Explicit Peck formula applied to ground displacement based on an elastic analytical solution for a shallow tunnel

Using the complex variable method,an elastic analytical solution of the ground displacement caused by a shallow circular tunneling is derived.Non-symmetric deformation relative to the horizontal center line of the tunnel cross-section is used as a boundary condition.A comparison between the proposed analytical method and the Finite Element Method is carried out to validate the rationality of the obtained analytical solution.Two parameters in the Peck formula,namely the maximum settlement of the ground surface center and the width coefficient of settlement curve,are fitted and determined.We propose a modified Peck formula by considering three input parameters,namely the tunnel depth,tunnel radius,and the tunnel gap.The influence of these three parameters on the modified Peck formula is analyzed.The applicability of the modified Peck formula is further investigated by reference to six engineering projects.The ground surface displacement obtained by the explicit Peck formula is in good agreement with the field data,and the maximum error is only 1.3 cm.The proposed formula can quickly and reasonably predict the ground surface settlement caused by tunnelling.

Fractional viscoelastic solution of stratum displacement of a shallow tunnel under the surface slope condition

The unified displacement function(UDF)is presented to describe the deformation behaviours of the tunnel profile along with time under the surface slope condition.Based on the discrete Fourier method,the third-order UDF in the physical plane is expanded to the Laurent series in the complex variable plane.The complex variable method is employed to derive the elastic analytical solution of stra-tum displacement,when the third-order UDF is taken as the displacement boundary condition of tunnel cross-section(DBCTC).The proposed elastic solution agrees well with the results of the finite element method for the consistent model,which verifies the correctness of the proposed analytical solution.Combining the corresponding principle and fractional Generalized Kelvin viscoelastic constitutive model,the fractional viscoelastic solution under the surface slope condition is determined.The time effect of stratum displacement is presented in two aspects:time-dependent DBCTC and time-dependent material parameters.The parameter analysis is performed to investigate influences of deformation modes of the third-order UDF,slope angle,tunnel radius and fractional order on the time effect of stratum vertical and horizontal displacement.

Dynamical behaviors of the generalized hematopoiesis model with discontinuous harvesting terms

This paper is concerned with the generalized hematopoiesis model with discontinuous harvesting terms.Under the framework of Filippov solution,by means of the differential inclusions and the topological degree theory in set-valued analysis,we have established the existence of the bounded positive periodic solutions for the addressed models.After that,based on the nonsmooth analysis theory w让 h Lyapunov-like approach,we employ a novel argument and derive some new criteria on the uniqueness,global exponential stability of the addressed models and convergence of the corresponding autonomous case of the addressed models.Our results extend previous works on hematopoiesis model to the discontinuous harvesting terms and some corresponding results in the literature can be enriched and extended.In addition,typical examples with numerical simulations are given to illustrate the feasibility and validity of obtained results.