Analysis and Parametric Assessment of Reinforced Soil Wall

Due to rapid urbanization and growth of countries, the rate of building infrastructures is also on the higher side. Owing to a lack of adequate high bearing capacity soil, one is forced to select regions with lower bearing capacity, which can cause long-term instability problems. Various improvement techniques available in the field of Civil Engineering or Geotechnical Engineering are to be adopted in such cases to avoid instability issues. One such well known method is Reinforced Soil wall that has been investigated and focused here. In this paper, an effort is made to compare numerical and analytical analysis, as well as to investigate their consistency and understand the effect of various parameters on its performance. The numerical analysis, which is based on Lee et al.’s lateral earth pressure theory, has been paired with an analytical one using the Finite element method (FEM) to evaluate its performance and efficiency in the field. Furthermore, various parameters such as reinforcing element length, soil friction angle, spacing, height of the wall, and maximum tensile forces produced have been considered, with their variations affecting the overall efficiency of the system being investigated. Further, an attempt has been made to understand the behavioural pattern by comparing the results using Regression Analysis. The findings from both analyses are very consistent and complement one another.


Introduction
Slope instability is a troublesome issue and has a great significance in the fields of geotechnical and geological engineering as it is known to have claimed substantial loss of lives and properties over the time.Again, slope instability is not just limited to natural slopes but also man-made slopes as in the case of railway embankments, road embankments, road cuts, etc. Various improvement techniques such as earthworks, retaining walls, and reinforced earth mechanisms have also been suggested in the fields to stabilise the slope and achieve satisfactory performance [1].The field technique that is to be focussed in this paper is the mechanical stabilisation of earth (MSE) wall system, whereby reinforcements are provided within the earth mass and has been proved to be better over the other traditional retaining walls.MSE walls have developed as a solution to restrained right of way, complex sub-surface situations and the projects that were delayed in the past be accelerated with the use of MSE wall system.Over the past few decades, the mechanism of MSE wall has gained prominent utilisation in the field of civil engineering due to its design resiliency, relative flexibility in construction, and cost efficiency compared to other conventional methods [2][3].It can tolerate much higher settlements (differential) being more flexible and cost-effective than the conventional methods of the past.It is an improvement technique whereby mechanically stronger materials such as metallic or polymeric strips, sheets, geogrid, etc. are provided layer by layer with the compacted backfill in between them.It could have been accomplished because of the interaction that occurs through the inclusion of reinforcement in the compacted earth mass between the soil and the reinforcing component.The design and behaviour of reinforced earth wall is a complex system with a combination of various elements including facing, backfill soil, foundation soil, and reinforcements which requires a lot of experimentations and case studies of the existing ones, which is not always economically feasible.But have been made possible due to the development of analytical approaches using LEM or FEM models which allows analyzing the response and behaviour of reinforced soil wall corresponding to various parameters and loading conditions with great certainty that holds well with the field results [4][5].Further, the type of reinforcements used in reinforced soil structures have a significant effect on the length and lateral earth pressures endured by the walls [6].The lateral earth pressures endured by the walls can be largely affected by end conditions of the reinforcements, whether freely suspended or fixed to the walls.The length of the reinforcements (L) to height of the wall (H) ratio i.e., L/H influences the variation of resultant earth pressure and resultant overturning moments [7].In practical conditions, the optimum length (L) of the reinforcing strips to the height (H) of the wall was determined to be approximately 0.6-0.8[8][9][10].Again, the development of nondimensional design charts has aided in the determination of the lateral earth pressure formed on the wall and its point of application over the wall foundation.The point of load implementation has been proven to affect the behaviour of the wall that varies along the backfill with the pattern of reinforcement distribution [11].The reinforcement length to wall height (L/H) ratio is the most significant geometric parameter that influences the behaviour of reinforced soil wall structures, and evenly spaced truncated reinforcement with L/H=0.7 provides a reasonably efficient reinforcement force distribution [12][13].The overall characteristics of reinforced soil are influenced by the mechanical properties of the soil and the reinforcement, as well as the relative proportions and geometrical structure [14].When examining the lateral deformation pattern of the walls, it was found that the deformation pattern depends on multiple factors, such as loading conditions, structural geometry, type of facing, etc.The deformation of the front face at the base is minimal, but the deformation at the top is substantial, and the deformed shape is almost parabolic in deviation from base to top [15][16].The retaining wall system's maximum vertical settlement, as determined by FE study and in the field, is very similar to the wall facing, and settlements in the backfill soil can be managed by using higher reinforcement and wall facing stiffness [17].Further, if the desired backfill material is not available nearby the site, then one can utilize bottom ash which is a waste product of thermal power plants and would result in combatting waste management as well as cost-efficacy [18][19].Reinforced soil technology is not just limited to civil engineering fields but also extends to military fields as well as to safeguard staff and property against unintended detonation of concealed bombs, munitions, and ammunition plants [20].
The goal of the present study is to carry out stability analysis of a reinforced soil wall specifically on a mechanically stabilised earth (MSE) wall using a purely numerical approach and an analytical one to understand the influence of the various parameters of the wall system.From the parametric assessment of the wall system, the importance of each parameter has been analysed using SPSS software whose results have been compared with the 10% incremental and decremental method suggested by Pandey et al. [21].Furthermore, the data used for developing the models have been analysed statistically using Linear Regression Analysis in SPSS software and then validated.The numerical approach adopted in the study is founded on the concept of lateral earth pressure which has been investigated and tested by Lee et al [22] for the development of reinforced soil walls.The analytical analysis has been carried out using FEM approach employing PLAXIS 2D computer program.The study was conducted using various combinations of soil and reinforcement parameters and the results obtained have been compared from both the approaches.

Methodology
The methodology adopted for the present study is based on two approaches-numerical and an analytical using FEM approach, which are being described in detailed in the following sections.A conventional soil nail wall of varying heights and other parameters as mentioned in succeeding sections, with vertical face and horizontal backfill is considered along with homogeneous distribution of reinforcements in both horizontal and vertical direction for the analysis for exemplification and better understanding.

Numerical Analysis
For reinforced soil walls, there are primarily three design approaches: lateral earth pressure of Rankine, lateral earth pressure of Coulomb and concept theories of Equivalent Confining Stress.Compared to Coulomb's, Rankine's approach is usually easy; it is therefore more commonly used than any other design approaches.The lateral earth pressure concepts, as developed for the design of traditional retaining structures, can be applied to the design of reinforced earth walls.Lee et al [22] have studied and investigated this design process for their applicability in the fields of reinforced soil walls.Similar design proposals were subsequently issued by Bell [23] and Koerner [24] for the design of mechanically reinforced earth walls using geogrids as material reinforcement.1282 (2023) 012016 IOP Publishing doi:10.1088/1757-899X/1282/1/0120163 Tie length calculation: Two lengths are included in the total tie length to be provided: length inside the Rankine failure zone (La) and length outside the Rankine failure zone, i.e., the effective length (Le) (Fig 1).In order to resist tie pull-out failure, the length of the tie at any stage should be such that it must establish adequate bond strength with the surrounding medium (granular soil).The length within the Rankine failure zone or active zone, La has been calculated using the following expression The tie length required beyond the Rankine failure zone, i.e., the effective length, Le has been determined using the following expression Further, the stress induced, σ i at each reinforcement level using the lateral earth pressure concept has been worked out using the following expression Finally, the tensile force, Ti at each reinforcement level has been calculated using the following equation The above steps have been followed for numerical analysis of reinforced soil wall for various friction angles, wall heights and spacing of the reinforcement elements employed in the system.

Analytical Method using PLAXIS 2D
The Finite Element Method (FEM) is a computational technique for computing approximate numerical solutions for various engineering problems.It enables accurate visualization that displays the distribution of pressures and strains within a structure.PLAXIS is a geotechnical application finite element software in which soil simulations are used to predict the behaviour of the soil.For different types of geotechnical applications, PLAXIS is a special purpose two-dimensional finite element computer software used to perform deformation and stability analysis.This uses a convenient graphical user interface that helps users to easily create a geometry model and a finite element mesh depending on the condition at hand in a representative vertical cross-section.In this study, PLAXIS is used to simulate the reinforced soil wall using finite element dependent models under drained conditions and as a plane strain case.A finite element mesh with a sufficient fineness is generated using 15-noded triangular elements.The model of reinforced soil wall considered along with metallic strips as reinforcement elements has been represented in figure 2. The input parameters that have been utilised in modelling are represented in table 1.

Results and Discussions
Several physical properties of the soil play a major role on the consistency and structural behaviour of the reinforced soil wall.The results obtained shall be discussed in this section with numerical results succeeded by the analytical ones then sensitivity analysis, Multilayer Perceptron and Linear Regression Analysis in SPSS software.

Variation of Tmax w.r.t Spacing
Following the numerical analysis methodology, the maximum tensile force developed in the metallic strips from the concept of lateral earth pressure at various depths have been computed.The variation of Tmax with respect to spacing has been represented graphically for better understanding in figure 3.
It can be concluded from the graph that as spacing increases, the area enclosed by the strips also increases along with the increase in embedment depth of the reinforcements which influences the tensile forces induced in the wall.Again, the highest tensile force can be experienced by the reinforced soil wall whose reinforced soil has lower angle of internal friction, i.e., 30 degree and lowest by the one with higher friction angle, i.e., 42 degree in this analysis.The internal friction angle of the adjacent soil must also be considered when constructing reinforced soil wall structures.This is due to the fact that the distribution of ground pressure is mostly determined by the soil's internal friction angle.For example, the term K, which denotes the soil's lateral earth pressure coefficient, can be measured using the formula, K = 1sin ø (i.e., for at-rest earth pressures).A higher value of ø results in a lower K, lowering the amount of stress the soil exerts on the retaining walls.

Variation of length w.r.t Spacing
The variation of lengths w.r.t spacing for various angle of internal friction taken into consideration is represented graphically in figure 4. It can be concluded that the length (L) required for developing sufficient bond strength as well as to prevent pull-out failure have decreased significantly upon increasing the values of internal friction angle from 30 degree to 42 degree.Thus, the length of the metallic strips is directly dependent on the type of soil to be employed for construction of reinforced fill.Further, the lengths of the metallic strips have indeed showed significant variations with spacing, implying that the lengths of the strips are to be increased to cope up with the increased risk associated with it.Therefore, it can be concluded that with increase in height of the wall and reinforcement spacings, the risk factor or the probability of un-stabilisation increases.Hence, the length of the metallic strips required to cope up with the increased failure probability is boosted up.

Variation of FOS w.r.t Spacing for different soil
The lengths of the metallic strips obtained from the Lee et al. method have been used to develop the model in PLAXIS 2D simulating the field conditions.The outputs obtained after evaluating the models on PLAXIS 2D are in the form of Factor of Safety (FOS) or Ʃmsf, which were obtained by analyzing the models of problem interest.The variations of FOS w.r.t spacing and friction angle of the soil have been graphically represented to understand their relationship in a better way, i.e., FOS increases with higher friction angle soil but decreases with increasing spacing when the lengths of the reinforcements are kept constant.

Sensitivity Analysis
The most influential parameter affecting the performance of the MSE wall system can be determined by performing sensitivity analysis of the data considered.It is done by taking the averages of all the dependent and independent parameters of the wall system and considering 10% incremental and decremental parameters.It is being assumed that each input variable is an error independent variable for the analysis [21].Further, the SPSS software has been used to predict the independent variable importance and normalised percentage for the parameters using Multilayer perceptron in ANN.The results obtained satisfy each other with friction angle of the soil having the most crucial influence on the wall system and length of the reinforcements the least role among the parameters considered.

Conclusions
In this paper, the parametric assessment of the RSW, i.e., MSE wall has been studied using a numerical method and analysed analytically by FEM using PLAXIS 2D program.Based on our study, the following are the main findings obtained, which are presented below: 1.The length of the metallic strips is directly dependent on the type of soil to be employed for construction of reinforced fill as well as the spacings between them.As it has been observed that as friction angle and length required for developing sufficient bond strength as well as to prevent pull-out failure follows inversely proportional relationship whereas the friction angle and spacing follows directly proportional relationship.
2. The FOS values obtained varies with length of the reinforcements.This indicates that the performance or design of the structure is directly dependent on the lengths of the reinforcements employed, indicating that higher the lengths employed, higher will be the FOS values.Hence, in many works involved in the past have focused on maintaining a proper proportionate of length to height (L/H) so that it can develop full bond strength as well as be economic enough to serve the purpose of method adoption.
3. The FOS values also varies with spacing between the reinforcements as well as friction angle of the soil employed.It has been observed that with the increase in friction angle and spacing, the FOS values also showed an increasing trend though with increased lengths to compensate the higher risks involved.This indicates that the performance or design of the structure is dependent on the soil type, spacing as well as on the position of the reinforcements employed.
4. Development of maximum tensile forces generally occurs at the bottom or lower part of the structure, which varies significantly with the area encompassed by the metallic strips.As the spacing increases, the encompassing area also increases and hence, the Tmax.Therefore, the variation of Tmax with respect to spacing have shown similar pattern with different types of soil involved, i.e., increasing trend line, but it shows a descending pattern when higher friction angle has been employed.It indicates that in cases of generation of higher tensile forces, increasing the friction angle of the soil can be an aid.
5. The friction angle of the soil is the most critical parameter that influences the performance of the MSE wall system followed by spacing, height of the wall and length of the reinforcements used.This compares well with the Multilayer Perceptron in SPSS software which also states that friction angle is the most influential parameter followed by wall height, spacing and length of the reinforcements.
6.The RMSE and R 2 values of the training and testing data obtained are 0.095, 0.094, 0.965 and 0.918 respectively which complements each other and fits really well.

Fig 2 .
Fig 2. Representation of reinforced soil wall model considered for the analysis.

Fig 3 .
Fig 3. Graphical representation of Spacing v/s Tmax for different friction angles.

Fig 5
Fig 5 Graphical representation of Spacing v/s FOS for different friction angles.

Fig 6 . 5 )Fig 7 .
Fig 6.Sensitivity analysis and normalised importance from SPSS software respectively.3.4 Linear Regression Analysis using SPSSOut of 126 model data, around 112 model data (89%) have been used to perform linear regression analysis for developing the mathematical relationship between the input parameters and the output parameters of the wall system.The remaining data have been used to test the mathematical relationship obtained from the training data set and validated by comparing the RMSE and R 2 values.The mathematical relationship obtained for the parameters of the MSE wall system by performing Multiple Linear Regression Analysis can be written as Predicted FOS = 0.086 + 0.038 .ø − 0.058 .H + 0.653 .S + 0.028 .L(5)

Table 1 .
Input parameters for model analysis