Constrained Vertex Optimization and Simulation of the Unconfined Compressive Strength of Geotextile Reinforced Soil for Flexible Foundation Construction

Extreme vertex design (EVD) provides an efficient approach to mixture experiment design whereby the factor level possesses multiple dependencies expressed through component constraints formulation. Consequently, the derived experimental points are within the center edges and vertices of the feasible constrained region. EVD was deployed for the modeling of the mechanical properties of the problematic clayey soil-geogrid blends. Geogrids are geosynthetic materials that possess an open mesh-like structure and are mostly used for soil stabilization. The geotextile materials present a geosynthetic and permeable layer to support the soil and foundation by improvement of its stiffness characteristics and at a cheaper cost to procure compared to other construction materials and possess unique lightweight properties with greater strength improvement on the soil layer when used. Minitab ۱۸ and Design Expert statistical software was utilized for the mixture design experiment computation; to fully explore the constrained region of the simplex, I-optimal designs with a special cubic design model were utilized to formulate the mixture component ratios at ten experimental runs. I-optimality and D-optimality of ۰.۳۹۰۹۳ and ۱۷۴۷.۴۷۴, respectively, were obtained with a G-efficiency of ۶۴.۸%. The generated laboratory responses were taken together with the mixture ingredients’ ratio and taken as the system database for the model development. Statistical influence and diagnostics tests carried out on the generated EVD model indicate a good correlation with the experimental results. Graphical and numerical optimizations were incorporated using a desirability function that ranged from ۰ to ۱, which helped to arrive at the optimal combination of the mixture components. ۰.۲% of geogrid, ۹.۸% of water, and ۹۰ % of soil yielded the optimal solution with a response of ۴۱.۲۷۰kN/m۲ and a desirability score of ۱.۰. The model simulation was further carried out to test the model’s applicability with the results compared with the actual results using student’s t-test and analysis of variance. The statistical results showed a p-value>۰.۰۵ which indicates a good correlation.

Keywords:

Geogrid , Unconfined Compressive Strength , constrained simplex method , Design Expert , Soil reinforcement