地应力是控制煤矿瓦斯动力灾害的核心因素，现有地应力模型主要基于弹性煤岩体属性而建立，而对于黏弹性煤层介质不适用，需要建立适合煤层属性的地应力分布模型。煤层尤其是构造煤呈现显著的蠕变和应力松弛特性，基于此，构建了黏弹性煤层分数阶麦克斯韦应力松弛数学模型，对扩展伊顿模型中构造应力项改进为黏弹性煤层的应力松弛项，建立了黏弹性煤层地应力分布模型。结果表明，在地质时间尺度内，煤层黏弹性对差应力有显著影响，煤体蠕变和应力松弛程度随黏性系数和分数阶因子的增加而增加；并随弹性模量下降，泊松比、构造比及瓦斯压力增加，煤层应力特征表现为静水压力状态分布趋势，其中弹性模量和泊松比对垂直主应力与水平应力之间差异贡献较大，构造比对水平应力之间差异贡献较大，瓦斯压力对3个主应力贡献相等，应力松弛效应可改变最大、最小水平主应力相对大小及降低应力各向异性。基于临界应力模型，在不同地应力状态下同样获得了摩擦因数降低及瓦斯压力升高的煤层趋近静水压力分布。构造煤力学属性更有利于在地质时间尺度中趋向于静水压力状态。运用地应力模型验证了现场实测结果，并对构造煤瓦斯富集和渗透率降低提出了新的认识。

In-situ stress is a core factor controlling dynamic gas disasters in coal mines. Existing in-situ stress models are primarily based on the elastic properties of coal-rock formations and are not suitable for viscoelastic coal media. There is a need to establish an in-situ stress distribution model suitable for viscoelastic coal properties. Coal seams, especially tectonic coal, exhibit significant creep and stress relaxation characteristics. In this study, a Fractional Maxwell stress relaxation mathematical model was developed for viscoelastic coal reservoirs. The stress component of the extended Eaton model was improved to account for the stress relaxation in viscoelastic coal seams and an in-situ stress distribution model was established for viscoelastic coal seams. The results indicate that over geological time scales, viscoelasticity significantly affects the differential stress in coal seams. The degree of coal body creep and stress relaxation increases with the increase in viscosity coefficient and fractional order factor. As the elastic modulus decreases, the Poisson’s ratio, tectonic ratio, and gas pressure increase. The stress characteristics of coal seams exhibit a trend of hydrostatic pressure state distribution. Among them, the elastic modulus and Poisson's ratio contribute significantly to the difference between vertical principal stress and horizontal stress. The tectonic ratio contributes significantly to the difference between horizontal stresses. Gas pressure contributes equally to all three principal stresses. The stress relaxation effect can alter the relative magnitudes of maximum and minimum horizontal principal stresses and reduce stress anisotropy. Based on the critical stress model, a reduction in friction coefficient and an increase in gas pressure were similarly observed in coal seams under different in-situ stress conditions, leading to an approach towards hydrostatic pressure distribution. The mechanical properties of tectonic coal are more conducive to approaching hydrostatic pressure states over geological time scales. The application of the in-situ stress model established in this study validated the field measurements and provided new insights into gas enrichment and permeability reduction in tectonic coal.