## 1 Introduction  
The characterization of the brittleness of rocks or rock masses is a fundamental topic in rock mechanics and engineering, and it can be affected by a variety of factors, e.g., the in situ stress environment and the physical properties of the rock itself [1; 2; 3]. To ensure the safe building and operation of rock-related engineering structures, it is crucial to propose a straightforward and reasonable brittleness index.  
Rock brittleness is considered an indirect test parameter as it cannot be obtained directly from tests but needs to be acquired via substituting test data into a series of formulas derived from different definitions [4]. Due to the complexity of rock stress vs. strain curve characteristics and the effects of different coupled factors on the rock damage characteristics [5], it is challenging to establish a uniform standard for quantifying the brittleness characteristics of rocks. Numerous brittleness definitions for rock-like materials have been proposed, including mineral composition-based, mechanical parameter-based, stress-strain curve-based and strain energy-based definitions [6; 7; 8; 9]. Recently, there has been a growing recognition that the deformation process of rocks can be considered as the evolution of various strain energies (including elastic energy, dissipation energy, etc.) [10], and this concept has gained attention in the establishment of rock-like material brittleness evaluation indexes based on strain energy. For example, [PERSON] et al. [11] put forward an energy-based brittleness index applicable to coal that can avoid the subjectivity of human experience. [PERSON] et al. [12] proposed a new index applicable to the evaluation of the brittleness of rock-like materials subjected to a true triaxial stress state and used the index to accurately identify the brittleness strength of basalt, granite and marble. [PERSON] and [PERSON] [13] proposed a new brittleness index for rock-like materials via the peak elastic energy consumption proportion and tested the validity of the index with multiple rocks.  
The deformation and destabilization process of rocks involves both strain energy and damage evolution [14; 15]. The degree of damage in rock-like materials is typically described by a dimensionless damage variable ranging from 0 to 1. Statistical damage models based on phenomenological models, particularly statistical damage theory, have attracted attention for modelling rock deformation due to their simplicity and small number of parameters [16; 17; 18]. [PERSON] et al. [19] and [PERSON] et al. [20] used the exponential function, Weibull function and Gaussian function distributions to develop statistical damage models and correlated brittleness with damage parameters. Their approaches demonstrated the relationship between the damage and brittleness of rocks. Nevertheless, these brittleness indexes are still based on strain energy and their calculation processes are complicated. Furthermore, existing studies on brittleness evaluation mainly focus on intact rocks and there are few studies related to jointed rock masses.  
Given the significant need and existing deficiencies, a novel brittleness index for rock-like materials is put forward via the statistical damage theory and rock damage mechanics. The proposed brittleness index represents the rate of damage development and is expressed concisely. It can identify brittleness responses to changes in confining pressure and temperature. Uniaxial compression tests of rock-like materials are performed using the proposed index to investigate the impact of model size and joint dip angle on rock brittleness.