Sand and gravel soils in a dam foundation with a suspended cutoff wall may lead to fine grains loss due to the effect of suffusion, which further results in the reduction of strength and deformation modulus. As a result, the cutoff wall and the dam above the foundation experience an adverse impact. The effect of loss amount of fine particles on the stress-strain relationship of soil is known as one of preconditions to quantitatively assess the impact. In this study, an experimental program was presented to study the constitutive model. Triaxial and confined compression tests were conducted to investigate the effect of the loss amount of fine particles on the strength and stress-strain relations of sand and gravel soils. It is found that stress-strain characteristics of soil are not influenced by fine grain loss, but both the strength and deformation modulus are decreased. By establishing the relationship between model parameters and the amount of the loss, a single model was utilized to describe the stress-strain relationships of sand and gravels with spatio-temporal changes of particle loss amount. Based on Duncan E-B model, we proposed an expression to quantitatively describe the relationship between the loss amount of fine particles and the stress-strain of the soil, and parameters of the constitutive model were given as well.