Abstract: Acid fracturing technology is one of the effective ways to improve the permeability of low permeability coal seam. The corrosion and splitting effect of acid solution is the key to softening and fracturing of coal. In order to explore the failure mechanism of coal under the action of acid solution, the acid-based CO₂ foam fracturing fluid (formula∶NA∶K–12 = 6∶4, foaming agent concentration 0.6%, thickener concentration 0.6%) was used to carry out the fracturing fluid erosion test of raw coal samples, and the peak stress, elastic modulus, failure morphology and fracture development characteristics were obtained. The acidizing corrosion process of coal was analyzed, and the damage statistical constitutive model of acid fracturing coal was constructed. The results show that: Increasing the erosion time of fracturing acid solution, the properties of glass medium of coal body will lead to the reorganization of its physical structure, which increases the free volume of polymer system and improves the compressibility and brittleness of coal rock. With the increase of fracturing fluid erosion time, the chemical reaction degree of minerals in the pores and fissures of coal will be intensified, resulting in the increase of mineral crystallization precipitation on the surface of coal, and the decrease of uniaxial compressive strength and elastic modulus of coal will increase. It shows that the internal connectivity of the pores and fissures of the eroded coal rock under this formula is better, and the fracture effect of coal rock is more significantly affected by the erosion time, and the brittle damage of coal body is obvious. Based on the Weibull distribution of coal strength, the statistical damage constitutive relation of brittle strength of saturated carbonate eroded coal is constructed. The accuracy of the key parameters E, m and F of the model is verified, which shows that the constitutive relation can accurately characterize the basic law of stress-deformation of low permeability coal seam under acid fracturing. The above research results provide theoretical calculation basis for the determination of fracturing radius of acid fracturing coal body, and play an important guiding role in the arrangement of fracturing boreholes.