It is still a common practice to calculate the foundation settlement through the layer-wise summation method using the e-p curve obtained with a compression test. In recent years the secant modulus method (SMM) is increasingly used to calculate the foundation settlement

which is not affected by the initial void ratio of the soil and convenient for computer. The compression stress-strain relationship of soil is expressed as a form of hyperbola in the traditional SMM. The compression stress-strain relationship of loess is discussed and the differences between the secant modulus and compression modulus are analyzed. It is found that the main reason for the discrepancy of calculated results between the SMM and the e-p curve-based method is related to a hyperbolic hypothesis

which assumes that the stress-strain relationship of compacted soils follows hyperbola. To fix the problem

we define the stress-strain relationship of compacted loess using a power function

which can match the actual situation correctly. The settlement formulation using the compression stress-strain relationship with a power function is developed. The proposed method is applied to a practical engineering problem

indicating that the calculated results agree well with measurements.