An experimental investigation of vertical vibration of model footings on sand

Many free and forced vertical vibrations tests were conducted on surface and embedded models for footings on dry and moist poorly graded sand that has the following properties: D₁₀ = 0·21 mm, D₃₀ = 0·305 mm, D₆₀ = 0·423 mm, C_u = 2, C_c = 1·05, G_s = 2·66, γ_max = 1·74 cm⁻³ and γ_min = 1·4 g cm⁻³. The tests were conducted at relative density Dr = 82%. The effect of mass, area, geometry, embedment, saturation, load amplitude and frequency were studied. For this purpose square, rectangular and circular models of concrete footings were chosen. Swieleh sand was chosen as the foundation soil. Results have been obtained for models having different mass, same base shape and area; models of different base area and equal base shape and mass; and models of different base shape geometry and about equal masses and base areas.Forced vertical vibration tests results showed an increase in natural frequency and a reduction in amplitude with the increase in embedment depth, degree of saturation and footing base area. Increasing the mass of model footing resulted in a decrease in the natural frequency while the dynamic response increased. Also, results showed that the circular model footing gives low values of dynamic response in comparison to other models.Free vertical vibration test results showed an increase in damping ratio with increase in the base area of the model footing, depth of embedment and saturation of sand. On the other hand, the results showed a decrease in damping ratio with increase in the footing mass. Circular footing gives the highest value of damping ratio among other footings.Results showed that the best method for evaluating the dynamic stiffness for vertical vibration is using Dobry and Gazetas¹ (J. Geotech. Engng, ASCE, 1986, 112, 109–133) equations together with the formula proposed by Ronald and Bojan² (J. Geotech. Engng, ASCE, 1995, 121, 274–286) for evaluating the equivalent shear modulus.