# Mathematical model of dry stack structural elements with geometric imperfections under a cyclic bending moment

## TL;DR

This paper proposes a mathematical model to describe the behavior of dry stack structures under cyclic bending, incorporating geometric imperfections and energy dissipation.

## Contribution

A novel mathematical model combining linear, nonlinear, and hysteresis springs to simulate dry stack behavior under cyclic loading.

## Key findings

- The model accurately captures nonlinear stiffness and energy dissipation in dry stack elements.
- Experimental validation confirmed the model's effectiveness in describing cyclic bending behavior.
- The model's parameters can be determined from test results of physical structures.

## Abstract

Dry stack structural elements are characterized by nonlinear stiffness that arises from geometric imperfections of their components and the absence of any bonding between them. Moreover, such elements dissipate energy under cyclic loading because of their internal structure. The authors considered dry stack structural elements loaded with a bending moment to propose a relatively simple mathematical model of dry stacks composed of only three elements. The model consists of a linear spring, a nonlinear spring, and a spring with hysteresis in series. In this model, the first element describes the idealized properties of a dry stack element, while the second and third elements correspond to the influence of geometric imperfections and the behaviour of dry joints. Furthermore, the authors described a procedure for determining the parameters of the model based on test results. The proposed solution was verified via experimental studies of temporary support structures consisting of a stack of cuboid elements and a hydraulic jack typically used in the process of building rectification. This study showed that the proposed model adequately describes both the nonlinearity and the energy dissipation under a cyclic bending moment.