Multi-scale damage and fracture analysis and statistical damage constitutive model of shallow coral reef limestone based on digital core

Abstract

Coral reef limestone (CRL) constitutes a distinctive marine carbonate formation with complex mechanical properties. This study investigates the multiscale damage and fracture mechanisms of CRL through integrated experimental testing, digital core technology, and theoretical modelling. Two CRL types with contrasting mesostructures were characterized across three scales. Macroscopically, CRL-I and CRL-II exhibited mean compressive strengths of 8.46 and 5.17 MPa, respectively. Mesoscopically, CRL-I featured small-scale highly interconnected pores, whilst CRL-II developed larger stratified pores with diminished connectivity. Microscopically, both CRL matrices demonstrated remarkable similarity in mineral composition and mechanical properties. A novel voxel average-based digital core scaling methodology was developed to facilitate numerical simulation of cross-scale damage processes, revealing network-progressive failure in CRL-I versus directional-brittle failure in CRL-II. Furthermore, a damage statistical constitutive model based on digital core technology and mesoscopic homogenisation theory established quantitative relationships between microelement strength distribution and macroscopic mechanical behavior. These findings illuminate the fundamental mechanisms through which mesoscopic structure governs the macroscopic mechanical properties of CRL.

1. Introduction

Coral reef limestone (CRL), widely used in marine and reef engineering projects [1,2], exhibits remarkable mechanical heterogeneity. Experimental studies reveal substantial variability in uniaxial compressive strength: 0.84 to 26.93, 3.48 to 54.05, and 1.5 to 16.0 MPa in the South China Sea region [3,4]; 5.0 to 11.0 MPa in Nansha Islands versus 12.0 to 20.0 MPa in Zhongsha Islands [5]; and 21.52 to 61.89 MPa in the South China Sea compared to 3.08 to 18.6 MPa in the Maldives [6]. Even specimens from identical geological conditions show multi-fold strength variations, with different deformation patterns and failure modes. Burton et al. [7] documented strength variations from 0.3 to 12.5 MPa within the same stratigraphic layers in Barbados, with stress–strain curves typically showing double-peak or yield plateau characteristics. This heterogeneity complicates engineering design and introduces safety risks, necessitating comprehensive investigation into its underlying mechanisms.

Advanced characterization technologies have enabled mesoscopic structural examination of CRL, with several researchers employing optical/acoustic microscopy [8], CT scanning [9], and digital core methodology [10] to analyze pore structures and networks. These studies reveal that CRL has unique characteristics derived from its biological origin and is different from ordinary carbonate rocks. Formed through the accumulation and cementation of coral skeletons, CRL features distinctively high porosity (typically 40% to 70%) compared to conventional carbonate rocks (5% to 30%). These biological and diagenetic processes produce highly heterogeneous pore. Although researchers have begun relating mesoscopic structure to macroscopic properties through in-situ CT [11], post-dynamic failure scanning [12], and X-ray micro-CT [13], these investigations remain largely phenomenological, providing limited understanding of how pore structures influence stress distribution and damage evolution mechanisms.