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GEOLOGY, ECOLOGY, AND LANDSCAPES INWASCON https://doi.org/10.1080/24749508.2023.2167434 Correlations between factor of safety with distributed load and crest length – Zariwam landslide as case study Muhammad Israr Khan School of Resources and Civil Engineering, Northeastern University China, Shenyang city, Liaoning province, China ABSTRACT ARTICLE HISTORY Received 25 July 2022 This paper examines the impact on Factor of Safety (FS) value due to the variation in distributed Accepted 8 January 2023 load (L ), Crest length (C ), shear strength (τ), and shear stress (σ) both in seismic and non- D L seismic conditions. The main purpose of this paper is to develop correlations between these KEYWORDS parameters, which can be used in any slope stability analysis design project. Forty number of Slope stability; factor of analyses are performed by considering different soil material properties. Slope stability analysis safety; numerical modelling; is performed using Slide software and correlations are developed using Statistical Package for surcharge load; correlations Social Sciences (SPSS) software as well as with the help of Microsoft Excel. The analysis results indicate that the seismic slope stability analysis gives optimum value for slope FS and therefore it is highly recommended to perform and give preference to seismic slope stability analysis of any soil slope to compute and recommend FS value. The main novelty of this paper are the eight new correlations. These correlations can be used in slope stability projects like earthfill dams design, embankments, or any slope design project or case study to know about the slope factor of safety in detail. 1. Introduction There are many reasons which lead to the decrease in shear strength of soil and increase in shear stress, such It is important to understand slope stability analysis as, increased pore pressure due to raining, swelling, issues for two major reasons. First, for the purpose of cracking, development of slickensides, decomposition designing and constructing new soil slopes, it is of clayey rock fills, creep under sustained loads, leach- important to be able to identify changes in soil struc- ing, strain softening, weathering, cyclic loading, water tures and materials within the slope that may occur pressure in cracks at the top of the slope, increase in with the passage of time and the various loading and soil weight due to increased water content, excavation unloading conditions in which the slope will be set for at the bottom of the slope, drop in water level at the its lifetime. Second, in order to repair failed slopes, it is base of a slope, earthquake shaking, and loads at the important to understand the key elements of the situa- top of the slope. All these reasons are well explained in tion that lead to the failure, in order to avoid repetition one of the book (Duncan et al., 2014). Recently, many of failure. Experience is the best teacher and from researchers investigated seismic slope stability analysis experience the slope failure comes with important and provided very useful results (see, for example, lessons that what steps are needed to design, build, Bandara et al., 2018; Havenith et al., 2016; Ishii et al., and repair slopes so that it remains stable and safe. In 2012; HW Huang et al., 2018; Johari et al., 2015; Johari discussing the various causes of slope failure, it is & Khodaparast, 2015; Kalantari & Johari, 2022; Marc useful to begin by considering the basic requirement et al., 2016; Rodríguez-Ochoa et al., 2015; Xiao et al., for slope stability. The shear resistance of the soil must 2016; Serey et al., 2019; Tian et al., 2017; Wu, 2015). be greater than the shear stresses. Given this basic Even if the shear strength of the soil does not change, requirement, it follows that the most important cause the slopes may fail if the distributed loads acting on of instability is that, for some reason, the shear resis- slope changes, leading to increased shear stresses tance in the ground is less than the shear destabilizing within the soil. If the ground at the top of the slope forces required for equilibrium. This situation is is loaded, the shear resistance required for the slope to because of two reasons: withstand against the loads will increase. To avoid increasing the shear stresses on the slope, such loads (1) With a decrease in ground shear strength should be kept at a reasonable optimum distance of (2) With increasing shear stresses required for the slope. An acceptable distance can be determined equilibrium. through slope stability analysis. The crest length must CONTACT Muhammad Israr Khan 1727011@stu.neu.edu.cn Room number 309, School of Resources and Civil Engineering, Northeastern University China,110819, China © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the International Water, Air & Soil Conservation Society(INWASCON). This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 2 M. I. KHAN be such that at least 1.5 value for Factor of Safety (FS) FS ¼ FS xR (3) 3Dm 2Dm 3D=2D is achieved, which is the minimum requirement for where FS is 3-dimensional slope factor of safety, 3Dm a safe slope as mentioned (Das et al., 2010). There is FS is 2-dimensional slope factor of safety, and 2Dm a strong correlation between the slope failure and the R is the ratio of 3d and 2d slope factor of safety. 3D/2D ground acceleration within the study area, which are This equation is valid only in high-risk areas where large mainly due to the different geographical features all uncertainty is found in the soil parameters. In case of over the world (Tiwari et al., 2017). Accurate and medium uncertainty in the soil properties and para- rapid forecasting of the stability of a landslide is cri- meters, the following correlations are developed in the tical for emergency response planning. However, cur- same work: rent methods of predicting rapid landslides cannot fully address the impact of soil size distribution FS FS 3D 2Dm FS ¼ FS þ (4) 3Dm 2Dm (Shan et al., 2020). As the material properties are FS 2Dm different at different places, the mapping slope stabi- A simplified version of Eq. (4), including R3D/2D, is lity predictions or analysis based on Geographical shown in Eq. (5): Information System (GIS) provided in many of the research papers (Ba et al., 2017; Ballabio & Sterlaccini, FS ¼ FS þ R 1 (5) 3Dm 2Dm 3D=2D 2012; Feizizadeh et al., 2013, 2014; L Liu et al., 2019) Similarly, for low uncertainty in soil parameters, the are not useful to apply for other regions. Every site following correlations are developed: must be properly investigated and tested to find out the material properties of that specific site. Boreholes FS FS 3D 2Dm FS ¼ FS þ (6) 3Dm 2Dm and non-destructive tests are required to compute the FS 3D mechanical properties of soil. Research (Deng et al., Assuming the 2D FS in R is the minimum 2D FS, 2016) results show that the external load calculation 3D/2D a simplified version of Eq. (6) is shown in Eq. (7): mode has little effect on slope stability. If the different external load patterns are equal, the slope stability R 1 3D=2D FS ¼ þ FS (7) under these external loads is the same, and if not, the 3Dm 2Dm 3D=2D external load leads to a better position of the slopes, as the position of the external load effect is closer to the Many other research works are done on the same topic lower slide slip point. FS value is dependent on the to compute the slope factor of safety in different con- surcharge load (S ) as well as the crest length (C ) of ditions and different soil properties. For example, L L the slope. some of the research papers titles on the same topic Keeping all these points in consideration, a pre- are as follows: defined soil slope is analyzed in this paper to examine and correlate FS with the variation of surcharge dis- (1) Discussion of “Probabilistic seismic slope sta- tributed load and its position on the slope surface. bility analysis and design” (W. Huang, 2019) (2) Influence of cross correlation between soil parameters on probability of failure of simple cohesive and c-ϕ slopes (Javankhoshdel & 1.1. Previous research on the topic Bathurst, 2015) Considering c-ϕ soil, Javankhoshdel and Bathurst (3) Evaluation of slope stability by finite element (2014) developed a correlation for slope factor of method using observed displacement of land- safety as slide (Ishii et al., 2012) (4) Revisiting strength concepts and correlations Fs ¼ (1) with soil index properties: insights from the γHN Dobkovičky landslide in Czech Republic where Su is undrained shear strength; γ is total unit (Roháč et al., 2020) weight; H is the height of slope; and Ns is a stability (5) Reliability analysis of slope stability under seis- number. mic condition during a given exposure time J Xiao et al. (2016) correlated the slope factor of (Huang et al., 2018) safety with the total elastic deformation energy (e ) (6) Development of empirical correlations for limit and ultimate deformation energy (e ) as equilibrium methods of slope stability analysis rffiffiffiffi (Moawwez et al., 2020) Fs ¼ (2) (7) Reliability approach to slope stability analysis with spatially correlated soil properties (Kim & Stark and Ruffing (2017) developed correlations Sitarb, 2013) between 2-dimensional and 3-dimensional slope sta- (8) Probabilistic slope stability analysis in sensitive bility analysis, such as clay area (Liu et al., 2015) GEOLOGY, ECOLOGY, AND LANDSCAPES 3 A very interesting conclusion is drawn by Shiferaw considered to correlate the slope factor of safety (2021) in one of the latest research works in 2021 as with different soil parameters. the research shows that the failure mechanism of the three soil types varies with the steepness and inclina- 1.3. Objective of the study tion of the slope. Toe slide is the most common kind of slope failure on clay and sandy clay soils. The failure The main objective of this study is to develop correla- mode of the slope slide is the most common for sandy tions between slope factor of safety with distributed soil. The failure mode in sandy clay and clay soils surcharge load and crest length of a slope in seismic tends to be base slide at lower heights (less than 2 and non-seismic conditions. m), while in sandy soil, the failure mode tends to be toe slide. The failure mode of sandy clay soils shifts 2. Materials and methods from slope slide to toe slide as the slope steepness increases. As a general rule, toe slip is the most com- Soil samples are collected from a slope at Mozishan mon failure mode in clayey soils. When the slope angle Park, which is local site at Shenyang city of China. is less than 18 degrees, the base slide takes place. Slope Figure 1 presents the site area having coordinates: failure is the dominant failure mode of sand. Failure of 41.666959, 123.477453. the base occurs at a steeper slope, namely at an angle of A local slope site is selected for analysis. Soil sam- 36.87 degrees. ples are collected from the site through boreholes at The factor of safety of slopes improves almost lin- various points. All required tests were performed to early with decreasing slope angle but increases at vary- compute the soil properties essential for the analysis. ing rates with decreasing slope height. The factor of The soil properties’ ranges are set for each and every safety can be increased by reducing either the slope analysis. The range of cohesion, friction, unit weight, angle or the height of the slope, depending on the and other input values is mentioned in the material specific slope in concern. To effectively increase properties section of every phase. Some of the impor- slope stability, it is important to understand the failure tant laboratory tests considered in this work are as mode and the effect of geometric change on the slope follows: factor of safety. A very useful related work can be checked in previous papers (Khan et al., 2019, 2022a, (a) Water content test 2022b; Khan & Wang, 2020a, 2020b, 2020c, 2020d, (b) Sieve analysis 2021a, 2021b, 2021c, 2021d, 2022a, 2022b). (c) Measurement of unit weight/specific gravity (d) Consolidation test (e) Atterberg’s limit test (f) Unconfined compression test 1.2. Existing problems and research idea to solve (g) Direct shear test the issue (h) Measurement of consistency limits The existing and normal trend to compute the slope (i) Falling head permeability test stability of any soil slope is to model a specific posi- tion of the soil slope, collect soil samples from that Figure 2 presents the boreholes and soil sampling at specific point, and then model it to check the stability site while Figure 3 presents the experiments per- of the slope. Main problem in such focused analysis is formed in the laboratory to determine the mechanical that the results are not applicable to any other point properties of soil which was brought from the site by on the same slope. For example, if a slope is 4 kilo- conducting four number of boreholes at different loca- meters in longitudinal direction, then the slope sta- tions of the site. bility analysis by collecting soils samples from only Three number of boreholes, twenty number of one position is not applicable to other point on the Atterburg’s limit test, eighteen triaxial tests, twenty same slope. To overcome this problem, correlations one direct shear test, and almost thirty sieve analysis are required between all the soil parameters such as tests were performed to compute the mechanical factor of slope safety, cohesion, friction, unit weight, properties of soil in detail. Similarly, all other tests slope angle, etc. to simply use those correlations and such as moisture content test, porosity, compaction, know about the slope safety at any point throughout and specific gravity tests were also conducted. All the length of let suppose 4 kilometers. This is the these tests were conducted repeatedly to make sure main idea behind this research work in which corre- the material properties are accurately computed. lations are developed between soil and slope para- Mechanical properties of soil after all the required meters in various multivariate conditions. Second, testings are mentioned in Table 1. Figure 4 shows the the results in case of seismic and non-seismic condi- slice details considered in the limit equilibrium tions are also not same; therefore, in this research 2-dimensional approach. It also explains the boundary both seismic and non-seismic conditions are conditions in both x and y directions. 4 M. I. KHAN Figure 1. Site location at Mozishan Park (Maps, accessed 14 January 2022). a. Borehole to collect soil sample b. Deep soil samples collected at site Figure 2. Boreholes and sampling at site. Details of other boreholes are available in the supple- ðCþ N tanϕÞ i¼1 F ¼ P P P (8) n n n mentary section. A A A 5 6 7 i¼1 i¼1 i¼1 where 2.1. Analysis method A ¼ ½Wð1 k ÞþU cosβþ Qcosσ� Rsinα (9) 5 u β Soil is not a homogenous material and hence its proper- � � ties vary from place to place and with time to time. � � Computing the soil properties is one of the most challen- A ¼ U sinβþ Qsinσ cosα (10) 6 β ging work for geotechnical engineers. Many number of boreholes are required in much depth to calculate the � � true soil properties. A ¼ k W cosα (11) 7 h Therefore, to know about the average properties of soil, many boreholes are required at different spots of the Locations of boreholes and the cross-section layout of testing sight. Normally, boreholing is done at different Borehole 1 are shown in Figures 5 and 6, respectively. corners and central points of the site at reasonable GEOLOGY, ECOLOGY, AND LANDSCAPES 5 d. Triaxial test c. Aerburg’s Limit test e. Sieve analysis f. Direct shear test Figure 3. Laboratory testings. Table 1. Mechanical properties of soil. S. No. Description Borehole 1 Borehole 2 Borehole 3 Average 1 Unit weight (KN/m ) 18.5 18 19 18.5 2 Cohesion (KN/m ) 28 29.5 35 30.83 3 Friction 19.5 22 21.5 21 4 Specific gravity 2.76 2.8 2.71 2.76 5 Moisture content (%) 29 27 22 26 6 Strength type Mohr-Coulomb Mohr-Coulomb Mohr-Coulomb Mohr-Coulomb Figure 4. Details of boundary conditions with forces acting on slices. where F = FS = C + N tan ϕ, S = Available strength, S = a m Mobilized strength, U = Pore water force, U = Surface water force, W = Weight of slice, N’ = Effective normal force, Q = External α β surcharge, K = Vertical seismic coefficient, K = Vertical seismic coefficient, Z = Left interslice force, Z = Left interslice force, θ = v h L R L Left interslice force angle, θ = Left interslice force angle, h = Z Force height, left, h = Z Force height, right, α = Slice base R L L, R L, inclination, β = Slice top inclination, σ = Surcharge inclination, b = width of slice, h Height of centroid of slice. c = distance. For this analysis, three number of boreholes are is changed with a constant rate of 5 kN/m . It ranges 2 2 drilled and average soil properties are computed from the from 100 KN/m to 55 kN/m . Similarly, the value of C boreholes presented in Table 1. The average depth of varies with a constant rate of 1 m. It ranges from 16 m to each borehole is kept as 15 m. Normally, the water table 7 m. In seismic analysis, 0.3 is taken as the maximum at this site is at 20 m depth. The strength analysis method horizontal coefficient while the vertical seismic coeffi- used is Mohr-Coulomb as it gives optimum results. In cient is neglected as the value of vertical seismic coeffi- this paper, analysis is performed such that the value of L cient is very small in most of the cases. The seismic D 6 M. I. KHAN load is applied at the total surface of the slope in nonseismic conditions. In this case, the minimum FS value came out to be 1.982, which is greater than 1.5 and hence the slope is safe. Figure 8 presents the analysis for 95 and 90 kN/m L applied on total surface of the slope in non-seismic condition. All values of FS for the varying L are presented in Table 2, while FS values with varying C are presented in Table 3. Using SPSS linear regression analysis, the correla- tion between FS and (L ) from Table 2 comes out to be FS ¼ 2:346 0:004L (12) Applicability value such as R of Eq. (12) is 98.8%. Similarly, using SPSS linear regression analsis, the Figure 5. Locations of the boreholes. correlation between FS and (C ) from Table 3 comes out to be analysis is performed using Slide software which gives an option to apply seismic load. Once the seismic coefficient FS ¼ 2:590 0:035C (13) is applied at each and every analysis, the slope factor of safety is computed using the same slope stability analysis Applicability value such as R of Eq. (13) is 88.3%. software namely Slide version 6.0. The applicability value of both these correlations is very high. For any slope stability design project, these correlations can be used to know about the 3. Results and discussions value of FS in case of varying L and C . Table 4 D L 3.1. Non-seismic analysis presents the SPSS linear regression analysis sum- Figure 7 presents the slope model analyzed in this mary in case of FS equals 1.982 and L equals 100 phase, where the value of L is 100 and this surcharge kN/m . Figure 6. Cross-section of borehole 1. GEOLOGY, ECOLOGY, AND LANDSCAPES 7 Figure 7. Analysis for 100 kN/m L applied on total surface of the slope – nonseismic. b. FS for 90 kN/m - Nonseismic a. FS for 95 kN/m - Nonseismic Figure 8. Analysis for 95 and 90 kN/m L applied on total surface of the slope – non-seismic. Table 2. FS with varying L – non-seismic. Surcharge load Crest length Shear strength Shear stress 2 2 2 (kN/m ) (m) (kN/m ) (kN/m ) FS 100 16 85.2329 42.9974 1.982 95 16 81.2697 40.5568 2.004 90 16 81.2697 40.1098 2.026 85 16 78.9119 38.5101 2.049 80 16 78.9119 38.0994 2.071 75 16 96.8169 46.4241 2.085 70 16 96.8169 46.1116 2.100 65 16 96.8169 45.7964 2.114 60 16 96.8169 45.4789 2.129 55 16 95.4556 44.544 2.143 3.2. Seismic analysis model analyzed, where the value of L is 100 and is applied on the total surface of the slope in seismic Seismic analysis of any slope provides the best idea conditions. Figure 10 presents the analysis for 95 and about its stability. Because even a normal stable slope 90 kN/m L applied on total surface of the slope in can give an unstable FS value in case of seismic analy- seismic conditions. sis. Many slope failure cases are observed in past which Tables 5 and 6 present the values of FS with varying failed due to minor earthquakes in the region. L and FS with varying C , respectively. D L Therefore, in second phase, seismic analysis is per- Using SPSS linear regression analysis, the correla- formed by considering the horizontal seismic coeffi- tion between FS and (L ) from Table 5 comes out cient as 0.3 (maximum) for same slope with same D to be material properties. Figure 9 presents the slope 8 M. I. KHAN Table 3. FS with varying C – non-seismic. Surcharge load Crest length Shear strength Shear stress 2 2 2 (kN/m ) (m) (kN/m ) (kN/m ) FS 100 16 85.2329 42.9974 1.982 100 15 107.542 52.1478 2.062 100 14 108.743 51.56 2.109 100 13 109.953 50.9648 2.157 100 12 112.425 50.9434 2.207 100 11 122.434 54.2017 2.259 100 10 90.14 39.3869 2.289 100 9 90.14 39.3869 2.289 100 8 90.14 39.3869 2.289 100 7 90.14 39.3869 2.289 Table 4. Regression analysis summary in case of FS equals 1.982 and L equals 100 kN/m – non-seismic. Variables Model Variables entered Variables removed Method 1 FS and L N/A Linear Model summary Model R R square Adjusted R square Standard error of the estimate 1 0.994 0.988 0.987 0.00628 Anova Model 1 Sum of squares df Mean square F Sig. Regression 0.026 1 0.026 660.117 0 Residual 0.000 8 0.000 Total 0.026 9 Coefficients Model Unstandardized coefficients Standardized coefficients t Sig. B Standard error Constant 2.346 0.011 215.217 0 L −0.004 0.000 −0.994 −25.693 0 Figure 9. Analysis for 100 kN/m L applied on total surface of the slope – seismic. Figure 11 presents the shear strength versus dis- FS ¼ 1:19 0:0005L (14) tance graphs. Applicability value such as R of Eq. (14) is 99.8%. In seismic analysis, FS value is less than 1.5 in Using SPSS linear regression analysis, the correla- all the cases, which can be seen in Tables 5 and 6. tion between FS and (C ) from Table 6 comes out to be Less than 1.5 means an unstable or risky slope. So, this slope needs stability solutions, i.e., either to FS ¼ 1:242 0:006C (15) L insert nails or apply stepping technique. Another solution is to improve the soil strength by replacing Applicability value such as R of Eq. (15) is 80.4%. the soil or compaction, etc. Constructing GEOLOGY, ECOLOGY, AND LANDSCAPES 9 a . FS for 95 kN/m - Seismic b. FS for 90 kN/m - Seismic Figure 10. Analysis for 95 and 90 KN/m L applied on total surface of the slope – seismic. Table 5. FS with varying L – seismic. Surcharge load Crest length Shear strength Shear stress 2 2 2 (kN/m ) (m) (kN/m ) (kN/m ) FS Difference between non-seismic and seismic FS 100 16 96.0252 84.192 1.141 0.841 95 16 96.0252 84.0057 1.143 0.861 90 16 96.0252 83.818 1.146 0.880 85 16 96.0252 83.6296 1.148 0.901 80 16 96.0252 83.4392 1.151 0.920 75 16 86.5466 75.051 1.153 0.932 70 16 86.5466 74.899 1.156 0.944 65 16 86.5466 74.7464 1.158 0.956 60 16 86.5466 74.5924 1.160 0.969 55 16 86.5466 74.4378 1.163 0.980 Table 6. FS with varying C – seismic. Surcharge load Crest length Shear strength Shear stress 2 2 2 (kN/m ) (m) (kN/m ) (kN/m ) FS Difference between non-seismic and seismic FS 100 16 96.0252 84.192 1.141 0.841 100 15 97.0079 84.2997 1.151 0.911 100 14 97.0079 84.2997 1.151 0.958 100 13 99.0334 84.4332 1.173 0.984 100 12 91.3068 77.114 1.184 1.023 100 11 85.3679 71.7438 1.190 1.069 100 10 85.3679 71.7438 1.190 1.099 100 9 85.3679 71.7438 1.190 1.099 100 8 85.3679 71.7438 1.190 1.099 100 7 85.3679 71.7438 1.190 1.099 a retaining wall is also an alternative solution to FS ¼ 1:154þ 0:012τ 0:014σ R is99:7% (18) make the slope stable. During this research, it is observed that FS, τ, and σ FS ¼ 1:192þ 0:012τ 0:014σ R is100% (19) also have very close relation. From Table 2, a correlation between these three parameters with varying L is established in nonseismic conditions as 4. Zariwam landslide Pakistan – case study follows by using SPSS analysis. Zariwam landslide in Waziristan area of Pakistan was FS ¼ 2:069þ 0:023τ 0:048σ R is100% (16) triggered out by the failure of retaining wall con- structed along the outer edge of the road side. From Table 3, the correlation between FS, τ, and σ Retaining wall displaced along the sliding mass as with varying C comes out to be shown in Figure 12. Field observations have revealed that retaining FS ¼ 2:226þ 0:022τ 0:049σ R is99:1% (17) wall slided due to the nullah erosion at the toe of slide area. Second, this nullah is also crossing the Similarly, from Tables 4 and 5, correlations between road portion, wherein seepage water is passing these three parameters are also developed in seismic underneath the road by a conduit. It may also conditions which are given below as Eqs. (18) and happen that seepage water is hitting the shale (19), respectively. area underneath the road near and around the 10 M. I. KHAN a. b. d. c. Figure 11. Shear strength graphs with variation of L and C in seismic and nonseismic conditions. D L Figure 12. Displaced retaining wall along the sliding mass. conduit, because additional significant signs of Retaining wall is proposed along the outer edge of road cracks are visible at the same location of the road, which will be placed over the compacted nullah conduit. It is therefore necessary to control foundation. Beneath the foundation of retaining wall, the seepage of water and direct it into the under- dowels bars have been proposed to increase the shear ground conduit or by constructing new culverts strength of foundation material. In addition, it is sug- over there. Google Earth satellite imagery of land- gested that the road portion in the slid area should be slide area is shown in Figure 13. placed over the 0.5 meter compacted granular fill in GEOLOGY, ECOLOGY, AND LANDSCAPES 11 Figure 13. Google earth satellite imagery of Zariwam landslide – Pakistan. Table 7. Results comparison using analysis methods and developed correlations. S. No Description Correlation Result by SSA methods Results by the developed correlations 1 Factor of Safety FS = 2.346–0.004 L 1.30 1.33 2 Factor of Safety FS = 2.590–0.035 C 1.38 1.40 3 Factor of Safety FS = 1.19–0.0005 L 1.32 1.35 4 Factor of Safety FS = 1.242–0.006 C 1.56 1.59 5 Factor of Safety FS = 2.069 + 0.023 τ − 0.048 σ 1.29 1.33 6 Factor of Safety FS = 2.226 + 0.022 τ − 0.049 σ 1.33 1.34 7 Factor of Safety FS = 1.154 + 0.012 τ − 0.014 σ 1.49 1.52 8 Factor of Safety FS = 1.192 + 0.012 τ − 0.014 σ 1.37 1.41 Table 8. Factor of safety values. S. No Description Input parameters Correlation Condition Results by the developed correlations 1 FS L = 110 kN/m FS = 2.346–0.004 L Non-seismic 1.91 D D 2 FS C = 17 m FS = 2.590–0.035 C Non-seismic 1.99 L L 3 FS L = 110 kN/m FS = 1.19–0.0005 L Seismic 1.14 D D 4 FS C = 17 m FS = 1.242–0.006 C Seismic 1.14 L L 5 FS τ = 97 κΝ/μ FS = 2.069 + 0.023 τ − 0.048 σ Non-seismic 1.66 σ = 55 κΝ/μ 6 FS τ = 97 κΝ/μ FS = 2.226 + 0.022 τ − 0.049 σ Non-seismic 1.67 σ = 55 κΝ/μ 7 FS τ = 97 κΝ/μ FS = 1.154 + 0.012 τ − 0.014 σ Seismic 1.55 σ = 55 κΝ/μ 8 FS τ = 97 κΝ/μ FS = 1.192 + 0.012 τ − 0.014 σ Seismic 1.59 σ = 55 κΝ/μ order to drain the seepage water. A drain is proposed known values, FS value can be computed using the to be constructed at the toe of upside slope. Downside correlations developed in this paper. For example, the slopes are proposed to be protected with dry stone shear strength, shear stress, crest length, and surcharge 2 2 pitching. In order to avoid toe erosion, river training load in case of any soil slope are 97 kN/m , 55 kN/m , works, i.e., gabion wall, has also been proposed. 17 m, and 110 kN/m , respectively. Using these values Table 7 presents the correctness percentage of all the as input, the slope factor of safety values computed developed correlations after applying in the landslide using the developed correlations are shown in Table 8. analysis. Table 7 proves that all the four developed correla- 5. Conclusions tions in this work have applicability value higher than 97%. Normally, the shear strength and shear stress A soil slope embankment is analyzed in detail con- values can be computed using triaxial test in the sidering the local soil material and its proposed laboratory. Similarly, surcharge load and crest length model in two phases, i.e., seismic and non-seismic are also known or can be computed for any soil slope. conditions. Correlations between FS, τ, L , and C , D L All these four values such as shear strength, shear τ, and σ are developed both in seismic and non- stress, surcharge load, and crest length are known to seismic conditions. It is found that all these diffent an engineer as input for any soil slope, and using these parameters have very close relation as the 12 M. I. KHAN applicability value R of the correlations, such as Das, B. M., & Sobhan, K. (2010). Principles of geotechnical engineering. In C. M. Shortt, Global engineering (Eighth, from Eqs. (12) to (19) is 98.8%, 88.3%, 99.8%, p. 580). 80.4%, 100%, 99.1%, 99.7%, and 100%, respectively. Deng, D. P., Zhao, L. H., & Li, L. (2016). Limit equilibrium This high R is a clear indication that all these para- stability analysis of slopes under external loads. Journal of meters are interdependent. These correlations can be Central South University, 23(9), 2382–2396. https://doi. used in design projects provided that the material org/10.1007/s11771-016-3297-4 properties are in range of the specific material prop- Duncan, J. M., Wright, S. G., & Brandon, T. L. (2014). Soil strength and slope stability (Second ed.). John Wiley & erties given in this work. Considering Zariwam land- Sons, Inc. slide and applying the correlations to get perfect Feizizadeh, B., Blaschke, T., Nazmfar, H., & Rezaei- results proves the correctness of the developed cor- Moghaddam, M. H. (2013). Landslide susceptibility map- relations. Further work can be done considering ping for the urmia lake basin, Iran: A multi-criteria eva- other soil parameters and other soil material types, luation approach using GIS. International Journal of such as silty clay, clayey sand, sand and clayey Environmental Research, 7(2), 319–336. https://doi.org/ 10.1080/17538947.2012.749950 silt, etc. Feizizadeh, B., Roodposhti, M. 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Geology Ecology and Landscapes – Taylor & Francis
Published: Jan 22, 2023
Keywords: Slope stability; factor of safety; numerical modelling; surcharge load; correlations
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