“…Studies on foundation structures and mathematical models for footings have been successfully investigated in various geotechnical engineering problems. The main contributions of various researchers in the last decade are: "Behavior of repeatedly loaded rectangular footings resting on reinforced sand" (El Sawwaf and Nazir, 2010); "Nonlinear vibration of hybrid composite plates on elastic foundations" (Chen et al, 2011); "Stochastic design charts for bearing capacity of strip footings" (Shahin and Cheung, 2011); "Modified particle swarm optimization for optimum design of spread footing and retaining wall" (Khajehzadeh et al, 2011); "Design of isolated footings of rectangular form using a new model" (Luévanos-Rojas et al, 2013); "Design of isolated footings of circular form using a new model" (Luévanos-Rojas, 2014a); "Design of boundary combined footings of rectangular shape using a new model" (Luévanos-Rojas, 2014b); "Determination of the ultimate limit states of shallow foundations using gene expression programming (GEP) approach" (Tahmasebi poor et al, 2015); "Design of boundary combined footings of trapezoidal form using a new model" (Luévanos-Rojas, 2015); "New iterative method to calculate base stress of footings under biaxial bending" (Aydogdu, 2016); "A comparative study for the design of rectangular and circular isolated footings using new models" (Luévanos-Rojas, 2016a); "Influence of footings stiffness on punching resistance" (Fillo et al, 2016); "A new model for the design of rectangular combined boundary footings with two restricted opposite sides" (Luévanos-Rojas, 2016b); "Structural design of isolated column footings" (Abdrabbo et al, 2016); "Optimal design for rectangular isolated footings using the real pressure on the ground" (Luévanos-Rojas et al, 2017a); "Experimental and finite element analyses of footings of varying shapes on sand" (Anil et al, 2017); "A comparative study for design of boundary combined footings of trapezoidal and rectangular forms using new models" (Luévanos-Rojas et al, 2017b); "Performance of isolated and folded footings" (El-kady and Badrawi, 2017); "Analysis and Design of Various Types of Isolated Footings" (Balachandar and Narendra Prasad, 2017); "A new model for T-shaped combined footings Part II: Mathematical model for design" (Luévanos-Rojas et al, 2018); "Punching shear resistance of reinforced concrete footings: evaluation of design codes" (Santos et al, 2018); "Soil foundation effect on the vibration response of concrete foundations using mathematical model" (Dezhkam and Yaghfoori, 2018); "Nonlinearity analysis in studying shallow grid foundation" (Ibrahim et al, 2018); "Modeling for the strap combined footings Part II: Mathematical model for design" …”