乌蒙山区特长极深隧道隧址区地应力场分布特征及反演分析

郭延辉; 罗毅; 刘敬; 鲍国能; 何开国; 董亚生; 杨俊坤; 方南波

doi:10.19509/j.cnki.dzkq.tb20250272

乌蒙山区特长极深隧道隧址区地应力场分布特征及反演分析

doi: 10.19509/j.cnki.dzkq.tb20250272

1.
昆明理工大学公共安全与应急管理学院，昆明 650093
2.
云南建投第五建设有限公司，昆明 650106
3.
云南建投第六建设有限公司，云南玉溪 653199

基金项目: 云南省基础研究计划重点项目（202501AS070107）；云南省基础研究计划面上项目（202301AT070454）；云南省兴滇英才支持计划青年人才专项项目（KKXX202467043）；昆明理工大学分析测试基金项目（2024M20232239007）；昆明理工大学省级人才培养基金项目（KKZ3202367014）

详细信息

通讯作者:
E-mail：guoyanhui0818@kust.edu.cn

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出版历程
- 收稿日期: 2025-06-14
- 录用日期: 2025-10-29
- 修回日期: 2025-10-28
- 网络出版日期: 2025-12-29

Distribution characteristics and inversion analysis of in-situ stress field at tunnel site of an extra-long and ultra-deep tunnel in Wumeng Mountain area

1.
School of Public Safety and Emergency Management, Kunming University of Science and Technology, Kunming 650093, China
2.
The Fifth Construction Co., Ltd. of Yunnan Construction and Investment Holding Group Co. LTD., Kunming 650106, China
3.
The Sixth Construction Co., Ltd. of Yunnan Construction and Investment Holding Group Co. LTD., Yuxi Yunnan 653199, China

More Information

Corresponding author: E-mail：guoyanhui0818@kust.edu.cn

摘要

摘要:
以鲁甸—巧家高速巧家特长极深分离式隧道为研究对象，隧址地处乌蒙山区复杂构造带，隧道最大埋深超1600 m，区域构造挤压作用显著，地应力以水平构造应力为主，有限钻孔测点难以反映全域应力分布，为精准揭示隧址区三维初始地应力空间分布特征、完善深埋隧道地应力反演手段，依托勘察报告中K67+910 m钻孔346～637 m深度范围内6组水压致裂原位地应力实测数据，系统分析深部岩体三向主应力随埋深的演化规律；采用MIDASGTSNX有限元软件构建2400 m×2400 m三维地质力学模型，选取地层勘察获取的多组围岩力学参数，分别开展位移约束、应力加载、混合边界、初始应变能理论4类边界条件的反演对比试验，筛选匹配实测应力场最优的边界加载方案，再将最优边界应用于全域模型完成地应力反演，并以相对误差±20%为精度标准，对比实测与反演应力值验证方法可靠性。现场测试表明，三向主应力随埋深近似线性增大，应力量级关系为最大水平主应力S_H>垂直自重应力S_v>最小水平主应力S_h，实测最大主应力优势方向NW32°；数值反演得到最大主应力集中于NW30°～35°，与实测方向高度吻合，各测点应力反演相对误差多控制在15%以内，均处于允许误差区间，应力随深度增长趋势与实测规律统一，证明基于初始应变能理论的反演模型可靠。研究明确了4类边界条件各自适用场景与局限性，证实该应变能反演方法可同时兼顾自重与构造应力场重构，所得分布规律与量化数据能够为同类型超深埋高地应力隧道的地应力反演、围岩支护优化及施工地质灾害防控提供理论支撑与工程借鉴。
- 地应力 /
- 分布规律 /
- 边界条件 /
- 反演分析 /
- 数值模拟
Abstract:
Objective
In-situ stress is a fundamental geological parameter dominating the design and construction safety of deep mountain tunnels. With the rapid expansion of transportation infrastructure in southwest China, numerous extra-long and deeply buried tunnels inevitably pass through complex tectonic zones with intense horizontal tectonic compression, where severely high in-situ stress easily triggers large deformation of surrounding rock and rockburst hazards. The Qiaojia Tunnel on the Ludian-Qiaojia Expressway, located on the northeastern margin of the Wumeng Mountain tectonic belt, is a separated double-line extra-long tunnel with a maximum burial depth exceeding 1 600 m. Restricted by field construction conditions, only limited borehole measuring points can be arranged for hydraulic fracturing tests, which fail to reflect the overall spatial distribution of the three-dimensional in-situ stress field across the entire tunnel site. To fully characterize the initial in-situ stress distribution and develop a reliable inversion framework applicable to ultra-deep tunnels under strong tectonic extrusion, this paper carries out systematic field measurement and numerical comparative research.
Methods
First, six sets of hydraulic fracturing in-situ stress data ranging in depths from 346-637 m were collected from borehole K67+910 m in the tunnel exit section and were used to analyze the variation patterns of the three principal stresses with burial depth. The finite element software MIDAS GTS NX was utilized to establish a three-dimensional geomechanical model with a plane size of 2 400 m × 2 400 m. Multiple sets of mechanical parameters for dolomite, limestone, and mudstone are assigned to the model according to official geological investigation documents. Four types of boundary schemes, namely displacement constraint boundary, stress loading boundary, hybrid boundary, and the boundary scheme derived from initial strain energy theory, were separately implemented for comparative inversion tests. The strain-energy-based scheme was selected as the optimal boundary condition due to its superior fitting performance with the measured stress data. After applying the optimal boundary condition to the full-domain model, the inversion results at each measuring point were extracted and compared with field test values, with ±20% defined as the allowable relative error threshold for evaluating inversion accuracy.
Results
Field test results demonstrated that the magnitudes of the three principal stresses increased approximately linearly with burial depth. The magnitude sequence of in-situ stress ranked as follows: maximum horizontal principal stress (S_H) > vertical overburden stress (S_v) > minimum horizontal principal stress (S_h). The dominant azimuth of the measured S_H was NW32°, proving that the regional stress field was dominated by horizontal tectonic stress. The numerical inversion results indicated that the simulated S_H azimuth was concentrated between NW30° and NW35°, which achieved high consistency with field measurement. The relative errors at most measuring points were controlled within 15%, and all errors fell within the permissible range. In addition, the simulated growth gradient of principal stress with depth was consistent with field measurements, verifying the stability and reliability of the strain-energy-based inversion method.
Conclusion
This study systematically clarifies the applicable scope and inherent limitations of four commonly used boundary schemes for in-situ stress inversion. Compared with traditional single-boundary inversion methods, the proposed strain-energy-based approach can simultaneously reconstruct both gravity-induced stress and regional tectonic stress fields without obvious distortion of stress contour distribution. The distribution patterns and quantitative stress data obtained in this research can provide solid theoretical support and practical engineering references for the in-situ stress inversion of analogous ultra-deep extra-long tunnels, and can guide the optimization of surrounding rock support parameters and the early warning of high-stress geological disasters such as rockbursts and large deformation caused by extrusion.
- in-situ stress /
- distribution pattern /
- boundary condition /
- inversion analysis /
- numerical simulation

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图 1 巧家隧道纵断面图

Figure 1. Longitudinal profile of Qiaojia Tunnel

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图 2 水压致裂法的应力场及弹性力学模型示意图^[37]

a. 三维单元体应力状态；b. 极坐标下钻孔围岩应力状态；c. 钻孔围岩应力场与裂纹起裂位置；d. 钻孔孔壁切向应力分布。σ_x，σ_y，σ_z分别为直角坐标系下x，y，z方向的正应力分量；τ_xy（τ_yx），τ_yz（τ_zy），τ_zx（τ_xz）分别为x，y，z方向的剪应力分量；σ_r为径向应力；σ_θ为切向应力；r为钻孔外任意点K到钻孔中心的距离；σ₁，σ₂分别为原地应力场中的最大水平主应力和最小水平主应力；a为钻孔半径；θ为点K与σ₁方向的夹角；A，A'为σ₁作用方向的孔壁点（水平轴端点）；B，B'为σ₂作用方向的孔壁点（垂直轴端点）

Figure 2. Stress field and elastic mechanics model diagrams of hydraulic fracturing method

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图 3 水压致裂典型测试曲线

①～⑨为水压致裂测试标准操作流程的9个关键阶段，分别代表初始注水阶段、升压阶段、破裂点、压力骤降、瞬时关闭、重张阶段、裂缝重张点、裂缝扩展、测试结束；P_b为临界破裂压力；P_s为瞬时关闭压力；P_r为裂缝重张压力

Figure 3. Typical test curve of hydraulic fracturing

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图 4 最大水平主应力优势方向图（红色箭头代表最大水平主应力优势方向）

Figure 4. Dominant direction diagram of maximum horizontal principal stress

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图 5 K67+910 m钻孔三向主应力随深度变化曲线

Figure 5. Variation curves of three principal stresses with depth for borehole K67+910 m

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图 6 最大（a）、最小（b）水平主应力随深度拟合曲线

Figure 6. Fitting curves of maximum (a) and minimum (b) horizontal principal stresses versus depth

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图 7 位移约束边界下初始地应力等值线剖面图（白色线为应力等值线，下同）

Figure 7. Contour cross-sections of initial in-situ stress under displacement constraint boundary condition

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图 8 应力加载边界下初始地应力等值线剖面图

Figure 8. Contour cross-sections of initial in-situ stress under stress loading boundary condition

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图 9 2类混合边界条件下初始地应力等值线剖面图

Figure 9. Contour cross-sections of initial in-situ stress under two hybrid boundary conditions

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图 10 基于初始应变能理论的初始地应力等值线剖面图

Figure 10. Contour cross-sections of initial in-situ stress based on initial strain energy theory

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图 11 巧家隧道隧址区三维地应力反演数值计算模型

Figure 11. Three-dimensional numerical calculation model for in-situ stress inversion in Qiaojia Tunnel site area

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图 12 巧家隧道隧址区三向主应力数值模拟云图

Figure 12. Numerical simulation contour maps of three principal stresses in Qiaojia Tunnel site area

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图 13 钻孔测点三向主应力实测值与数值反演值对比曲线

Figure 13. Comparison curves of measured and inverted three principal stresses at borehole measuring points

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表 1 巧家隧道K67+910 m钻孔地应力测试结果^[39]

Table 1. In-situ stress test results of borehole K67+910 m in Qiaojia Tunnel

测点编号	测点深度/m	临界破裂压力P_b/MPa	裂缝重张压力P_r/MPa	瞬时关闭压力P_s/MPa	孔隙水压力P₀/MPa	抗拉强度T/MPa	最大水平主应力S_H/MPa	最小水平主应力S_h/MPa	垂直主应力S_v/MPa	最大主应力方向
1	346.0	10.28	7.92	3.55	0.16	2.36	9.49	7.01	9.17
2	404.0	9.70	7.40	3.86	0.74	2.30	11.52	7.90	10.71	NW23°
3	471.0	9.56	6.59	4.44	1.41	2.97	14.74	9.15	12.48	NW42°
4	494.0	10.84	9.32	5.11	1.64	1.52	14.25	10.05	13.09	NW32°
5	620.0	11.33	9.02	5.56	2.90	2.31	17.16	11.76	16.43
6	637.0	8.80	8.57	5.38	3.07	0.23	17.25	11.75	16.88
最大水平主应力优势方向										NW32°

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表 2 场区各类围岩岩体物理力学参数

Table 2. Physical and mechanical parameters of various surrounding rock masses in study area

名称	弹性模量 E/GPa	泊松比μ	容重γ/ (KN·m⁻³)	黏聚力 c/MPa	内摩擦角φ/(°)
白云质灰岩	30.00	0.25	22.0	0.25	27
页岩	7.53	0.33	23.0	1.05	21
灰岩	45.20	0.28	26.2	0.54	37
白云岩	25.00	0.27	26.0	2.60	40
泥质白云岩	20.00	0.20	26.0	10.00	40
泥岩	5.00	0.30	22.0	2.50	23

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表 3 钻孔测点地应力实测值与数值反演结果对比

Table 3. Comparison between measured and inverted in-situ stress values at borehole measuring points

测点编号	测点深度/m	对比项	最大主应力S_H/MPa	最小主应力S_h/MPa	垂直应力 S_v/MPa	最大主应力方向
1	346.0	实测值/MPa	9.49	7.01	9.17
		反演值/MPa	10.89	6.73	10.23
		相对误差/%	14.75	−3.99	11.56
2	404.0	实测值/MPa	11.52	7.90	10.71	NW23°
		反演值/MPa	12.25	7.27	11.77	NW30°
		相对误差/%	6.34	−7.97	9.89
3	471.0	实测值/MPa	14.74	9.15	12.48	NW42°
		反演值/MPa	14.38	8.51	13.03	NW35°
		相对误差/%	−2.44	−6.99	4.41
4	494.0	实测值/MPa	14.25	10.05	13.09	NW32°
		反演值/MPa	16.16	10.66	15.01	NW33°
		相对误差/%	13.40	6.07	14.67
5	620.0	实测值/MPa	17.16	11.76	16.43
		反演值/MPa	18.13	12.17	17.36
		相对误差/%	5.65	3.49	5.66
6	637.0	实测值/MPa	17.25	11.75	16.88
		反演值/MPa	19.28	13.04	17.94
		相对误差/%	11.77	10.98	6.28

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