Based on the special characteristic of multi-resolution of wavelet function

Daubechies wavelet has strong superiority in solving some engineering problems such as high stress gradient

strong nonlinearity and some other singular problems in engineering. But because of the limited computation scope of connection coefficient

Daubechies wavelet finite element method has only been used in the computation of bar

beam

and beam on elastic foundations with a constant foundation coefficient. In the computation of pile foundations based on ‘m’ theory

the foundation coefficient is assumed as linear function. So the foundation coefficient of load in deflection curve differential equation is a linear variable. But the computation methods or results of relative connection coefficient have not been proposed in any documents up till now. Thus Daubechies wavelet method cannot be employed to conduct the computation of pile foundations based on ‘m’ theory. Aiming at the feature of computation model of pile foundations

a new type of connection coefficient is put forward based on ‘m’ theory. Thus Daubechies wavelet is applied to the computation of pile for the first time. Typical models of pile foundations are computed using the new type of connection coefficient mentioned above. The calculation result verifies the correctness of the educed new type of wavelet connection coefficient; and it is shown that pile foundations can be calculated with high accuracy by using wavelet finite element method.