Analytical methods for horizontal stiffness coefficient at pivots of inner support structures in deep foundation pits

The row piles with inner support structures are often used for retaining and protection of deep foundation pits, and the horizontal stiffness coefficient at the pivots of inner support structures is one of the most important design parameters of retaining and protection structures. In view of the stress-strain linear elasticity theory and deformation coordination hypothesis for compressed bars, the analytical solutions of horizontal stiffness coefficient at pivots of eight basic types of inner support structures face-to-face support, splayed support, inclined support, angle support, vertically inclined support, ideal-ring support, single-ring support and polycyclic-ring support are derived. The formulae for calculating the horizontal stiffness coefficient of the above eight structures are put forward. The horizontal stiffness coefficients of four commonly-used structures are calculated through examples, and the finite element method is used for checking. The results show that the analytical solutions are in good agreement with those calculated by the finite element method, and they can be used as the initial input data for calculation of support structures. This research improves the deficiency that the “Technical specification for retaining and protection of building foundation excavations JGJ120—2012” only affords the formula for calculating the horizontal stiffness coefficient at pivots of horizontal face-to-face support, and the research results can be used as a reference for the design and construction personnel in deep foundation pit engineering.