Polluted drainage from weathering of sulfide-rich waste rock deposits can cause long-term impairment to waterways and biodiversity near mining sites. Mechanistic models represent established tools to support the predictions of the quantity and quality of waste rock drainage, and their associated risks. Yet, model-based predictions in typical waste rock systems are ubiquitously uncertain because of the strongly heterogeneous nature of these waste deposits. Embedding heterogeneity within predictive modeling is complicated by the magnitude and level of knowledge of the waste rock heterogeneity, and the large number of scale-dependent parameters feeding the model equations. This review encompasses deterministic and stochastic modeling approaches that emphasize consolidated tools and emerging modeling solutions to deal with heterogeneity for the modeling of waste rocks. Physical (e.g., variability of texture, hydraulic and pneumatic properties), geochemical (e.g., variability of mineralogy and kinetic parameters), and thermal heterogeneities are evaluated. The review points out the importance of stochastic modeling as a fundamental approach to embed uncertainty in long-term model-based decisions. Regulators and decision makers must be convinced of the benefit of using stochastic modeling, which is still considered to belong mainly to the academic sphere.

风化富含硫化物的废石沉积物造成的排污污染可能对采矿场附近的水道和生物多样性造成长期损害。力学模型代表了已建立的工具，可以支持对rock石排水量和质量及其相关风险的预测。然而，由于这些废物沉积物的强烈异质性，因此在典型的废物岩石系统中基于模型的预测普遍存在不确定性。由于对rock石异质性的了解程度和知识水平以及大量与模型相关的比例相关参数，使得将异质性嵌入预测模型中变得很复杂。这篇综述涵盖了确定性和随机性建模方法，这些方法强调了合并工具和新兴的建模解决方案，以处理废石建模的异质性。评估了物理（例如质地，水力和气压特性的变化），地球化学（例如矿物学和动力学参数的变化）和热非均质性。该评论指出了随机建模作为将不确定性嵌入基于模型的长期决策中的基本方法的重要性。监管者和决策者必须确信使用随机建模的好处，该模型仍被认为主要属于学术领域。和热异质性进行了评估。该评论指出了随机建模作为将不确定性嵌入基于模型的长期决策中的基本方法的重要性。监管者和决策者必须确信使用随机建模的好处，该模型仍被认为主要属于学术领域。和热异质性进行了评估。该评论指出了随机建模作为将不确定性嵌入基于模型的长期决策中的基本方法的重要性。监管者和决策者必须确信使用随机建模的好处，该模型仍被认为主要属于学术领域。