Cement is the most widely used additive in soft soil stabilization due to its high strength and availability. The cement content and curing time have a direct influence on the stabilization cost and hence it is prudent to minimize these variables to achieve optimality. Thus, it is a classical multi-objective optimization problem to find the optimum combination of cement content used and the curing time provided to achieve the target strength. This paper brings out the use of Vector Evaluated Artificial Bee Colony (VEABC) algorithm, a multi-objective variant of Artificial Bee Colony (ABC) technique, for the problem on hand. VEABC is a swarm intelligence algorithm, which employs multiple swarms to handle the multiple objectives and the information migration between these swarms ensures a global optimum solution is reached. Due to the stochastic nature of ABC algorithm, the resulting Pareto Curve will cover a good range of data with smooth transition. The Pareto fronts obtained for target strength could be used as calibration charts for scheduling the soft soil stabilization activities.
Top1. Introduction
Soft soil engineering is often challenging to geotechnical engineers. The Chek Lap Kok International Airport at Hong Kong (Zhu et al., 2001), Surnabhumi International Airport at Thailand (Moh et al., 2003) and Trans-Tokyo Bay Highway Project of Japan (Tatsuoka et al., 1997) are some of the examples of massive infrastructure projects constructed on soft soils. Soft soils are wide spread and cover many regions of the world such as Japan, Eastern Canada, Norway, Sweden and other Scandinavian countries, India and the South East Asian countries. Inadequate strength of soft soils is a serious constraint to take up any developmental activity on soft soils. The strength and stiffness of soft ground are often improved by cement stabilization. The extent of the strength improvement of soft soil depends on physico-chemical factors such as the type of the stabilizing agent, the type of soil, the type and content of organic matter, the water content, the curing period and the curing conditions (Horpibulsuk, 2001; Horpibulsuk, Bergado, & Lorenzo, 2003; Miura, Horpibussuk, & Nagaraj, 2001; Narendra, Sivapullaiah, Suresh, & Omkar, 2006; Narendra, 2006; Porbaha, 1998; Suzuki, Fujimoto, & Taguchi, 2014; Tan, Goh, & Yong, 2002; Uddin, Balasubramaniam, & Bergado, 1997; Yin and Lai, 1998). Advanced cement stabilization techniques such as deep mixing (Tan, Goh, & Yong, 2002) have been developed, and widely used for improving the strength of soft grounds. In deep mixing, the cement grout or dry cement is injected into the natural soil at the depth required and a blade is pushed into the ground to mix the soil and cement (Porbaha, 1998; Tan, Goh, & Yong, 2002). This technique has become quite common and presently many countries have their deign guides for practice.
In the cement stabilization of soft soil, the cement content used and the curing period involved has a direct effect on the cost of the project. Hence, the cement stabilization of soft soil could be viewed as an optimization problem, with the objective to find the optimum combination of cement content to be used and the curing time to be provided to achieve the required soil strength. Since, both cement content and curing time has a direct effect on the total cost incurred, one has to minimize both cement content and the curing time to ensure optimality. The two objectives; minimizing cement content and minimizing curing time are both conflicting. So this becomes a classical multi-objective optimization problem with competing objectives.
In case of a multi-objective optimization problem with conflicting objective, instead of a single optimal solution that satisfies all the objectives, a number of solutions, which indicate the trade-off between the multiple objectives, exist. Hence the concept of Pareto optimality (Schaffer, 1984; Eckart, Marco, & Stefan, 2004) is introduced. A Pareto Front (Eckart, Marco, & Stefan, 2004) gives a set of optimal solutions, for a given set of conflicting objectives. A typical Pareto Front is shown in Figure 1, where the solid line represents the Pareto Front and the symbols represent all the feasible solutions (both optimal and non optimal). The Pareto Fronts obtained, in the present case, which is cement content versus curing period for a given target strength could be used as calibration charts or a ready reference for scheduling the cement stabilization activities.
Figure 1. Typical Pareto curve (after Grosset et al., (2001))