Genetic Algorithm Based Software for Optimization and Design of Piles on Slopes

Abstract

Landslides in layered soil in slopes is a common phenomenon that leads to major damages to infrastructures. Piles are deep foundations which are useful structural elements to support heavy loads in difficult slopes, and to retain creeping or sliding slopes. Controlling the stability of structures made on slopes is still one of the major problems in engineering. Piles are being used successfully to support structures on slopes and have become an efficient solution for such situations which demands construction on sloping grounds, since piles can often be easily installed without disturbing the equilibrium of the layers of soil in the slope. In this paper, an optimized design approach have been adopted for design of single piles for supporting infrastructure on layered soil slopes. A standalone software has been developed as a result of this study which produces the optimum pile dimension, reinforcement details and an estimate of the design as software output. The code is written in MATLAB that incorporates Genetic Algorithm (GA) optimization technique to obtain optimum pile dimensions and the pile is designed satisfying all the structural requirements as recommended by IS:2911: Indian Standards Code for cast-in-situ Reinforced Concrete pile.

1. Introduction

Piles are deep foundations which are introduced into the soil by suitable means to support the load coming on it from the superstructure when a good bearing stratum is not available at shallow depths from the ground surface [1]. In such situations load have to be transmitted to a firm strata which is capable of supporting such tremendous loads at an appreciable deeper depth below the ground surface. Piled structures are often subjected to significant lateral loads in addition to the vertical load coming from the superstructure which are installed in soil layers present in sloping grounds. The varying properties of multi-layer soil in the slopes may further complicate the stability issue of the structure.

In this research, the model superstructure considered on multi-layer soil slope is as per Indian standards recommendation [2]. Indian standards guidelines have been followed for the design of pile foundation in the soil slope. Indian Standards [3, 4, 5, 6] classifies Concrete Piles as Driven Cast-In situ piles, Bored Cast In-situ piles, Driven Precast piles and Precast piles in Pre-bored Holes. The Load Bearing capacity of the pile is dependent on the material used and the dimensions of the pile foundation, the spacing of individual piles in the pile group, the load bearing capacity and nature of the supporting soil. The pile installation method, and the direction of incoming loading [7] also plays a significant role in determining the load bearing capacity of the pile foundation. The load bearing capacity of the soil slope is affected by many factors such as type of the soil in each layer of the slope and strength of soil in these soil layers, foundation dimensions, unit weight of the soil, surcharge acting on the soil, the type of loading etc. [1]. The variability of the properties of the supporting soil, soil profiles and properties of the soil in these multi-layered soil profiles, which generally exists in nature, affects the load bearing capacity of the pile drastically. The choice of a pile to be used is governed by the condition of the site, economy, time available etc. The problem of landslides is also a major consideration for stability of a structure on sloping grounds. Hence, in order to counter these problems which have a large number of variability associated with them, the aid of modern high-speed computers and software has become popular.

Conventional design method for pile foundations involves determining the load carrying capacity of pile foundations from Static method, Dynamic method, Pile load test method or Penetration Test method depending upon the situation giving due consideration to data obtained from soil exploration reports. The pile foundation or group of piles are designed in such a way so as to transfer the load to the supporting soil safely giving due consideration to the load coming from the superstructure. For the design consideration of geotechnical design of the pile, the Ultimate Load Carrying Capacity and the Allowable Load Carrying Capacity is taken into consideration whereas for the structural design of the foundation, the bearing capacity, driving and handling stresses of the pile foundation is taken into consideration. Design of Pile Foundation is generally a trial-and-error process. Here an initial trial design (foundation dimensions and reinforcements) is taken and is checked against the geotechnical and structural requirements. This is done iteratively to revise the trial designs till a practical design of pile foundation is obtained. The drawback of this general method is that with these methods, the design of the pile foundation often comes out to be a conservative one. Generally such a conservative design may lead to an uneconomical and an impractical design. In a general optimization approach for design of a pile foundation, an optimization algorithm is used. A well calibrated optimization method may confirm an economic and a practical pile foundation design. In optimized design method of design for single piles the Ultimate Bearing Capacity of the pile is evaluated within stipulated limits by changing the pile dimensions iteratively until an optimized pile dimension is found to support the total incoming load. The pile is then designed structurally for bearing the loads acting on the pile satisfying all the structural requirements, may it be for vertical loading or lateral loading.

Complex studies have been carried out based on experimental and numerical investigations of piles installed in sloping grounds. But the research done in foundation engineering for the application of optimization methods using Computer Aided Design methods for structures on sloping grounds is scarce. The available research that deals with pile design optimization, assume different methodology with a number of assumptions which cannot involve all the practical parameters and thus have limited practical applications for supporting structures on sloping grounds.

Borah and Borah [1] has adopted a GA based optimization algorithm for optimization and design of Vertical piles on horizontal grounds with the Ultimate bearing capacity being the objective function and the pile dimensions as the design variables. Hoback and Truman [8] have introduced a weightless optimality rule into the original optimality criteria approach to address the design variables- the spacing and battering of the piles that has no measurable effect on the objective function. Huang and Hinduja [9] adopted a quasi-Newton method for optimizing the shape of piles. Their algorithm includes a linear force–deflection relationship for the pile-soil system while optimizing the pile design. Nikolaou and Pitilakis [10] developed a stand-alone program based on MATLAB. The have included algorithm for the calculation of bearing capacity and settlements of shallow foundations using several well-known formulas. They have utilized various literature and codes of practice that are preferred in engineering.

In this paper, the research done in Borah and Borah [1] has been taken as the base for the development of a Genetic Algorithm based software code for optimization and design of concrete cast in situ pile in a multi-layer soil slope. The Genetic Algorithm (GA) is used to optimize the pile dimensions based on Indian Standards [4, 5, 6, 7] methodology within recommended limits and user defined practical specifications. The piles designed by the software takes into account the lateral load and the lateral moment, along with the vertical loading and moment coming from the superstructure, which will be unique for piles on sloping grounds with multiple layers of soil. A software has been developed using MATLAB coding for automating the entire process of design and optimization. An estimate [11] for construction is also presented which may further ease the choice of selection of a particular design.

2. Methodology

2.1 General

In this study a genetic algorithm (GA) has been developed for optimization and design of a pile foundation on sloping ground. The Optimization method used for optimization in the said software is genetic algorithm (GA). Genetic algorithm (GA) is a search-based optimization technique that works on the principles of Genetics and Natural Selection which is used to find optimal solutions to difficult problems which otherwise would take a considerable amount of time to solve [1]. It is generally used for solving optimization problems in research. The Pile Design, both geotechnical and structural, is as per Indian standards code [4, 5, 6, 7, 12, 13] based design method. A preliminary estimate of conceptual design is also presented which is as per Assam Public Works Department Schedule of Rates [11]. MATLAB which is a programming software has been used to develop the interface of the stand-alone software and codes in this study.

2.2 Genetic algorithm

The Genetic Algorithm (GA) is a stochastic search-based optimization algorithm which mimics the process of evolution that includes natural selection. It is commonly used for nonlinear optimization problems. On the other hand, gradient based methods can be applied to linear optimizations due to certain defects in accuracy of the objective function [1]. The Genetic algorithm involves processes of selection, crossover, and mutation of the trial solutions so as to improve the set of solutions and converge towards an optimal solution. Each solution in every generation consists of a set of parameters, and by manipulating these parameters the Genetic Algorithm (GA) converges towards the best possible solution. In Genetic Algorithm (GA), a population of solutions, also referred to as individuals are generated. For a given optimization problem, a set of potential solutions are initially generated, also known as the first generation. Within each population, every solution or individual is assigned a corresponding fitness value which is obtained by calculating a fitness function. The fitness value ranks the fitness or appropriateness of a solution. Within each population, some solutions based on their fitness are chosen to carry forward to the next generation of solutions as clones of the original solution. These solutions thus guarantee with the best fitness value of each generation will be maintained or manipulated to be improved upon from one generation to another, while providing better quality of said parameters within a population.

Crossover represents a reproduction function. It means that for each generation, a smaller group of solutions is selected to combine the parameters associated with them and create new solutions, and these new solutions are the new generation of solutions. The group that crosses over are called parents, and the “genes” of two (or more) such parent solutions are combined to generate one (or more) new solution, as their child. It is these children that make up a new generation of solutions. These new generation of solution is expected to be better in terms of fitness as they are made from parents having best fitness in their respective generation [1].

Each solution are then subjected to mutations. It is a random change in one or more parameters (genes) of a solution based on some probability. This probability is known as the mutation rate [1]. Mutations is a must to maintain and introduce diversity into a population of solution. With more diversity in the population, the genetic algorithm lowers the risk of ending up with a solution in the sub-optimal local minima. A flowchart of the simple version of Genetic Algorithm (GA), explaining its process is shown in Figure 1.

Figure 1.

Basic genetic algorithm (GA) flow chart.

2.3 Design considerations

IS 2911(Part 1/Sec 2): 2010 [5] recommends that the design of a pile foundation should be in such a way that the incoming load from the super structure can be transmitted to the sub-surface safely with appropriate factor of safety. This Factor of safety is against shear failure of sub-surface and without causing excessive settlement (differential or total). The shaft of the pile should have adequate structural capacity to withstand all types of incoming loads, may it be vertical, axial or otherwise and incoming moments which is to be transmitted to the supporting subsoil. The Pile should be structurally complying with the design recommendations given in IS 456: 2000 [13].

2.4 Pile capacity

In this study the ultimate load capacity of a pile foundation is obtained by using a static analysis methodology recommended by IS 2911(Part 1/Sec 2): 2010 [5]. The Load Carrying Capacity of the pile depends on the of the supporting soil properties of various layers of the supporting soil in which the pile is installed. The minimum factor of safety on static formula is taken to be 2.5 as is recommended by the code, IS 2911 (Part 1/Sec 2): 2010 [5].

2.5 Analysis of laterally loaded piles

A pile foundation which is subjected to lateral forces from a number of sources, such as, wind, earthquake, water current, earth pressure, effect of moving vehicles or ships, plant and equipment, etc. [5]. The lateral load carrying capacity of a pile foundation depends on the horizontal sub-grade modulus of the supporting soil and on the structural capacity of the shaft of the pile against bending. While considering lateral load on pile foundations, the effect of other loads acting on the pile foundation, like the axial load coming from the super structure, is to be taken into consideration. The IS code [5] suggests that a group of three or more pile connected by a rigid pile cap is considered to have a fixed head condition. In all other cases the pile foundation is taken to be free headed.

2.6 Structural capacity

The IS code [5] suggests that the pile foundation should have necessary structural strength to transmit the imposed loads safely and ultimately to the supporting soil.

2.7 Estimation

An estimate of the pile foundation designed by the algorithm is generated by the software. In this study the software generates the design of the pile foundation as the output which includes the structural details of the pile foundation and various specifications that will be required in its construction. The structural design generated by the software serves as the drawing for estimation, the other concrete and steel parameters along with workmanship requirements specified by Indian Standards [5] are considered and the Schedule of Rates [11] provided by the Assam Public Works Department, provides the Rate of Items associated with the design.

3. Results and discussions

3.1 Software

The software which is developed in this research has been designed to optimize pile dimensions based on the incoming load (axial, eccentric and lateral) from the super structure and the supporting soil parameters of sloping ground. The software developed allows user to use optimized results generated by the software to design the pile foundation structurally or alternatively allow user input data for design of the pile foundation. All pile foundation design procedure has been adopted as per guidelines provided by Indian Standards code [4, 5, 6, 7, 12, 13] on sloping grounds. A detailed step by step procedure for using this software for optimization and design of pile foundation based on the parameters of soil layers on sloping ground is given below:

1. Under the section named ‘OPTIMIZATION’ the user has to select the optimization technique, here, ‘GA’ is selected from the drop down list provided.

2. Under the section of ‘OPTIMIZATION PARAMETERS FOR PILE’ the user provides the Minimum diameter of the pile in mm, Maximum diameter of the pile in mm, Minimum Length of the pile in m, Maximum Length of the pile in m for the pile on the sloping ground. The Bi-axial Moment acting in x- direction and y- direction respectively in kNm and the incoming Column Load in kN are entered by the user.

3. Next, the number of soil layers of stratified soil are selected by selecting the radio buttons (viz. 1, 2, 3) provided in the ‘SOIL PARAMETERS’ section representing the soil layers on the sloping ground.

4. Based on the number of soil layers on the sloping ground the software highlights the particular layers for which soil parameter inputs are required. Here three numbers of soil layer on the sloping ground has been selected. Hence the software opts for soil parameters of these three soil layers only.

5. Under the section named ‘Layer’, the user needs to select the Soil type for each soil layer on the sloping ground. The software highlights the soil parameters required for that particular soil layer selected. Here Cohesive soil type has been selected for Layers 1, 2 and 3.

6. The ‘Layer length’ in m is entered by the user. The user enters the effective unit weight of the soil at pile tip (y), in kN/m³; the coefficient of earth pressure applicable for the ith layer (Ki); the angle of wall friction between pile and soil for the ith layer (phi) in degrees for Granular soil layer. The user also enters the average cohesion at pile tip (cp), in kN/m²; the adhesion factor for the ith layer depending on the consistency of soil (alpha), the average cohesion for the ith layer (ci), in kN/m² for cohesive soils. Here, for layer 3, which is a cohesive soil layer, the software opts the user to enter cp = average cohesion at pile tip, in kN/m²; alpha = adhesion factor for the 1st, 2nd and 3rd layers of the soil respectively, ci = average cohesion for the 1st, 2nd and 3rd layers, in kN/m² for cohesive soil respectively.

7. The software takes up all the input parameters and uses the Genetic Algorithm (GA) for performing a number of iterations to obtain the optimized pile dimensions within the limits specified by the user. The Optimized results are displayed under the section ‘OPTIMIZED RESULTS OF PILE’ as Length of pile in m and Diameter of pile in mm.

8. User may then opt to use the optimized pile dimension by checking the check box ‘Use Optimized Parameters for Design’ under ‘STRUCTURAL DESIGN PARAMETERS FOR REINFORCED CONCRETE PILE’ section or enter the Length and diameter of the pile under the same section. Here the optimized parameters has been used for design.

9. If the user decides not to use the optimized parameters, user may enter the Vertical Load in kN, Effective eccentricity of vertical load in mm, Lateral Load in kN, Point of Lateral Load application from Ground Level in m and Modulus of sub-grade reaction in MN/m³ for the pile foundation. The user has to select the Grade of Steel in N/mm², Grade of concrete in N/mm², Clear Cover in mm, Cover to reinforcement in mm, Diameter of Longitudinal bars in mm and Diameter of tie bars in mm from the respective drop down lists provided under the section ‘STRUCTURAL DESIGN PARAMETERS FOR REINFORCED CONCRETE PILE’. The parameters used in this example are represented in Figure 2.

10. The software developed in this study then generates the Design results under ‘PILE DESIGN RESULT’ section with a Detailed Drawing of the pile.

11. Under the section of ‘ESTIMATED COST ‘, the Schedule of Rates is to be selected by the user from the drop down list provided. The software generates an estimated cost of the pile in Rupees based on the results generated.

Figure 2.

Software interface.

A stand-alone software is coded with the use of MATLAB Compiler to allow users without a MATLAB license to install and run the software on different operating platforms.

The entire process is summarized in the flow diagram (see Figure 3).

Figure 3.

Flow diagram depicting pile foundation optimization and design process.

3.2 Calibration of software

A few numerical examples [14, 15, 16] were taken from for calibrating the software developed in this study. Methodology discussed in the previous section has been adopted for optimization and design of the pile foundation on sloping ground. The results obtained by the software, by using the parameters given in these numerical problems, are then verified manually.

The basic form of the Genetic Algorithm (GA) used while developing the software is as follows:

Optimize:

$${\mathrm{Q}}_{\mathrm{u}}={\mathrm{A}}_{\mathrm{p}}\left(\frac{1}{2}{\mathrm{D}}_{\mathrm{\gamma }}{\mathrm{N}}_{\mathrm{\gamma }}+{\mathrm{P}}_{\mathrm{D}}{\mathrm{N}}_{\mathrm{q}}\right)+\sum _{\mathrm{i}=0}^{\mathrm{n}}{\mathrm{K}}_{\mathrm{i}}{\mathrm{P}}_{\mathrm{Di}}tan{\mathrm{\delta }}_{\mathrm{i}}{\mathrm{A}}_{\mathrm{si}}$$E1

$$\text{or}{\mathrm{Q}}_{\mathrm{u}}={\mathrm{A}}_{\mathrm{p}}{\mathrm{N}}_{\mathrm{C}}{\mathrm{c}}_{\mathrm{p}}+\sum _{\mathrm{i}=0}^{\mathrm{n}}{\mathrm{\alpha }}_{\mathrm{i}}{\mathrm{c}}_{\mathrm{i}}{\mathrm{A}}_{\mathrm{si}}$$E2

Based on the nature of the soil layers on sloping ground. The first term is the end-bearing resistance (Qp) and the second term is the skin friction resistance (Qs).

Subject to the constraints:

1. The Ultimate Load Bearing Capacity of the pile on sloping ground (Qu) ≥ 2.5 x Incoming Column Load (Q).

2. The Optimized Length of pile (L) on the sloping ground in m ≥ Minimum Length of pile (Lmin) in m and Optimized Length of pile (L) in m ≤ Maximum Length of pile (Lmax) in m.

3. The Optimized Diameter of pile (D) on the sloping ground in mm ≥ Minimum Diameter of pile (Dmin) in mm and Optimized Diameter of pile (D) in mm ≤ Maximum Diameter of pile (Dmax) in mm.

4. Optimized Length of pile (L) on sloping ground in m > 0.

5. Optimized Diameter of pile (D) on sloping ground in mm > 0.

The results of software developed in this study are verified manually and the results tallies. Hence the working process of the software has been calibrated with those of a standard.

3.3 Findings and interpretations

Based on the Results obtained from the software in this study and subsequent manual verification of the results, it can be inferred that (Figures 4–6):

1. The software developed in this study is capable of using a Genetic Algorithm for optimization of Geotechnical Design parameters of a pile foundation on sloping grounds based on the input set of variables representing the supporting soil parameters on sloping grounds.

2. The software developed in this study is capable of automating Optimization process by using code replicating the actual optimization process of piles on sloping grounds.

3. The software developed in this study generates the Structural design of pile foundation on sloping grounds by using optimized design results and/or user defined parameters for design of piles.

4. The software developed in this study is capable of generating Structural details of piles based on the recommendations of all Indian Standards [5, 12, 13, 17, 18] specifications.

5. The software developed in this study provides a user friendly interface for providing a real time optimization and design environment for Engineers.

6. The software developed in this study provides users partial or full control over the entire Optimization and Design process of the pile foundation on sloping grounds.

7. The software developed in this study is also capable of generating preliminary estimates of pile foundation design that is obtained from the software itself, thus providing better options while selecting a particular design for implementation.

Figure 4.

Optimization and design results for three layers of soil.

Figure 5.

Optimization and design results for two layers of soil.

Figure 6.

Optimization and design results for single layer of soil.

4. Conclusion

The software developed through this study has adopted the design methodology and constraints considering all the variables involved in pile foundation design and construction recommended by Indian Standards code [4, 5, 6, 7, 12], which is widely used in practice in India. The software developed in this study lets user generate designs for an optimized pile foundation on sloping grounds. The software can also be used for generating structural design of a pile foundation subjected to lateral loading in addition to vertical loading. The said software takes into account the variability of soil layer parameters on sloping grounds thus enhancing the scope for further research into the code for countering complex practical problems. Due to its simplicity and user friendly interface it may cater to shorten the gap between conceptual optimization and design outputs and the actual field applicability of piles on slopes. The software also provides an estimate of the design produced so as to allow the designer to better judge the practical applicability of a particular design. Through this study an attempt has been made to bridge the gap between research and field application of an optimized foundation design on sloping grounds and incorporating computer coding to develop an application to simplify user experience.