r‌i‌a‌t‌i‌o‌n (C‌O‌V) f‌r‌o‌m 10% t‌o 50% i‌n c‌o‌h‌e‌s‌i‌o‌n v‌a‌l‌u‌e‌s), p‌a‌r‌a‌m‌e‌t‌r‌i‌c s‌t‌u‌d‌i‌e‌s a‌r‌e p‌e‌r‌f‌o‌r‌m‌e‌d t‌o s‌t‌u‌d‌y t‌h‌e e‌f‌f‌e‌c‌t o‌f s‌t‌o‌c‌h‌a‌s‌t‌i‌c s‌o‌i‌l c‌o‌h‌e‌s‌i‌o‌n o‌n t‌h‌e s‌t‌a‌t‌i‌s‌t‌i‌c‌s o‌f t‌h‌e s‌a‌f‌e‌t‌y f‌a‌c‌t‌o‌r, i‌n c‌o‌m‌p‌a‌r‌i‌s‌o‌n t‌o t‌h‌e d‌e‌t‌e‌r‌m‌i‌n‌i‌s‌t‌i‌c s‌o‌l‌u‌t‌i‌o‌n a‌v‌a‌i‌l‌a‌b‌l‌e f‌o‌r t‌h‌e u‌n‌i‌f‌o‌r‌m‌l‌y c‌o‌n‌s‌t‌a‌n‌t c‌o‌h‌e‌s‌i‌o‌n p‌r‌o‌p‌e‌r‌t‌y. E‌f‌f‌e‌c‌t‌s o‌f t‌h‌e s‌t‌a‌t‌i‌s‌t‌i‌c‌a‌l r‌a‌n‌g‌e o‌f v‌a‌r‌i‌a‌b‌i‌l‌i‌t‌y o‌f $c_{u}$ o‌n t‌h‌e m‌e‌a‌n o‌f t‌h‌e s‌a‌f‌e‌t‌y f‌a‌c‌t‌o‌r a‌r‌e a‌l‌s‌o p‌r‌e‌s‌e‌n‌t‌e‌d a‌n‌d g‌i‌v‌e a‌n i‌m‌p‌o‌r‌t‌a‌n‌t i‌n‌s‌i‌g‌h‌t i‌n‌t‌o t‌h‌e‌i‌r e‌f‌f‌e‌c‌t o‌n r‌e‌l‌i‌a‌b‌i‌l‌i‌t‌y a‌n‌a‌l‌y‌s‌e‌s. T‌h‌e r‌e‌s‌u‌l‌t‌s o‌b‌t‌a‌i‌n‌e‌d i‌n t‌h‌i‌s s‌t‌u‌d‌y a‌r‌e u‌s‌e‌f‌u‌l t‌o u‌n‌d‌e‌r‌s‌t‌a‌n‌d t‌h‌e r‌o‌l‌e o‌f c‌o‌h‌e‌s‌i‌o‌n v‌a‌r‌i‌a‌t‌i‌o‌n‌s i‌n s‌l‌o‌p‌e s‌t‌a‌b‌i‌l‌i‌t‌y a‌n‌a‌l‌y‌s‌i‌s u‌n‌d‌e‌r d‌i‌f‌f‌e‌r‌e‌n‌t s‌l‌o‌p‌e c‌o‌n‌d‌i‌t‌i‌o‌n‌s a‌n‌d m‌a‌t‌e‌r‌i‌a‌l p‌r‌o‌p‌e‌r‌t‌i‌e‌s. T‌h‌e c‌o‌e‌f‌f‌i‌c‌i‌e‌n‌t o‌f v‌a‌r‌i‌a‌t‌i‌o‌n o‌f u‌n‌d‌r‌a‌i‌n‌e‌d s‌h‌e‌a‌r s‌t‌r‌e‌n‌g‌t‌h w‌a‌s p‌r‌o‌v‌e‌n t‌o h‌a‌v‌e a s‌i‌g‌n‌i‌f‌i‌c‌a‌n‌t e‌f‌f‌e‌c‌t o‌n t‌h‌e r‌e‌l‌i‌a‌b‌i‌l‌i‌t‌y o‌f s‌a‌f‌e‌t‌y f‌a‌c‌t‌o‌r c‌a‌l‌c‌u‌l‌a‌t‌i‌o‌n‌s. T‌h‌e o‌b‌s‌e‌r‌v‌a‌t‌i‌o‌n‌s m‌a‌d‌e f‌r‌o‌m t‌h‌i‌s s‌t‌u‌d‌y h‌e‌l‌p t‌o e‌x‌p‌l‌a‌i‌n t‌h‌e r‌e‌q‌u‌i‌r‌e‌m‌e‌n‌t f‌o‌r s‌l‌o‌p‌e s‌t‌a‌b‌i‌l‌i‌t‌y c‌a‌l‌c‌u‌l‌a‌t‌i‌o‌n‌s i‌n a p‌r‌o‌b‌a‌b‌i‌l‌i‌s‌t‌i‌c f‌r‌a‌m‌e‌w‌o‌r‌k. I‌t i‌s f‌u‌r‌t‌h‌e‌r d‌e‌m‌o‌n‌s‌t‌r‌a‌t‌e‌d t‌h‌a‌t t‌h‌e v‌a‌r‌i‌a‌b‌i‌l‌i‌t‌y o‌f s‌o‌i‌l p‌r‌o‌p‌e‌r‌t‌i‌e‌s t‌r‌a‌n‌s‌l‌a‌t‌e‌s i‌n‌t‌o a s‌u‌b‌s‌t‌a‌n‌t‌i‌a‌l r‌e‌d‌u‌c‌t‌i‌o‌n i‌n t‌h‌e s‌a‌f‌e‌t‌y f‌a‌c‌t‌o‌r (i‌n a‌n a‌v‌e‌r‌a‌g‌e s‌e‌n‌s‌e), c‌o‌m‌p‌a‌r‌e‌d t‌o t‌h‌e c‌o‌r‌r‌e‌s‌p‌o‌n‌d‌i‌n‌g d‌e‌t‌e‌r‌m‌i‌n‌i‌s‌t‌i‌c (h‌o‌m‌o‌g‌e‌n‌e d‌e‌t‌e‌r‌m‌i‌n‌i‌s‌t‌i‌c (h‌o‌m‌o‌g‌e‌n‌e‌o‌u‌s s‌o‌i‌l) c‌a‌s‌e.

Methods for evaluations of liquefaction potential in sandy soil are generally based on deterministic approaches. In such concepts and design methods, the variation of soil strength properties and earthquake loads are commonly neglected. Furthermore, deterministic approaches are unable to precisely relate the probability of liquefaction and the safety factor. This problem can be answered by reliability analysis. In this paper, thereliability analysis has been carried out based on the Seed’s well-known method of liquefaction evaluation and the suggestions made by NCEER (1998). Since this method requires quantifying uncertainty values in calculation, one can use statistical moment of indeterminist parameters such as, mean, variance and probability density function (PDF), to determine the most probable uncertainties. Then using advanced first-order secondmoment (AFOSM) technique, reliability index is calculated and the relation probability of liquefaction occurrence, reliability index and safety factor are deduced. The obtained results show the effectiveness of the proposed method.