都市快轨交通

语言变量	标记	直觉模糊数
非常重要	(VI)	(0.90,0.10,0.00)
重要	(I)	(0.75,0.20,0.05)
中等	(M)	(0.50,0.45,0.05)
不重要	(U)	(0.35,0.60,0.05)
非常不重要	(VU)	(0.10,0.90,0.00)

语言变量	标记	直觉模糊数
非常重要	(VI)	(0.90,0.10,0.00)
重要	(I)	(0.75,0.20,0.05)
中等	(M)	(0.50,0.45,0.05)
不重要	(U)	(0.35,0.60,0.05)
非常不重要	(VU)	(0.10,0.90,0.00)

语言变量	标记	直觉模糊数
极高	(EH)	(0.95,0.05,0.00)
非常高	(VH)	(0.85,0.10,0.05)
高	(H)	(0.75,0.15,0.10)
中等偏上	(MH)	(0.65,0.25,0.10)
中等	(M)	(0.50,0.40,0.10)
中等偏下	(ML)	(0.35,0.55,0.10)
低	(L)	(0.25,0.65,0.10)
非常低	(VL)	(0.15,0.80,0.05)
极低	(EL)	(0.05,0.95,0.00)

语言变量	标记	直觉模糊数
极高	(EH)	(0.95,0.05,0.00)
非常高	(VH)	(0.85,0.10,0.05)
高	(H)	(0.75,0.15,0.10)
中等偏上	(MH)	(0.65,0.25,0.10)
中等	(M)	(0.50,0.40,0.10)
中等偏下	(ML)	(0.35,0.55,0.10)
低	(L)	(0.25,0.65,0.10)
非常低	(VL)	(0.15,0.80,0.05)
极低	(EL)	(0.05,0.95,0.00)

专家信息	评价	直觉模糊数	专家权重
专家 1	VI	(0.90,0.10,0.00)	0.258
专家 2	I	(0.75,0.20,0.05)	0.227
专家 3	M	(0.50,0.45,0.05)	0.151
专家 4	VI	(0.90,0.10,0.00)	0.258
专家 5	U	(0.35,0.60,0.05)	0.106

专家信息	评价	直觉模糊数	专家权重
专家 1	VI	(0.90,0.10,0.00)	0.258
专家 2	I	(0.75,0.20,0.05)	0.227
专家 3	M	(0.50,0.45,0.05)	0.151
专家 4	VI	(0.90,0.10,0.00)	0.258
专家 5	U	(0.35,0.60,0.05)	0.106

评价准则	标记	-	二	三	四	五
地质情况	${B}_{1}$	VI	I	M	I	M
施工管理	${B}_{2}$	VI	I	M	VI	I
基坑施工技术风险	${B}_{3}$	I	M	VI	I	VI
周围环境	${B}_{4}$	M	I	I	M	VU

评价准则	标记	-	二	三	四	五
地质情况	${B}_{1}$	VI	I	M	I	M
施工管理	${B}_{2}$	VI	I	M	VI	I
基坑施工技术风险	${B}_{3}$	I	M	VI	I	VI
周围环境	${B}_{4}$	M	I	I	M	VU

目标	评价准则	标记	B₁	B₂	B₃	B₄
基坑施工安全	地质情况	${C}_{1}$	EH	M	VH	M
${C}_{2}$	ML	MH	M	MH
施工管理	${C}_{3}$	H	ML	VH	VH
${C}_{4}$	EH	VH	VH	H
${C}_{5}$	VH	H	EH	MH
基坑施工技术风险	${C}_{6}$	VH	MH	EH	ML
${C}_{7}$	EH	VH	EH	MH
${C}_{8}$	ML	ML	MH	L
${C}_{9}$	VH	VH	VH	H
周围环境	${C}_{10}$	M	MH	M	ML
${C}_{11}$	MH	VL	ML	M

目标	评价准则	标记	B₁	B₂	B₃	B₄
基坑施工安全	地质情况	${C}_{1}$	EH	M	VH	M
${C}_{2}$	ML	MH	M	MH
施工管理	${C}_{3}$	H	ML	VH	VH
${C}_{4}$	EH	VH	VH	H
${C}_{5}$	VH	H	EH	MH
基坑施工技术风险	${C}_{6}$	VH	MH	EH	ML
${C}_{7}$	EH	VH	EH	MH
${C}_{8}$	ML	ML	MH	L
${C}_{9}$	VH	VH	VH	H
周围环境	${C}_{10}$	M	MH	M	ML
${C}_{11}$	MH	VL	ML	M

目标	评价准则	标记	B₁	B₂	B₃	B₄
基坑施工安全	地质情况	${C}_{1}$	(0.648,0.295,0.056)	(0.556,0.332,0.112)	(0.641,0.297,0.062)	(0.412,0.496,0.091)
${C}_{2}$	(0.391,0.512,0.097)	(0.511,0.370,0.120)	(0.490,0.399,0.111)	(0.388,0.509,0.103)
施工管理	${C}_{3}$	(0.577,0.333,0.090)	(0.393,0.438,0.169)	(0.681,0.272,0.047)	(0.502,0.427,0.071)
${C}_{4}$	(0.615,0.327,0.058)	(0.634,0.269,0.098)	(0.534,0.397,0.069)	(0.416,0.483,0.101)
${C}_{5}$	(0.626,0.298,0.076)	(0.671,0.254,0.075)	(0.647,0.311,0.041)	(0.451,0.467,0.082)
基坑施工技术风险	${C}_{6}$	(0.570,0.350,0.081)	(0.521,0.358,0.121)	(0.682,0.268,0.050)	(0.265,0.643,0.092)
${C}_{7}$	(0.690,0.270,0.039)	(0.594,0.297,0.109)	(0.652,0.289,0.059)	(0.503,0.428,0.068)
${C}_{8}$	(0.418,0.481,0.101)	(0.277,0.593,0.130)	(0.491,0.403,0.105)	(0.315,0.583,0.102)
${C}_{9}$	(0.515,0.392,0.093)	(0.693,0.244,0.063)	(0.625,0.307,0.068)	(0.462,0.446,0.092)
周围环境	${C}_{10}$	(0.392,0.512,0.096)	(0.311,0.602,0.087)	(0.263,0.660,0.077)	(0.251,0.660,0.089)
${C}_{11}$	(0.323,0.579,0.098)	(0.357,0.548,0.095)	(0.406,0.503,0.091)	(0.266,0.647,0.087)

目标	评价准则	标记	B₁	B₂	B₃	B₄
基坑施工安全	地质情况	${C}_{1}$	(0.648,0.295,0.056)	(0.556,0.332,0.112)	(0.641,0.297,0.062)	(0.412,0.496,0.091)
${C}_{2}$	(0.391,0.512,0.097)	(0.511,0.370,0.120)	(0.490,0.399,0.111)	(0.388,0.509,0.103)
施工管理	${C}_{3}$	(0.577,0.333,0.090)	(0.393,0.438,0.169)	(0.681,0.272,0.047)	(0.502,0.427,0.071)
${C}_{4}$	(0.615,0.327,0.058)	(0.634,0.269,0.098)	(0.534,0.397,0.069)	(0.416,0.483,0.101)
${C}_{5}$	(0.626,0.298,0.076)	(0.671,0.254,0.075)	(0.647,0.311,0.041)	(0.451,0.467,0.082)
基坑施工技术风险	${C}_{6}$	(0.570,0.350,0.081)	(0.521,0.358,0.121)	(0.682,0.268,0.050)	(0.265,0.643,0.092)
${C}_{7}$	(0.690,0.270,0.039)	(0.594,0.297,0.109)	(0.652,0.289,0.059)	(0.503,0.428,0.068)
${C}_{8}$	(0.418,0.481,0.101)	(0.277,0.593,0.130)	(0.491,0.403,0.105)	(0.315,0.583,0.102)
${C}_{9}$	(0.515,0.392,0.093)	(0.693,0.244,0.063)	(0.625,0.307,0.068)	(0.462,0.446,0.092)
周围环境	${C}_{10}$	(0.392,0.512,0.096)	(0.311,0.602,0.087)	(0.263,0.660,0.077)	(0.251,0.660,0.089)
${C}_{11}$	(0.323,0.579,0.098)	(0.357,0.548,0.095)	(0.406,0.503,0.091)	(0.266,0.647,0.087)

类型	A⁺	A^-
${B}_{1}$	(0.323,0.579,0.098)	(0.690,0.270,0.039)
${B}_{2}$	(0.693,0.244,0.063)	(0.277,0.602,0.121)
${B}_{3}$	(0.263,0.660,0.077)	(0.682,0.268,0.050)
${B}_{4}$	(0.251,0.660,0.089)	(0.503,0.427,0.070)

类型	A⁺	A^-
${B}_{1}$	(0.323,0.579,0.098)	(0.690,0.270,0.039)
${B}_{2}$	(0.693,0.244,0.063)	(0.277,0.602,0.121)
${B}_{3}$	(0.263,0.660,0.077)	(0.682,0.268,0.050)
${B}_{4}$	(0.251,0.660,0.089)	(0.503,0.427,0.070)

目标	评价准则	风险因素	标记	S_i⁺	S_i^-	C_i	归一化	排序
基坑施工安全	地质情况	地下水分布	${C}_{1}$	0.261	0.146	0.359	0.073	9
不良地质情况	${C}_{2}$	0.167	0.206	0.552	0.113	3
施工管理	违规操作	${C}_{3}$	0.297	0.088	0.229	0.047	11
施工方法	${C}_{4}$	0.212	0.193	0.477	0.098	5
施工质量	${C}_{5}$	0.255	0.191	0.428	0.087	6
基坑施工技术风险	支护体系不规范	${C}_{6}$	0.247	0.175	0.415	0.085	8
止水帷幕失效	${C}_{7}$	0.286	0.156	0.353	0.072	10
土方施工不规范	${C}_{8}$	0.236	0.174	0.424	0.087	7
基坑降水方案	${C}_{9}$	0.229	0.212	0.482	0.099	4
周围环境	基坑旁堆载	${C}_{10}$	0.188	0.274	0.593	0.121	1
基坑旁动荷载	${C}_{11}$	0.177	0.246	0.581	0.119	2

目标	评价准则	风险因素	标记	S_i⁺	S_i^-	C_i	归一化	排序
基坑施工安全	地质情况	地下水分布	${C}_{1}$	0.261	0.146	0.359	0.073	9
不良地质情况	${C}_{2}$	0.167	0.206	0.552	0.113	3
施工管理	违规操作	${C}_{3}$	0.297	0.088	0.229	0.047	11
施工方法	${C}_{4}$	0.212	0.193	0.477	0.098	5
施工质量	${C}_{5}$	0.255	0.191	0.428	0.087	6
基坑施工技术风险	支护体系不规范	${C}_{6}$	0.247	0.175	0.415	0.085	8
止水帷幕失效	${C}_{7}$	0.286	0.156	0.353	0.072	10
土方施工不规范	${C}_{8}$	0.236	0.174	0.424	0.087	7
基坑降水方案	${C}_{9}$	0.229	0.212	0.482	0.099	4
周围环境	基坑旁堆载	${C}_{10}$	0.188	0.274	0.593	0.121	1
基坑旁动荷载	${C}_{11}$	0.177	0.246	0.581	0.119	2

基于TOPSIS方法的明挖基坑风险识别

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刘培路

都市快轨交通 | 土建技术 2024,37(2): 84-91

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都市快轨交通 | 土建技术 2024, 37(2): 84-91

基于TOPSIS方法的明挖基坑风险识别

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刘培路

作者信息

中铁十六局集团北京轨道交通工程建设有限公司北京 101100

刘培路，男，硕士，高级工程师，从事地下工程安全施工管理，463692239@qq.com

Identification of Risk Factors of Excavation Based on the TOPSIS Method

Peilu LIU

Affiliations

China Railway 16 Bureau Group, Beijing Metro Engineering Construction Co., Ltd. Beijing 101100

doi: 10.3969/j.issn.1672-6073.2024.02.013

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摘要

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针对深基坑工程施工过程中潜在风险因素众多而难以识别的问题,提出基于直觉模糊优劣解距离法(TOPSIS)的多属性评价方法对风险因素进行评估。首先,基于基坑安全事故案例、专家工程经验和实际工程,分析并确定潜在的风险因素;进而,根据风险因素构建风险评价体系,应用直觉模糊数确定专家和评价准则的权重;最后,运用 TOPSIS 多属性决策方法识别和评估潜在的风险因素。最终通过实例验证了该方法的可行性。研究表明:本方法可有效识别施工过程的高风险因素,可作为基坑施工安全风险分析与控制的决策工具。

关键词

城市轨道交通 / 安全施工 / 基坑工程 / 明挖法 / 风险因素识别 / 直觉模糊优劣解距离法

Abstract

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The complexity of deepexcavation construction arises from the influence of various potential risk factors on the construction procedure. To address this issue, this study introduces an intuitionistic fuzzy TOPSIS method aimed at identifying potential highrisk factors. Initially, potential risk factors were determined through an analysis of the failure modes derived from prior excavation accidents, insights from practical engineering projects, and the expertise of engineering professionals. Subsequently, a risk evaluation hierarchy was established, and weights were assigned to experts and criteria using intuitionistic fuzzy numbers. A practical project involving a deep excavation was conducted to validate the feasibility of the proposed method. The results indicate that the TOPSIS method effectively identified highrisk factors. The developed method serves as a valuable decisionmaking tool for the safety risk analysis and control of excavation construction in similar engineering projects.

Key words

urban rail transit / safety construction / excavation engineering / cut-and-cover method / risk factor identification / intuitionistic fuzzy TOPSIS

引用本文

刘培路. 基于TOPSIS方法的明挖基坑风险识别. 都市快轨交通, 2024 , 37 (2) : 84 -91 . DOI: 10.3969/j.issn.1672-6073.2024.02.013

Peilu LIU. Identification of Risk Factors of Excavation Based on the TOPSIS Method[J]. Urban Rapid Rail Transit, 2024 , 37 (2) : 84 -91 . DOI: 10.3969/j.issn.1672-6073.2024.02.013

正文

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地下轨道交通的建设伴随着大量基坑工程的涌现 ^{[ 1 ]} 。地铁车站深基坑施工工序繁杂,存在众多安全隐患,一旦发生安全事故,将严重危及人身安全,造成巨大的经济损失。近年来, 基坑安全事故呈现上升的趋势, 例如, 2019 年广西南宁东葛路基坑支护发生坍塌,导致路面大面积塌陷[ 2 ]。深基坑的建设大多在城市密集区, 管理和施工要求高; 同时工程体量大, 现场地质情况复杂, 具有很大的建设风险。因此, 建设过程中的施工安全控制与风险评估成为基坑建设的重要问题。

由于地层条件和功能设计的差异, 深基坑工程具有较强的个体差异性与区域性, 不同深基坑的施工技术无法直接转化应用。因而缺少类似工程的施工资料与监测数据, 专家评审仍是深基坑工程风险识别与评价的主要依据 ^{[ 3 - 4 ]} 。例如,曾小明等直接运用层次分析法对项目风险进行评估 ^{[ 5 ]} ; 张振中将改进的层次分析法与熵权法结合,提出了基坑工程风险分析方法 ^{[ 6 ]} ; 龚颖超等提出了基于层次分析法与控制记忆方法的基坑施工风险评价模型 ^{[ 7 ]} 。但是层次分析方法的使用需要满足矩阵一致性的要求, 若不满足, 则需要重新进行评估。此外, 由于专家的教育背景、工程经验、对施工现场的了解程度存在差异, 加上评估的事物存在一定的模糊性与不确定性, 专家评估的局限性进一步凸显。

基于此, 本文运用直觉模糊集为专家风险评估提供方便, 并降低了风险评估过程中可能出现的模糊性与不确定性。在使用直觉模糊集进行多属性风险评估中引入优劣解距离法(TOPSIS), 能基于专家评语快速识别高风险因素。这是由于 TOPSIS 方法能对多个样本与多指标进行同时评价与处理。基于 TOPSIS 方法的优点, 使得其在工程领域得到广泛应用。颜文运用改进 TOPSIS 方法对潜在的铁路线路方案进行了评估与比选 ^{[ 8 ]} 。陈仁鹏等运用模糊层次分析法与改进 TOPSIS 法评估了盾构隧道施工对邻近建筑物的影响 ^{[ 9 ]} 。陈宏俊结合熵权 TOPSIS 方法和灰色关联度方法对影响盾构隧道管片破损的原因进行了分析与评估, 并判定了管片的破损程度 ^{[ 10 ]} 。吴志军等运用 TOPSIS 方法实现了 TBM 隧道岩体可掘性分级 ^{[ 11 ]} 。王亮等用模糊层次分析与 TOPSIS 方法对岩溶隧道超前地质预报方案进行评估与选择 ^{[ 12 ]} 。根据上述情况可知, TOPSIS 方法在隧道工程方面得到了一定的应用。但相对于基坑工程, 由于其复杂性与受到众多因素的影响, 并且在某些情况下影响参数的数据难以获取, 基于此, 本文将 TOPSIS 方法耦合直觉模糊集应用于基坑工程项目,为基坑工程风险识别提供了一种新的方法与思路。

本文针对基坑工程中涉及大量参数取值难以获取或者不确定的情况下,依托专家的工程经验和提出的基于直觉模糊优劣解距离法(TOPSIS)对基坑施工过程中的潜在风险进行识别, 并通过了工程案例(珠机城际横琴至珠海机场段 HJZQ-2 标二工区明挖法基坑工程) 验证了该方法的可行性, 为工程施工安全风险防范和控制提供理论指导。

1 直觉模糊优劣解距离法

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直觉模糊优劣解距离法(TOPSIS)是多属性决策方法 ^{[ 13 ]} 。直觉模糊集的定义如下 ^{[ 13 ]} :

(1) $ Q =\{\langle y,\mu \left( y\right),\eta \left( y\right),\pi \left( y\right)\mid y \in Y\rangle \}$

式中, $\mu \left( y\right): y \rightarrow \left\lbrack {0,1}\right\rbrack$ 和 $\eta \left( y\right): y \rightarrow \left\lbrack {0,1}\right\rbrack$ 为元素 $y$ 属于 $Y$ 的隶属度与非隶属度; $\pi \left( y\right)= 1 -\mu \left( y\right)- \eta \left( y\right)$ 为元素 $y$ 属于 $Y$ 的犹豫度, $0 \leq \pi \left( y\right)\leq 1$ 。

假设 ${Q}_{1}= \left\{{y,{\mu }_{1}\left( y\right),{\eta }_{1}\left( y\right),{\pi }_{1}\left( y\right)}\right\}$ 和 ${Q}_{2}= \left\{{y,{\mu }_{2}\left( y\right)}\right.$ , $\left.{{\eta }_{2}\left( y\right),{\pi }_{2}\left( y\right)}\right\}$ 为两个直觉模糊数。两个模糊数的运算法则如下 ^{[ 13 ]} :

(2) ${Q}_{1}\oplus {Q}_{2}= \left\{\begin{array}{l}{\mu }_{1}\left( y\right)+ {\mu }_{2}\left( y\right)- {\mu }_{1}\left( y\right)\cdot {\mu }_{2}\left( y\right), \\{\eta }_{1}\left( y\right)\cdot {\eta }_{2}\left( y\right)\end{array}\right\}$

其中犹豫度为:

(3) ${\pi }_{{Q}_{1}\oplus {Q}_{2}}= 1 -{\mu }_{1}\left( y\right)- {\mu }_{2}\left( y\right)+ {\mu }_{1}\left( y\right)\cdot {\mu }_{2}\left( y\right)- {\eta }_{1}\left( y\right)\cdot {\eta }_{2}\left( y\right)\\{Q}_{1}\otimes {Q}_{2}= \left\{\begin{array}{l}{\mu }_{1}\left( y\right)\cdot {\mu }_{2}\left( y\right), \\{\eta }_{1}\left( y\right)+ {\eta }_{2}\left( y\right)- {\eta }_{1}\left( y\right)\cdot {\eta }_{2}\left( y\right)\end{array}\right\}$

其中犹豫度为:

(4) ${\pi }_{{Q}_{1}\otimes {Q}_{2}}= 1 -{\eta }_{1}\left( y\right)- {\eta }_{2}\left( y\right)- {\mu }_{1}\left( y\right)\cdot {\mu }_{2}\left( y\right)+ {\eta }_{1}\left( y\right)\cdot {\eta }_{2}\left( y\right)\\{\kappa Q}= \left\{\begin{array}{l} 1 -{\left\lbrack 1 -\mu \left( y\right)\right\rbrack }^{\kappa },{\eta }^{\kappa }\left( y\right), \\{\left\lbrack 1 -\mu \left( y\right)\right\rbrack }^{\kappa }- {\eta }^{\kappa }\left( y\right)\end{array}\right\}\\{Q}^{\kappa }= \left\{\begin{array}{l}{\mu }^{\kappa }\left( y\right),1 -{\left\lbrack 1 -\eta \left( y\right)\right\rbrack }^{\kappa },\\{\left\lbrack 1 -\eta \left( y\right)\right\rbrack }^{\kappa }- {\mu }^{\kappa }\left( y\right)\end{array}\right\}$

在 TOPSIS 中,假设有 $p$ 个目标,记为 $O =\left\{{O}_{1}\right.$ , $\left.{{O}_{2},\cdots ,{O}_{p}}\right\}$ ,例如本文的目标是基坑工程安全施工, 则 $p = 1$ ,有 $m$ 个风险源或风险因素,记为 $C =\left\{{{C}_{1},{C}_{2},\cdots }\right.$ , $\left.{C}_{m}\right\}, B =\left\{{{B}_{1},{B}_{2},\cdots ,{B}_{n}}\right\}$ 是评价准则,模型构建的具体步骤如下。

1.1 计算专家的权重

专家的重要性程度可以用直觉模糊集中的模糊数来表示。用直觉模糊数 ${D}_{k}= \left({{\mu }_{k},{\eta }_{k},{\pi }_{k}}\right)$ 来评价第 $k$ 位专家的重要性程度。第 $k$ 位专家的权重计算如下:

(6) ${\lambda }_{k}= \frac{{\mu }_{k}+ {\pi }_{k}\left\lbrack {{\mu }_{k}/\left({{\mu }_{k}+ {\eta }_{k}}\right)}\right\rbrack }{\mathop{\sum }\limits_{1}^{l}\left\{{{\mu }_{k}+ {\pi }_{k}\left\lbrack {{\mu }_{k}/\left({{\mu }_{k}+ {\eta }_{k}}\right)}\right\rbrack }\right\}} $

式中, ${\lambda }_{k}$ 为专家 $k$ 的权重; $l$ 为专家的数量。

1.2 计算评价准则的权重

假设共有 $l$ 位专家,每一位专家的模糊决策矩阵为 ${\mathbf{E}}_{k}$ ,其中 $\left\{{{\lambda }_{1},{\lambda }_{2},{\lambda }_{3},\cdots ,{\lambda }_{l}}\right\}$ 为专家的权重。在综合决策过程中,需要融合专家观点组成群决策观点。基于此, 直觉模糊权重平均运算符综合了专家的观点并获得准则层的权重。假设 ${\mathbf{E}}_{k}$ 为专家 $k$ 的决策矩阵,表示如下:

(7) ${\mathbf{E}}_{k}= \\\left\lbrack \begin{matrix}{O}_{1}& {O}_{2}& \cdots &{O}_{p}& \\{B}_{1}& \left({{\mu }_{11}^{k},{\eta }_{11}^{k},{\pi }_{11}^{k}}\right)& \left({{\mu }_{12}^{k},{\eta }_{12}^{k},{\pi }_{12}^{k}}\right)& \cdots &\left({{\mu }_{1p}^{k},{\eta }_{1p}^{k},{\pi }_{1p}^{k}}\right)\\{B}_{2}& \left({{\mu }_{21}^{k},{\eta }_{21}^{k},{\pi }_{21}^{k}}\right)& \left({{\mu }_{22}^{k},{\eta }_{22}^{k},{\pi }_{22}^{k}}\right)& \cdots &\left({{\mu }_{2p}^{k},{\eta }_{2p}^{k},{\pi }_{2p}^{k}}\right)\\\vdots &\vdots &\ddots &\vdots &\\{B}_{k}& \left({{\mu }_{1p}^{k},{\eta }_{1p}^{k},{\pi }_{1p}^{k}}\right)& \left({{\mu }_{2p}^{k},{\eta }_{2p}^{k},{\pi }_{2p}^{k}}\right)& \cdots &\left({{\mu }_{2p}^{k},{\eta }_{1p}^{k},{\pi }_{2p}^{k}}\right)\end{matrix}\right\rbrack $

式中, $\left({{\mu }_{ij}^{k},{\eta }_{ij}^{k},{\pi }_{ij}^{k}}\right)$ 表示第 $k$ 位专家对准则 ${B}_{i}$ 在目标 ${O}_{j}$ 下重要性评估的直觉模糊数。使用直觉模糊权重平均运算符(IFWA)计算评价准则的权重 ^{[ 13 ]} :

(8) ${\omega }_{i}= {IFWA}{\left({E}_{1},{E}_{2},\cdots ,{E}_{l}\right)}_{\lambda }$

式中, ${\omega }_{i}= \left({{\mu }_{\omega i},{\eta }_{\omega i},{\pi }_{\omega i}}\right)$ 为准则 ${B}_{i}$ 的权重,在一般情况下,目标只有 1 个,此时 $p = 1$ 。

1.3 构建模糊综合决策矩阵

在综合模糊决策过程中, 需要每位专家运用直觉模糊数构建风险因素模糊决策矩阵,第 $k$ 位专家的风险因素模糊决策矩阵表示如下:

(9) ${\mathbf{R}}_{k}^{B}= \\\left\lbrack \begin{matrix}{B}_{1}& {B}_{2}& \cdots &{B}_{n}& \\{C}_{1}& \left({{\mu }_{11}^{k},{\eta }_{11}^{k},{\pi }_{11}^{k}}\right)& \left({{\mu }_{12}^{k},{\eta }_{12}^{k},{\pi }_{12}^{k}}\right)& \cdots &\left({{\mu }_{1n}^{k},{\eta }_{1n}^{k},{\pi }_{1n}^{k}}\right)\\{C}_{2}& \left({{\mu }_{21}^{k},{\eta }_{21}^{k},{\pi }_{21}^{k}}\right)& \left({{\mu }_{22}^{k},{\eta }_{22}^{k},{\pi }_{22}^{k}}\right)& \cdots &\left({{\mu }_{2n}^{k},{\eta }_{2n}^{k},{\pi }_{2n}^{k}}\right)\\\vdots &\vdots &\vdots &\ddots &\vdots \\{C}_{m}& \left({{\mu }_{m1}^{k},{\eta }_{m1}^{k},{\pi }_{m1}^{k}}\right)& \left({{\mu }_{m2}^{k},{\eta }_{m2}^{k},{\pi }_{m2}^{k}}\right)& \cdots &\left({{\mu }_{mn}^{k},{\eta }_{mn}^{k},{\pi }_{mn}^{k}}\right)\end{matrix}\right\rbrack $

式中, ${\mathbf{R}}_{k}^{B}$ 第 $k$ 位专家构建的风险因素决策矩阵; ${C}_{1}$ , ${C}_{2},\cdots ,{C}_{m}$ 为风险因素; ${B}_{1},{B}_{2},\cdots ,{B}_{n}$ 是评价准则。

对于各位专家构建的风险因素模糊决策矩阵, 需采用公式(10)进行融合 ^{[ 13 ]} ,所得的模糊综合决策矩阵如(11)所示。

(10) ${\theta }^{B}= {IFWA}{\left({R}_{1}^{B},{R}_{2}^{B},\cdots ,{R}_{l}^{B}\right)}_{\lambda }\\= {\lambda }_{1}{R}_{1}^{B}\oplus {\lambda }_{2}{R}_{2}^{B}\oplus {\lambda }_{3}{R}_{3}^{B}\oplus \cdots \oplus {\lambda }_{l}{R}_{l}^{B}\\= \left\lbrack \begin{array}{l} 1 -\mathop{\prod }\limits_{1}^{l}{\left( 1 -{\mu }_{ij}^{k}\right)}^{{\lambda }_{k}},\mathop{\prod }\limits_{1}^{l}{\left({\eta }_{ij}^{k}\right)}^{{\lambda }_{k}}\\\mathop{\prod }\limits_{1}^{l}{\left( 1 -{\mu }_{ij}^{k}\right)}^{{\lambda }_{k}}- \mathop{\prod }\limits_{1}^{l}{\left({\eta }_{ij}^{k}\right)}^{{\lambda }_{k}}\end{array}\right\rbrack \\{\mathbf{R}}^{B}= \\\left\lbrack \begin{matrix}{B}_{1}& {B}_{2}& \cdots &{B}_{n}& \\{C}_{1}& \left({{\mu }_{11}^{A},{\eta }_{11}^{A},{\pi }_{11}^{A}}\right)& \left({{\mu }_{12}^{A},{\eta }_{12}^{A},{\pi }_{12}^{A}}\right)& \cdots &\left({{\mu }_{1n}^{A},{\eta }_{1n}^{A},{\pi }_{1n}^{A}}\right)\\{C}_{2}& \left({{\mu }_{21}^{A},{\eta }_{21}^{A},{\pi }_{21}^{A}}\right)& \left({{\mu }_{22}^{A},{\eta }_{22}^{A},{\pi }_{22}^{A}}\right)& \cdots &\left({{\mu }_{2n}^{A},{\eta }_{2n}^{A},{\pi }_{2n}^{A}}\right)\\\vdots &\vdots &\ddots &\vdots &\\{C}_{n}& \left({{\mu }_{n1}^{A},{\eta }_{n1}^{A},{\pi }_{n1}^{A}}\right)& \left({{\mu }_{n2}^{A},{\eta }_{n2}^{A},{\pi }_{n2}^{A}}\right)& \cdots &\left({{\mu }_{n1}^{A},{\eta }_{n2}^{A},{\pi }_{nn}^{A}}\right)\end{matrix}\right\rbrack $

(11)式中, ${\mathbf{R}}^{B}$ 为风险因素模糊决策矩阵。

1.4 构建综合权重直觉模糊决策矩阵

构建综合权重直觉模糊决策矩阵的公式如下。

(12) ${\mathbf{\omega }}_{i}\otimes {\mathbf{R}}^{B}= \left\{\left\langle {{\mu }_{ij}^{A}\cdot {\mu }_{\omega i},{\eta }_{ij}^{A}+ {\eta }_{\omega i}- {\eta }_{ij}^{A}\cdot {\eta }_{\omega i}}\right\rangle \right\}$

其中, 犹豫度为

${\pi }_{{\omega }_{i}\otimes {\mathbf{R}}^{B}}= 1 -{\mu }_{ij}^{A}\cdot {\mu }_{\omega i}- {\eta }_{ij}^{A}- {\eta }_{\omega i}+ {\eta }_{ij}^{A}\cdot {\eta }_{\omega i}$

${\mathbf{\omega }}_{i}$ 和 ${\mathbf{R}}^{B}$ 分别为准则 ${B}_{i}$ 的权重和构建的风险因素模糊决策矩阵。

构建的综合权重直觉模糊决策矩阵如下:

(13) ${\mathbf{R}}_{A\omega }^{B}= \left\lbrack \begin{matrix}{B}_{1}& \cdots &{B}_{n}& \\{C}_{1}& \left({{\mu }_{11}^{A\omega },{\eta }_{11}^{A\omega },{\pi }_{11}^{A\omega }}\right)& \cdots &\left({{\mu }_{1n}^{A\omega },{\eta }_{1n}^{A\omega },{\pi }_{1n}^{A\omega }}\right)\\\vdots &\vdots &\ddots &\vdots \\{C}_{m}& \left({{\mu }_{m1}^{A\omega },{\eta }_{m1}^{A\omega },{\pi }_{m1}^{A\omega }}\right)& \cdots &\left({{\mu }_{mn}^{A\omega },{\eta }_{mn}^{A\omega },{\pi }_{mn}^{A\omega }}\right)\end{matrix}\right\rbrack $

式中, ${\mathbf{R}}_{A\omega }^{B}$ 为综合权重直觉模糊决策矩阵。

1.5 确定正理想解与负理想解

TOPSIS 方法中的评价准则 $B =\left\{{{B}_{1},{B}_{2},\cdots ,{B}_{n}}\right\}$ 需要分为消耗性与收益性准则, 收益性准则越大越好, 而消耗性准则越小越好。采用 ${J}_{1}$ 表示收益性准则, ${J}_{2}$ 表示消耗性准则。 ${A}^{+ }$ 和 ${A}^{- }$ 分别表示正理想解与负理想解,如下所示 ^{[ 13 ]} :

(14) $\left\{\begin{array}{l}{A}^{+ }= \left({{\mu }_{A +\omega },{\eta }_{A +\omega },{\pi }_{A +\omega }}\right)\\{A}^{- }= \left({{\mu }_{A -\omega },{\eta }_{A -\omega },{\pi }_{A -\omega }}\right)\end{array}\right.$

其确定准则如下:

(15) $\left\{\begin{array}{l}{\mu }_{A +\omega }= \left\lbrack {\mathop{\max }\limits_{i}{\mu }_{ij}^{A\omega }\left|{j \in {J}_{1},\mathop{\min }\limits_{i}^{{A\omega }}}\right| j \in {J}_{2}}\right\rbrack \\{\eta }_{A +\omega }= \left\lbrack {\mathop{\min }\limits_{i}{\eta }_{ij}^{A\omega }\left|{j \in {J}_{1},\mathop{\min }\limits_{i}^{{A\omega }}{\eta }_{ij}^{A\omega }}\right| j \in {J}_{2}}\right\rbrack \\{\mu }_{A -\omega }= \left\lbrack {\mathop{\min }\limits_{i}{\mu }_{ij}^{A\omega }\left|{j \in {J}_{1},\mathop{\max }\limits_{i}^{{A\omega }}{\mu }_{ij}^{A\omega }}\right| j \in {J}_{2}}\right\rbrack \\{\eta }_{A -\omega }= \left\lbrack {\mathop{\max }\limits_{i}{\eta }_{i - 1}^{A\omega }\left|{j \in {J}_{1},\mathop{\min }\limits_{i}^{{A\omega }}}\right| j \in {J}_{2}}\right\rbrack \end{array}\right.$

1.6 计算风险因素与正负理想解的距离

在确定了综合权重直觉模糊决策矩阵的正、负理想解后,计算各风险因素 ${C}_{i}$ 在直觉模糊集中到正负理想解的距离, 可表示如下:

(16) ${S}_{i}^{+ }= \sqrt{\frac{1}{2n}\mathop{\sum }\limits_{{j = 1}}^{n}\left\lbrack \begin{array}{l}{\left({\mu }_{ij}^{A\omega }- {\mu }_{A +\omega }\right)}^{2}+ {\left({\eta }_{ij}^{A\omega }- {\eta }_{A +\omega }\right)}^{2}+ \\{\left({\pi }_{ij}^{A\omega }- {\pi }_{A +\omega }\right)}^{2}\end{array}\right\rbrack }$

(17) ${S}_{i}^{- }= \sqrt{\frac{1}{2n}\mathop{\sum }\limits_{{j = 1}}^{n}\left\lbrack \begin{array}{l}{\left({\mu }_{ij}^{A\omega }- {\mu }_{A -\omega }\right)}^{2}+ {\left({\eta }_{ij}^{A\omega }- {\eta }_{A -\omega }\right)}^{2}+ \\{\left({\pi }_{ij}^{A\omega }- {\pi }_{A -\omega }\right)}^{2}\end{array}\right\rbrack }$

式中, ${S}_{i}^{+ },{S}_{i}^{- }$ 分别为第 $i$ 个风险因素 $\left({C}_{i}\right)$ 在直觉模糊集中到正负理想解的距离; $n$ 为评价准则的数量。

最后,计算风险因素 ${C}_{i}$ 的相对贴近度,其计算公式如下:

(18) ${C}_{i}= \frac{{S}_{i}^{- }}{{S}_{i}^{- }+ {S}_{i}^{+ }},0 \leq {C}_{i}\leq 1 $

将公式(18)计算得到的结果对风险因素进行排序,从而确定高风险因素。

2 案例分析

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2.1 工程概况

珠机城际横琴至珠海机场段工程前接三灶站大桥, 后接珠海机场, 起于三灶岛中东部机场东路右侧的下角咀丘陵地段, 以地铁形式沿机场东路、机场中路前行, 止于珠海机场站。HJZQ-2 标二工区基坑工程作为本项目的一部分, 地处城市主干道, 周边施工环境比较复杂,地下管线众多,周围建筑物较多,给地铁设计和施工造成了许多限制和不利的条件。基坑深度 ${22.1}\sim {23.8}\mathrm{\;m}$ ,宽 ${14.0}\sim {21.9}\mathrm{\;m}$ 。基坑工程场区下伏基岩主要为燕山期花岗岩, 场区主要以黏土夹砂为主, 局部为花岗岩碎块石, 填土层结构松散, 基坑在施工过程中易发生坍塌。基坑施工方法采用明挖法。

该工程采用 ${\phi 800}\mathrm{\;{mm}}$ 、间距 ${1000}\mathrm{\;{mm}}$ 的钻孔灌注桩+内支撑进行支护,共设置 $3 \sim 4$ 道支撑,同时围护结构外侧设置了单排 ${\phi 800}\mathrm{\;{mm}}$ 、间距 ${600}\mathrm{\;{mm}}$ 旋喷桩止水帷幕。第 1 道支撑采用钢筋混凝土支撑, 支撑截面 ${1000}\times {1000}\mathrm{\;{mm}}$ ,水平间距为 ${6000}\mathrm{\;{mm}}$ ; 钢筋混凝土联系梁截面 ${300}\times {600}\mathrm{\;{mm}}$ ；其余道支撑采用 ${\phi 600}\mathrm{\;{mm}}$ 钢支撑,间距设置为 ${3000}\mathrm{\;{mm}}$ ; 冠梁截面为 ${1000}\times$ ${1000}\mathrm{\;{mm}}$ ,钢筋混凝土腰梁采用 I56a 双拼工字钢; 冠梁、钢筋混凝土支撑、联系梁支撑均采用 C30 混凝土。其中对于旋喷桩,要求水泥浆液压力大于 ${20}\mathrm{{MPa}}$ ,旋喷桩加固后土体无侧限抗压强度不小于 $2\mathrm{{MPa}}$ 。本工程基坑平面如图 1 (a)所示, 图 1 (b)展示了基坑工程的施工情况。

2.2 基坑工程安全风险评估流程

运用提出的基于直觉模糊集理论的风险识别方法进行基坑安全风险因素识别的技术路线, 流程如图 2 所示。该基坑安全风险因素识别流程主要包括 4 个阶段,具体如下。

阶段 1 , 搜集影响深基坑安全的相关资料与现场施工情况。依据现有的深基坑技术与安全施工手册, 在实际工程项目施工情况评估的基础上, 总结与分析影响基坑安全的因素, 并对实际工程资料进行相应处理。

阶段 2 , 确定基坑风险因素与建立风险评估结构体系。根据阶段 1 确定基坑建设过程中的潜在风险因素, 进而确定基坑评价准则和建立评估结构体系, 接着确定评估专家和评价准则的权重。

阶段 3 , 应用基于直觉模糊集理论的风险识别方法对基坑风险因素进行识别。首先确定消耗性与收益性准则, 并确定正负理想解, 计算各风险因素到正负理想解的距离, 最后对风险因素进行识别, 确定最高风险因素。

阶段 4 , 风险评估与采取相应的风险控制措施。通过阶段 3 得到的风险因素, 采取相对应的措施对基坑施工安全风险进行控制。

2.3 基坑工程安全风险因素识别

在基坑风险因素识别过程中, 需要专家结合实际工程状况, 根据工程经验与现场监测数据, 利用语言变量对潜在风险因素给出各自的评价信息 ^{[ 13 ]} 。将获得的语言变量转变成直觉模糊数后进行后续的数据处理。其中评价专家、准则和风险因素的重要性程度语言集分别见表 1 和表 2 。

1) 根据现场获得的监测数据和专家的实践工程经验确定安全风险因素。在本基坑工程中, 确定了涉及基坑安全的 4 个评价指标, 分别是地质情况、施工管理、基坑施工技术风险与周围环境。各评价指标的风险因素见图 3 ,如基坑施工监测 $\left({B}_{3}\right)$ 评价指标下有支护体系不规范、止水帷幕处理不当、土方施工不规范和基坑降水方案等 4 个风险因素。

2) 在基坑安全施工风险因素识别中, 采用该方法均需要专家评分, 而专家的工程经验、教育背景将影响方法的准确性。因此, 邀请了 5 位地下工程领域具有丰富工程经验的专家 (项目经理、工程师等)进行评估, 专家的信息见表 3 , 其中第一位专家的权重计算如下:

(19) ${\lambda }_{1}= \frac{{\mu }_{1}+ {\pi }_{1}\cdot {\mu }_{1}/\left({{\mu }_{1}+ {\eta }_{1}}\right)}{\mathop{\sum }\limits_{1}^{5}\left\lbrack {{\mu }_{k}+ {\pi }_{k}\cdot {\mu }_{k}/\left({{\mu }_{k}+ {\eta }_{k}}\right)}\right\rbrack }$

$= \frac{{0.90}+ {0.00}\times {0.90}/\left({{0.90}+ {0.10}}\right)}{3.484}= {0.258}$

表 3 专家重要性程度与对应的权重信息

专家根据工程经验对 4 个准则的语言集评价见表 4 。根据公式(7)和(8)计算获得准则层的权重如下:

(20) ${\mathbf{\omega }}_{\left\{{B}_{1},{B}_{2},{B}_{3},{B}_{4}\right\}} =\left\lbrack \begin{array}{lll}{0.7641}& {0.2060}& {0.0298}\\{0.8270}& {0.1581}& {0.0149}\\{0.7688}& {0.2012}& {0.0300}\\{0.5905}& {0.3564}& {0.0530}\end{array}\right\rbrack $

3) TOPSIS 综合评价法。表 5 展示了某一专家对风险因素的语言综合评价信息。在确定了专家的权重、准则的权重与风险因素的重要性程度评价后, 根据公式(8)、(10)、(12)确定综合权重 TOPSIS 矩阵见表 6 。在本基坑工程研究中, 地质情况、基坑施工风险与周围环境为消耗性准则 ${J}_{2}= \left\{{{B}_{1},{B}_{3},{B}_{4}}\right\}$ ; 施工管理为收益性准则 ${J}_{1}= \left\{{B}_{2}\right\}$ 。根据公式 (14)、(15) 确定直觉模糊优劣解距离法中的正理想解与负理想解, 见表 7 。

4) 根据公式(18)计算各风险因素的贴近度, 并对风险因素进行排序, 最终基坑工程风险识别结果如表 8 所示, 基坑风险主要来源于基坑旁的堆载与动荷载, 由于在基坑工程的建设过程中, 需要使用挖土机 (见图 4(a) )、起重机等施工机械,施工机械的操作会产生相应的振动, 将对基坑的稳定性产生一定的影响; 还有为方便材料的使用, 通常把材料堆放在基坑旁(见图 4(b) ), 这些都是基坑安全风险的隐患所在, 需要加强管理。

2.4 风险管理建议

根据风险评估结果, 基坑旁的堆载与动荷载为重要的风险来源。为了确保基坑工程的安全高效施工, 从管理、技术与基坑监测方面提出一些建议。

1)管理方面。加强基坑施工过程中,建筑材料堆放与运土车的管理, 并配合基坑施工方案优化运土车运输路线与调配, 提高施工现场不同施工方案的协调性, 强化施工现场的施工组织管理与施工人员安全意识。

2) 技术方面。编制深基坑、高支模专项施工方案, 合理优化基坑支撑布置, 制定应急预案, 邀请专家对深基坑专项方案进行论证, 对每个基坑的开挖顺序、开挖方法、支护方式和对主体结构施工高支模等提出有效建议。

3) 基坑监测方面。对于重要的工程项目, 应增加相应的监测项目与监测点, 合理优化监测点, 采用先进的监测仪器, 做到实时监测重要参数的变化, 并及时反馈信息用于指导施工。

3 结论

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本文依托珠机城际横琴至珠海机场段 HJZQ-2 标二工区明挖法基坑工程, 识别基坑施工过程中潜在的风险因素,得到以下结论。

1) 针对明挖法深基坑施工过程中多因素影响问题, 以 TOPSIS 方法为基础, 提出了基于直觉模糊集理论的基坑工程风险识别方法。从项目地质情况、施工管理、施工技术风险和周围环境等方面构建了基坑风险评估指标体系。提出的基坑工程风险识别方法使用直觉模糊集的形式表示专家、评价指标的权重, 降低了指标权重的确定难度, 且直觉模糊集也为专家风险评估提供了便利。

2) 将提出的风险识别方法应用到珠机城际 HJZQ-2 标二工区明挖法基坑工程潜在风险因素的识别, 得到基坑旁的堆载与动荷载是本工程的最危险的风险因素, 结果与实际情况相符, 验证了该方法用于基坑风险因素识别的可行性, 可作为基坑施工安全风险分析与控制的决策工具, 对类似的基坑工程的安全施工控制有一定的指导作用。

3) 对基坑工程风险管理从管理、技术与监测方面提出相应的措施, 确保基坑工程安全高效施工。为类似基坑工程风险评估与预警提供了一定参考与工程应用价值。

基金

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中铁十六局集团北京轨道交通工程建设有限公司重点研发计划项目(ZTSLSG2206)

参考文献

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参考文献引证文献

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2024年第37卷第2期

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文章信息

doi: 10.3969/j.issn.1672-6073.2024.02.013

接收时间：2023-06-15
首发时间：2025-07-09

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收稿日期：2023-06-15
修回日期：2024-01-03

基金

中铁十六局集团北京轨道交通工程建设有限公司重点研发计划项目(ZTSLSG2206)

作者信息

中铁十六局集团北京轨道交通工程建设有限公司北京 101100

参考文献

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https://castjournals.cast.org.cn/joweb/dskgjt/CN/10.3969/j.issn.1672-6073.2024.02.013

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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语言变量	标记	直觉模糊数
非常重要	(VI)	(0.90,0.10,0.00)
重要	(I)	(0.75,0.20,0.05)
中等	(M)	(0.50,0.45,0.05)
不重要	(U)	(0.35,0.60,0.05)
非常不重要	(VU)	(0.10,0.90,0.00)

语言变量

标记

直觉模糊数

非常重要

(VI)

(0.90,0.10,0.00)

重要

(I)

(0.75,0.20,0.05)

中等

(M)

(0.50,0.45,0.05)

不重要

(U)

(0.35,0.60,0.05)

非常不重要

(VU)

(0.10,0.90,0.00)

语言变量	标记	直觉模糊数
极高	(EH)	(0.95,0.05,0.00)
非常高	(VH)	(0.85,0.10,0.05)
高	(H)	(0.75,0.15,0.10)
中等偏上	(MH)	(0.65,0.25,0.10)
中等	(M)	(0.50,0.40,0.10)
中等偏下	(ML)	(0.35,0.55,0.10)
低	(L)	(0.25,0.65,0.10)
非常低	(VL)	(0.15,0.80,0.05)
极低	(EL)	(0.05,0.95,0.00)

语言变量

标记

直觉模糊数

极高

(EH)

(0.95,0.05,0.00)

非常高

(VH)

(0.85,0.10,0.05)

高

(H)

(0.75,0.15,0.10)

中等偏上

(MH)

(0.65,0.25,0.10)

中等

(M)

(0.50,0.40,0.10)

中等偏下

(ML)

(0.35,0.55,0.10)

低

(L)

(0.25,0.65,0.10)

非常低

(VL)

(0.15,0.80,0.05)

极低

(EL)

(0.05,0.95,0.00)

专家信息	评价	直觉模糊数	专家权重
专家 1	VI	(0.90,0.10,0.00)	0.258
专家 2	I	(0.75,0.20,0.05)	0.227
专家 3	M	(0.50,0.45,0.05)	0.151
专家 4	VI	(0.90,0.10,0.00)	0.258
专家 5	U	(0.35,0.60,0.05)	0.106

专家信息

评价

直觉模糊数

专家权重

专家 1

(0.90,0.10,0.00)

0.258

专家 2

(0.75,0.20,0.05)

0.227

专家 3

(0.50,0.45,0.05)

0.151

专家 4

(0.90,0.10,0.00)

0.258

专家 5

(0.35,0.60,0.05)

0.106

评价准则	标记	-	二	三	四	五
地质情况	${B}_{1}$	VI	I	M	I	M
施工管理	${B}_{2}$	VI	I	M	VI	I
基坑施工技术风险	${B}_{3}$	I	M	VI	I	VI
周围环境	${B}_{4}$	M	I	I	M	VU

评价准则

标记

二

三

四

五

地质情况

${B}_{1}$

施工管理

${B}_{2}$

基坑施工技术风险

${B}_{3}$

周围环境

${B}_{4}$

目标	评价准则	标记	B₁	B₂	B₃	B₄
基坑施工安全	地质情况	${C}_{1}$	EH	M	VH	M
${C}_{2}$	ML	MH	M	MH
施工管理	${C}_{3}$	H	ML	VH	VH
${C}_{4}$	EH	VH	VH	H
${C}_{5}$	VH	H	EH	MH
基坑施工技术风险	${C}_{6}$	VH	MH	EH	ML
${C}_{7}$	EH	VH	EH	MH
${C}_{8}$	ML	ML	MH	L
${C}_{9}$	VH	VH	VH	H
周围环境	${C}_{10}$	M	MH	M	ML
${C}_{11}$	MH	VL	ML	M

目标

评价准则

标记

B₁

B₂

B₃

B₄

基坑施工安全

地质情况

${C}_{1}$

${C}_{2}$

施工管理

${C}_{3}$

${C}_{4}$

${C}_{5}$

基坑施工技术风险

${C}_{6}$

${C}_{7}$

${C}_{8}$

${C}_{9}$

周围环境

${C}_{10}$

${C}_{11}$

目标	评价准则	标记	B₁	B₂	B₃	B₄
基坑施工安全	地质情况	${C}_{1}$	(0.648,0.295,0.056)	(0.556,0.332,0.112)	(0.641,0.297,0.062)	(0.412,0.496,0.091)
${C}_{2}$	(0.391,0.512,0.097)	(0.511,0.370,0.120)	(0.490,0.399,0.111)	(0.388,0.509,0.103)
施工管理	${C}_{3}$	(0.577,0.333,0.090)	(0.393,0.438,0.169)	(0.681,0.272,0.047)	(0.502,0.427,0.071)
${C}_{4}$	(0.615,0.327,0.058)	(0.634,0.269,0.098)	(0.534,0.397,0.069)	(0.416,0.483,0.101)
${C}_{5}$	(0.626,0.298,0.076)	(0.671,0.254,0.075)	(0.647,0.311,0.041)	(0.451,0.467,0.082)
基坑施工技术风险	${C}_{6}$	(0.570,0.350,0.081)	(0.521,0.358,0.121)	(0.682,0.268,0.050)	(0.265,0.643,0.092)
${C}_{7}$	(0.690,0.270,0.039)	(0.594,0.297,0.109)	(0.652,0.289,0.059)	(0.503,0.428,0.068)
${C}_{8}$	(0.418,0.481,0.101)	(0.277,0.593,0.130)	(0.491,0.403,0.105)	(0.315,0.583,0.102)
${C}_{9}$	(0.515,0.392,0.093)	(0.693,0.244,0.063)	(0.625,0.307,0.068)	(0.462,0.446,0.092)
周围环境	${C}_{10}$	(0.392,0.512,0.096)	(0.311,0.602,0.087)	(0.263,0.660,0.077)	(0.251,0.660,0.089)
${C}_{11}$	(0.323,0.579,0.098)	(0.357,0.548,0.095)	(0.406,0.503,0.091)	(0.266,0.647,0.087)

目标

评价准则

标记

B₁

B₂

B₃

B₄

基坑施工安全

地质情况

${C}_{1}$

(0.648,0.295,0.056)

(0.556,0.332,0.112)

(0.641,0.297,0.062)

(0.412,0.496,0.091)

${C}_{2}$

(0.391,0.512,0.097)

(0.511,0.370,0.120)

(0.490,0.399,0.111)

(0.388,0.509,0.103)

施工管理

${C}_{3}$

(0.577,0.333,0.090)

(0.393,0.438,0.169)

(0.681,0.272,0.047)

(0.502,0.427,0.071)

${C}_{4}$

(0.615,0.327,0.058)

(0.634,0.269,0.098)

(0.534,0.397,0.069)

(0.416,0.483,0.101)

${C}_{5}$

(0.626,0.298,0.076)

(0.671,0.254,0.075)

(0.647,0.311,0.041)

(0.451,0.467,0.082)

基坑施工技术风险

${C}_{6}$

(0.570,0.350,0.081)

(0.521,0.358,0.121)

(0.682,0.268,0.050)

(0.265,0.643,0.092)

${C}_{7}$

(0.690,0.270,0.039)

(0.594,0.297,0.109)

(0.652,0.289,0.059)

(0.503,0.428,0.068)

${C}_{8}$

(0.418,0.481,0.101)

(0.277,0.593,0.130)

(0.491,0.403,0.105)

(0.315,0.583,0.102)

${C}_{9}$

(0.515,0.392,0.093)

(0.693,0.244,0.063)

(0.625,0.307,0.068)

(0.462,0.446,0.092)

周围环境

${C}_{10}$

(0.392,0.512,0.096)

(0.311,0.602,0.087)

(0.263,0.660,0.077)

(0.251,0.660,0.089)

${C}_{11}$

(0.323,0.579,0.098)

(0.357,0.548,0.095)

(0.406,0.503,0.091)

(0.266,0.647,0.087)

类型	A⁺	A^-
${B}_{1}$	(0.323,0.579,0.098)	(0.690,0.270,0.039)
${B}_{2}$	(0.693,0.244,0.063)	(0.277,0.602,0.121)
${B}_{3}$	(0.263,0.660,0.077)	(0.682,0.268,0.050)
${B}_{4}$	(0.251,0.660,0.089)	(0.503,0.427,0.070)

类型

A⁺

A^-

${B}_{1}$

(0.323,0.579,0.098)

(0.690,0.270,0.039)

${B}_{2}$

(0.693,0.244,0.063)

(0.277,0.602,0.121)

${B}_{3}$

(0.263,0.660,0.077)

(0.682,0.268,0.050)

${B}_{4}$

(0.251,0.660,0.089)

(0.503,0.427,0.070)

目标	评价准则	风险因素	标记	S_i⁺	S_i^-	C_i	归一化	排序
基坑施工安全	地质情况	地下水分布	${C}_{1}$	0.261	0.146	0.359	0.073	9
不良地质情况	${C}_{2}$	0.167	0.206	0.552	0.113	3
施工管理	违规操作	${C}_{3}$	0.297	0.088	0.229	0.047	11
施工方法	${C}_{4}$	0.212	0.193	0.477	0.098	5
施工质量	${C}_{5}$	0.255	0.191	0.428	0.087	6
基坑施工技术风险	支护体系不规范	${C}_{6}$	0.247	0.175	0.415	0.085	8
止水帷幕失效	${C}_{7}$	0.286	0.156	0.353	0.072	10
土方施工不规范	${C}_{8}$	0.236	0.174	0.424	0.087	7
基坑降水方案	${C}_{9}$	0.229	0.212	0.482	0.099	4
周围环境	基坑旁堆载	${C}_{10}$	0.188	0.274	0.593	0.121	1
基坑旁动荷载	${C}_{11}$	0.177	0.246	0.581	0.119	2

目标

评价准则

风险因素

标记

S_i⁺

S_i^-

C_i

归一化

排序

基坑施工安全

地质情况

地下水分布

${C}_{1}$

0.261

0.146

0.359

0.073

不良地质情况

${C}_{2}$

0.167

0.206

0.552

0.113

施工管理

违规操作

${C}_{3}$

0.297

0.088

0.229

0.047

施工方法

${C}_{4}$

0.212

0.193

0.477

0.098

施工质量

${C}_{5}$

0.255

0.191

0.428

0.087

基坑施工技术风险

支护体系不规范

${C}_{6}$

0.247

0.175

0.415

0.085

止水帷幕失效

${C}_{7}$

0.286

0.156

0.353

0.072

土方施工不规范

${C}_{8}$

0.236

0.174

0.424

0.087

基坑降水方案

${C}_{9}$

0.229

0.212

0.482

0.099

周围环境

基坑旁堆载

${C}_{10}$

0.188

0.274

0.593

0.121

基坑旁动荷载

${C}_{11}$

0.177

0.246

0.581

0.119