# Laboratory Investigation on the Impact Force of Large Boulders in Debris Flows

## TL;DR

This study develops a model to predict the impact force of large boulders in debris flows using lab experiments and validates it with field data.

## Contribution

A new theoretical model and sensing system for quantifying boulder impact forces in debris flows is proposed and validated.

## Key findings

- Impact coefficient c is strongly influenced by debris flow yield stress, bulk density, and particle size.
- The proposed model aligns with field observations, with 76.3–86.8% of back-calculated boulder diameters in the 0.1–0.3 m range.
- A high-precision piezoelectric sensing system was developed for impact force measurement in debris flows.

## Abstract

The impact of large boulders transported by debris flows is a primary cause of structural damage to mitigation works. However, quantitative modeling remains difficult because of the scarcity of field measurements and the complexity of the flow medium. In this study, a theoretical model for boulder impact force in debris flows is developed using dimensional analysis based on the Buckingham theorem, subsequently simplified to two dimensionless parameters, and then validated through a series of controlled laboratory experiments. Marble spheres were used as impactors and were released to strike a rigid steel plate under three types of media: clear water, bentonite slurry, and debris flows containing particles of different size classes. The experiments were designed to isolate and quantify the influence of the flow rheology and the suspended solid phase on impact forces. The results show that the impact coefficient c is strongly governed by the debris flow yield stress, bulk density, and the size of suspended particles, following the relationship c = 0.183[τ/(rgd1)]−0.1(d/d0)0.05. Based on this relationship, a generalized formula for calculating boulder impact forces in debris flows is proposed. The model is further evaluated using field monitoring data from Jiangjiagou, Yunnan Province. The back-calculated boulder diameters fall predominantly within the range of 0.1–0.3 m (76.3–86.8%), which is consistent with field observations. These results indicate that the proposed model captures the essential physical mechanisms governing boulder impacts and provides a rational basis for selecting design parameters in debris flow mitigation engineering. The array-type piezoelectric impact sensing system designed in this study achieves high-precision and high-stability measurement of the impact force of large boulders in debris flows, providing a new sensing technology for debris flow impact monitoring.