Parametric Study on the Stability of Slopes Subjected to Earthquake Forces

For thousands of years, engineers have been grappling with slope instability as an issue in geotechnical and geological engineering. Earthquake loading has a great impact in slope stability. The present study is to investigate the impact of various soil properties and slope geometry on FOS in the presence as well as in the absence of seismic loading. Here, pseudo-static methods are used to analyses seismic slope stability under earthquake loading. From parametric studies, present work concluded that the FOS values start to decline drastically with earthquake impact. Moreover, various prediction models have been developed using Multiple Linear Regression (MLR) & Multiple Non-Linear Regression (MNLR) considering all the data. The input data of slope stability estimation consists of the values of soil parameter, slope parameter and earthquake loading parameters. As an output, MLR and MNLR predict FOS values as a function of these parameters. The model is then checked by comparing the results to another ten actual situations. It was found that the predicted FOS using MNLR gives satisfactory results.


Introduction
Geotechnical and Geological engineers have grappled with slope instability for thousands of years.It has resulted loss of life as well as property for the human race, and lakhs of crores have been spent on protecting and restoring the environment.Slope instability can be caused by a variety of factors such as soft or weak soil, erosion from wind and water, rainfall, external loading, deforestation, earthquakes, etc.Over the past few decades several slopes have been severely damaged by earthquakes.Hence there is a need of analyzing slope stability under seismic loading.Marrapu and Jakka [1] created two distinct multiple regression models, verified their precision in the estimation using actual field data, and were satisfied with the findings.Wang and Khan [2] found correlations between various soil and slope parameters using the SLIDE software to forecast slope stability assessment.Zhou et al [3] investigate slope prediction using logistic regression and conclude that it is the best predictive approach for slope stability prediction.Huang and Peng [4] conducted a seismic slope stability analysis for saturated and unsaturated soil and found that dynamic pore water pressure influence is significant towards stability.A soil slope was examined using limit equilibrium techniques by Choudhury et al. [5].They carried out in-depth analysis, which showed that the dynamic FOS depends on friction angle of the soil.With increasing horizontal and vertical acceleration, the dynamic FOS significantly decreases.According to some researchers, limit equilibrium analysis might be a little bit non-conservative.Using pseudo-static and upper-bound limit analysis, Zhao et al. [6] developed many stability charts and these charts were very helpful in determining the critical slope height and critical fracture depth.Limit analysis was used by Gong et al. [7] to access the seismic slope stability for non-homogeneous anisotropic slopes.The problem is made simpler by using the pseudo-static approach.They got to the conclusion that the anti-slide piles have a significant impact on the soil.Additionally, they observed that the anti-slide pile required a greater stabilizing force higher the anisotropic coefficient.The outcomes of an ANN model were shown to be trustworthy when compared to conventional limit equilibrium methods.Lin et al. [8] used a neural network to assess the likelihood that a roadway slope will fail.They constructed models to look at slope failure characteristics and identified the influence of various elements (variables) on slope stability.Abdalla et al. [9] use of ANN to forecast the FOS for slope failure in clay .Two multilayer perceptions ANN models based on various slope stability strategies were utilized to calculate the minimum FOS utilizing different sets of data related to geometry and shear strength properties.
The study's objectives include: •The effect of various parameters of soil properties and slope geometrics with respect to FOS of a slope both in presence and absence of seismic loading.
•To develop a correlation between soil parameter as well as geometrical parameters of a slope using statistical approach such as MLR and MNLR.
•To verify the prediction models using some of the case studies along National Highway of Assam Meghalaya boarder (NH-6) and also to carry out a comparison between the results obtained from MLR and MNLR.To calculate the FOS, 480 artificial slope cases with wide range of geometry, soil properties, and earthquake properties were analyses using ordinary methods of slice and FOS values were calculated.These values were used in the development of the regression models using MLR and MNLR.Here, height of the slope (H), cohesion (c), angle of internal friction (φ), slope inclination (β), unit weight of soil (γ), and Horizontal Seismic coefficient (K h ) were used as input parameters.FOS served as a parameter for the output.

Results and Discussion:
Parametric study of seismic slope stability has been carried out.All the results obtained from LEM approach has been complied together and FOS variation with respect to other parameter has been represented in a feasible and comprehensible manner.By examining the projected and analytical outcomes for 10 susceptible slope scenarios along NH6, the model's accuracy was determined.It can be clearly concluded from the graphical representation that as friction angle is increasing, the FOS values are also showing increasing trends.The trend is parabolic nature.This is due to the fact that higher friction angle of soil, better is the load handling features along with higher adhesion.For high value of cohesion and internal angle of friction it is observed that FOS is also large.
ii) With seismic loading conditions  ii) With seismic loading conditions: Considering the earthquake data by using PGAH as 0.267 m/s 2 and peak ground vertical acceleration as 0.139 m/s 2 .It is found that with the impact of seismic loading the FOS starts decreasing drastically as compared to without seismic loading condition case.It can be clearly concluded from the graphical representation that as slope angle is increasing, the FOS values are showing decreasing trends.That means slope angle is inversely proportional to FOS.The trend is linear.For high value of cohesion, it is observed that FOS is also large.ii) With seismic loading conditions: Considering the earthquake data by using PGAH as 0.267 m/s 2 and peak ground vertical acceleration as 0.139 m/s 2 .It is found that with the impact of seismic loading the FOS starts decreasing drastically as compared to without seismic loading condition case.For slope angle 36 degree and cohesion value 100 KN/m 2 the FOS of the model without considering seismic loading is found to be 2.985 and with considering seismic loading it is found to be 2.334.Hence dynamic load has a great impact on FOS of a slope.

Multiple Non-Linear Regressions Findings
From the table it has been found that the value of R 2 has found to be 0.88.Further a correlation has been established between soil and slope parameter to predict FOS value.The following equation has been from using MNLR technique.

Case Study
A few case studies are conducted to test the validity of prediction models independent of the data used to build them.Furthermore, error analysis is used to test the model's suitability.
For case studies the national highway from Jorabat to Shillong is taking into consideration as it includes lots of hillslope, slope collapse is prevalent along the Jorabat-Shillong roads.A survey work has been performed along Jorabat and Umling over a distance of 25 km to determine different slope geometry.Undisturbed soil samples are obtained usingShelby tubes having 20 cm length and 3.8 cm as diameter with an area ratio of 10%.Consolidated drained test is carried out to obtain the shear parameters.To incorporate seismic loading parameter the earthquake of magnitude of 6 which is occurs in Assam in the year 2021 is taking into consideration.The PGAH of that particular earthquake at epicenter (K h =0.5) and at Jorabat area (K h =0.25) is considered which is collected from USGS data center website.Finally, the FOS values are obtained for all the 10 vulnerable sites using LEM approach.The test results for 10 real slopes case studies are given in the Table 3.This study indicates that earthquakes are also responsible for land sliding along NH 6. Almost all the hill slopes along NH 6 are wet or moist, which becomes a serious issue during earthquakes.Earthquake having long duration weaken and destroy mountainous slopes, leading to instability.Engineers will benefit greatly from the results of this study and can be used to evaluate slope stability and produce sustainable hazard assessment maps that consider earthquake effects.Table 3. Case studies for 10 vulnerable slopes along NH 6.

Conclusions
A parametric study of seismic slope stability is conducted.Additionally, the FOS values are used for making prediction models using MLR, MNLR.The parameters such as slope height, cohesion, angle of internal friction, angle of slope, unit weight of the soil, and horizontal seismic coefficient are act as input variable and output parameter is FOS.Some case studies along NH-6 are used to test the accuracy of prediction models.Based on the above presented results, the following inference can be made.
a.In parametric studies, FOS values increase as friction angle increases at different values of cohesion, both in the presence and absence of seismic loading following the parabolic trends.The FOS values decrease when earthquake loads are applied.As friction angle increases, soil strength increases, therefore FOS values increase.Whereas Earthquakes cause failure in two different ways.Because of loss of effective stress, vibration from an earthquake can lead to liquefaction of uniformly graded, fine-grained sediments.As a result of earthquakes, factor of safety can also decrease due to increase in shear stress.b.From parametric studies it has been found that FOS values starts decreasing as the angle of slope increases at different values of cohesion both in presence and absence of seismic loading following the linear trends.In presence of earthquake loading FOS values starts decreasing drastically.Slopes with steeper gradients are more likely to fail.c.Regression analysis can be quite useful for forecasting slope stability.The results of the MLR and MNLR models generally agree with the results of LEM studies.d.The MNLR model is shown to have lower values of MSE of 0.003 and 0.012 for K h =0.5 and K h =0.25 respectively as against 0.11 and 0. 128.Therfore predicted results of MNLR model are found to be more closer as compared to MLR model.e.The MAE values obtained from MNLR model are 0.045 at K h =0.5 and 0.099 at K h =0.25 against 0.262 and 0.259 from MLR model respectively.Hence MNLR prediction is more accurate as compared to MLR. f.Accordingly, the present study is extremely valuable for engineers to develop a landslide hazard zone map taking earthquake impact into consideration.

3. 1
Parametric study findings: a) Variation of FOS with respect to internal angle of friction at different values of cohesion: i) Without seismic loading conditions: A graphical representation of the data has been attempted here with respect to FOS and internal angle of friction at different values of cohesion.

Fig 2 .
Fig 2. FOS vs Angle of internal friction at different values of cohesion in absence ofseismic loading.

Fig 3 .
Fig 3. FOS vs Angle of internal friction at different values of cohesion in presence of Seismic loading

Fig 4 .
Fig 4. FOS vs Angle of Slope at different values of cohesion in absence of seismic loading.It can be clearly concluded from the graphical representation that as slope angle is increasing, the FOS values are showing decreasing trends.That means slope angle is inversely proportional to FOS.The trend is linear.For high value of cohesion, it is observed that FOS is also large.

Fig. 5 .
Fig.5.FOS vs Angle of Slope at different values of cohesion in presence of seismic loading.

Fig 6
Fig 6 shows the results of MSE values for MLR and MNLR at different K h values.It has been found that MSE values for MNLR found to be lowest as compared to MSE values of MLR in both cases.Similarly in Fig 7 shows the results of MAE values for MLR, and MNLR at different K h values.It has

Fig 6 .
Fig 6.Mean Square error V/S Prediction methods

Table 1 .
Summary output of MNLR analysis

Table 2 .
Summary output of MNLR analysis