Proportionality Coefficient m for the Horizontal Foundation Reaction Coefficients Considering the Support Temperature Effect

When using the "m-method" to design and calculate the foundation pit support structure or other support structures subjected to horizontal loads， it is essential to first determine the proportional coefficient m of the foundation’s horizontal reaction force coefficient as a key parameter. The accuracy of the m value directly affects the rationality and safety of the engineering design. This paper summarized several common methods for determining the proportional coefficient m in the design and calculation of support structures or retaining structures. It also put forward a calculation method for the proportional coefficient m under the assumption of equivalent horizontal reaction force in layered soil foundations for foundation pit support projects. Combined with the practice of a specific foundation pit project， axial force monitoring data from the automatic monitoring platform of the support system were used to establish the correlation between the increment of axial force in the support system caused by temperature changes and the proportional coefficient m of the foundation's horizontal reaction force coefficient， under specific support arrangement conditions. This enables the inversion of the m value. Simultaneously， a mechanical model was established for this foundation pit project， and Plaxis software was employed to determine the m value by numerical simulations. Finally， the results obtained from field measurements and numerical simulations in this project were compared with both the method of equivalent horizontal reaction force proposed in this paper and the conventional method of average thickness of foundation soil layer， thereby verifying the feasibility of the formula proposed for the equivalent horizontal reaction force method.