为了研究一侧采空条件下基本顶板结构的破断规律，构建考虑煤柱宽度及承载能力与实体煤弹塑性变形的基本顶板结构力学模型，全面计算探究了侧方采空条件下基本顶板在煤柱区及实体煤区的断裂位置、顺序及形态等。结论如下：① 煤柱区基本顶的破断形态有3类且随着基本顶厚度h、弹性模量E及弹性煤体基础系数kt增大，而煤柱宽度Lm与煤柱基础系数ksm、煤体塑化范围Lts与塑化程度ξs及跨度L减小时的破断形态变化规律为“单一连续长弧形”→“临界对接双长弧形”→“分隔式双短弧形”；② Lm及ksm主要影响煤柱区基本顶的破断位态；Lm及ksm增大，实体煤区主弯矩减小；③ 实体煤区基本顶破断位态有5类且随着h,E及ξs增大，而Lts,kt及L减小时的断裂模式演变规律为：“长边与短边断裂线均处于塑化煤体区”→“长边断裂线处于塑化煤体区而短边处于煤体弹塑性分界区”→“长边断裂线位于塑化煤体区而短边断裂线位于弹性煤体区”→“长边断裂线位于煤体弹塑性分界区而短边断裂线位于弹性煤体区”→“长边与短边断裂线均处于弹性煤体区”，存在长边与短边断裂线同时位于煤体弹塑性分界区的情况；④ h,E及Lts较大而L及kt较小时，破断顺序为：中部(靠近煤柱侧)→长边(3类位置)→短边(3类位置)→煤柱侧(3类位置)；⑤ 整体破断形态分为3类且随着h,E及kt增大，而Lm,ksm,Lts，ξs及L减小时，整体破断形态的变化模式为：闭合贯通式“非对称-非对称X”型→临界贯通式“非对称-非对称X”型→开口非贯通式“非对称-非对称X”型。针对研究一侧采空基本顶板结构破断的3类力学模型，从模型特征、破断影响因素、初次破断位置、煤柱侧破断形态、实体煤侧破断位置、整体断裂位态及工程指导意义共7个方面，总结对比了“三边固支+简支模型”(第1类)、“三边弹性基础+考虑煤柱宽度和支撑能力的单一塑化模型”(第2类)与建立的“三边弹塑性基础+考虑煤柱宽度和支撑能力的双重塑化模型”(第3类)的重要区别。

In order to study the fracture rule of the main roof plate structure under the condition of one side goaf,the mechanical model of the main roof plate structure considering the width and bearing capacity of the coal pillar and the elastic plastic deformation of the solid coal was established.This paper comprehensively calculated and explored the fracture position,sequence and shape of the main roof above the coal pillar area and solid coal area under the condition of one side goaf.The conclusions are as follows.① There are three types of fracture modes of the main roof above the coal pillar area,and with the increase of the thickness h,the elastic modulus E of the main roof and the elastic coal foundation coefficient kt,while with the decrease of the coal pillar width Lm,the coal pillar foundation coefficient ksm,the range of plastic zone Lts,the plasticization degree ξs,and the span L,the change rule of the fracture modes are as follows：“single continuous long arc”→“critical butt joint double long arc”→“separated double short arc”.② The Lm and ksm mainly affected the fracture state of the main roof above the pillar area.With the increase of Lm and ksm,the main bending moment decreased above the solid coal area.③ There are five types of fracture states of main roof above the solid coal area.With the increase of h,E and ξs,while Lts,kt and L decrease，the change rules of main roof plate fracture modes are as follows：“the long edge and short edge fracture line are above the plasticized coal area”→“the long edge fracture line is above the plasticized coal area while the short edge fracture line is above the elastic plastic boundary area”→“the long edge fracture line is above the plasticized coal area while the short edge fracture line is above the elastic coal area”→“the long edge fracture line is above the elastic plastic boundary area of coal while the short edge fracture line is above the elastic coal area”→“the long edge and the short edge fracture line are both above the elastic coal area”.There is a case that the fracture line of the long edge and the short edge are both located above the elasto plastic boundary zone of the coal at the same time.④ The h，E and Lts are larger while L and kt are smaller,the main roof fracture order is as follows:middle part (near the coal pillar side) → long side (three types of location) → short side (three types of location) → coal pillar side (three types of location).⑤ The overall fracture patterns of the main roof can be divided into three types，with the increase of h,E and kt,while the decrease of Lm，ksm，Lts，ξs and L,the change modes of the overall fracture morphology are as follows：closed asymmetric “X” type → critical through asymmetric “X” type → open type asymmetric “X” type.Aiming at the three kinds of mechanical models of main roof plate structure fracture with one side goaf,the important differences among the “trilateral fixed + simply supported model” (the first category),“trilateral elastic foundation + considering the width and supporting capacity of coal pillar model” (single plasticization model,the second category) and the “trilateral elastic plastic foundation + considering the width and supporting capacity of coal pillar” (double plasticization model,the third category) established in this paper are summarized and compared from seven aspects,including model characteristics,fracture influencing factors,initial fracture position,pillar side fracture shape,solid coal side fracture position,overall fracture position and engineering guiding significance.The model in this paper obtains many new conclusions that the traditional models can not get,which effectively makes up for the defects and deficiencies of the traditional models,and has important value in improving the theoretical understanding level and practical guidance of plate fracture in mining engineering.

1 一侧采空边界条件对比

2 弹-塑性基础边界与一侧采空基本顶板结构力学模型构建

   2.1 力学模型建立

   2.2 边界条件

3 模型求解方法及破断准则

4 弹-塑性基础+煤柱条件下的基本顶全区域力学特征及破断模式分析

5 破断模式的直接因素分析

   5.1 破断模式的Lts效应

   5.2 破断模式的ξs效应

   5.3 破断模式的Lm效应

   5.4 破断模式的ksm效应

6 破断模式的间接因素分析

   6.1 破断模式的kt效应

   6.2 破断模式的h效应

   6.3 破断模式的跨度/长宽比效应

7 模型结论对比

   7.1 基本结论方面

   7.2 指导意义方面

8 工程案例

9 结论