Determination of ultimate bearing capacity of pile under static load test based on cusp catastrophe model
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摘要:
利用静载试验的荷载-沉降曲线确定基桩极限承载力的分析方法很多，但至今尚未找到合理、有理论依据的确定基桩极限承载力的评判方法。因此，尝试利用尖点突变模型分析基桩静载试验的荷载-沉降曲线来评判基桩极限承载力；利用Matlab软件直接拟合静载试验的荷载-沉降曲线，以突变特征值为评价标准，确定基桩极限承载力。研究表明：（1）对比分析目前常用的尖点突变模型求解方法与文章提出的直接拟合法，发现目前常用的一般求解法存在不稳定性、误判等不足，评判结果与静载试验实际情形不符；（2）直接拟合法求得的势函数具有唯一性、首位性、单调性等特征，计算结果与基桩静载试验的实际情况相符，解决了一般求解法存在不稳定性、误判等问题，且比现行基桩检测规范计算结果更为安全。研究结果为较大直径基桩在缓变形情形下，以0.05D桩顶沉降量为标准确定基桩极限承载力提供了理论依据。
Abstract:There are many analysis methods to determine the ultimate bearing capacity of single pile by using the load-settlement curve obtained from the static load test, but so far, reasonable and theoretical calculation method to solve the ultimate bearing capacity of single pile has not been found. Therefore, the cusp catastrophe model was used to attempt to analyze the load-settlement curve obtained from the static load test so as to evaluate the ultimate bearing capacity of single pile. Through using Matlab software to directly fit the load-settlement curve obtained from the static load test with the evaluation standard of the sudden change characteristic value, the ultimate bearing capacity of the single pile was determined. The results show that: (1) comparing and analyzing the widely used methods for solving the cusp mutation model with the direct fitting method proposed in the present study, the widely used solution methods have shortcomings such as instability and misjudgment, and the evaluation results do not match the actual situation of static load tests. (2) The potential function obtained by direct fitting method is characterized by uniqueness, primacy, and monotonicity, whose calculation results are consistent with the actual situation of the static load test of the single pile. The dirrect fitting method solved the problems of instability and misjudgment existing in the general solution method. Compared to the current pile detection code, the calculation results from direct fitting method are safer. The direct fitting method presented in this study provides a theoretical basis for determining the ultimate bearing capacity of larger diameter piles under slow deformation conditions using 0.05D of pile top settlement as the standard.
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表 1 3个样本试桩Q-s曲线数据
Table 1. Q-s curve data of three samples by static load test
物理量 样本1 样本2 样本3 Q/kN 本级沉降/mm s/mm Q/kN 本级沉降/mm s/mm Q/kN 本级沉降/mm s/mm 试验结果 0 0 0 0 0 0 0 0 0 1 710 1.72 1.72 2 175 0.39 0.39 2 000 2.85 2.85 2 565 1.08 2.80 3 262 0.68 1.07 3 000 0.91 3.76 3 420 1.78 4.56 4 350 1.20 2.27 4 000 1.19 4.95 4 275 2.07 6.65 5 437 1.46 3.73 5 000 1.28 6.23 5 130 2.36 9.01 6 523 1.71 5.44 6 000 2.28 8.51 5 985 2.34 11.25 7 612 2.10 7.54 7 000 17.15 25.66 6 840 2.50 13.75 8 699 2.85 10.39 8 000 23.25 48.91 7 695 2.67 16.42 9 787 11.89 22.28 9 000 43.45 92.36 8 550 3.69 20.11 10 874 48.96 71.24 
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表 2 3个样本的一般求解法计算结果
Table 2. Calculation results of three samples by the widely used method
样本号 累计荷载级数 $ a_{1} $ $ a_{2} $ $ a_{3} $ $ a_{4} $ $ u $ $ v $ $ \varDelta $ 样本1 第六级 1.3454 − 0.5160 0.2146 − 0.0192 −20.00 −94.55 1.178×105 第七级 1.1822 − 0.3532 0.1646 − 0.0144 −24.50 −128.79 3.301×106 第八级 0.7252 0.0561 0.0527 − 0.0049 −54.60 −363.29 2.261×106 第九级 0.4869 0.2731 − 5.2600 ×10−4− 8.8000 ×10−4−310.62 −426.44 −2.350×108 第十级 0.0470 0.5738 − 0.0674 0.0037 30.58 670.48 1.237×107 样本2 第六级 0.0014 0.0121 0.0377 − 0.0031 −60.57 −256.58 6.400×102 第七级 − 0.2134 0.1806 − 0.0030 3.0370 ×10−6−3.07×105 −9.13×107 −5.740×1015 第八级 − 0.4015 0.3130 − 0.0315 0.0019 61.98 586.23 1.120×107 第九级 − 2.8691 1.8820 − 0.3343 0.0199 −11.03 58.28 8.098×104 第十级 − 10.8300 6.4736 − 1.1371 0.0631 −19.12 21.48 −4.347×104 样本3 第六级 1.7923 − 0.2037 − 0.0022 0.0043 −47.59 405.60 3.580×106 第七级 − 4.5653 5.2187 − 1.4266 0.1212 −8.91 11.87 −1.854×103 第八级 1.0088 0.9503 − 0.4294 0.0489 −9.46 21.35 5.535×103 第九级 1.5409 0.5824 − 0.3522 0.0439 −10.85 23.80 5.091×103
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表 3 3个样本的直接拟合法计算结果
Table 3. Calculation results of three samples by the direct fitting method
样本号 累计荷载级数 $ a_{1} $ $ a_{2} $ $ a_{4} $ $ u （ \underline{u} ）$ $ \nu （ \underline{\nu} ）$ $ \varDelta （\underline{ \varDelta}） $ R2 样本1 第六级 0.5807 0.2139 0.0006 8.6600 3.6900 5.56×103 0.9995 第七级 0.4298 0.2845 − 0.0011 − 8.4200 − 2.3400 −4.63×103 0.9994 第八级 0.4297 0.2845 − 0.0011 − 8.4200 − 2.3400 −4.62×103 0.9996 第九级 0.4727 0.2686 − 0.0009 − 8.9500 − 2.7300 −5.53×103 0.9997 第十级 0.6428 0.2114 − 0.0002 − 15.0400 − 5.4200 −2.64×104 0.9992 样本2 第六级 − 0.2158 0.1752 − 0.0003 − 9.6022 1.5975 −7.01×103 0.9998 第七级 − 0.1896 0.1656 − 0.0002 − 12.1629 1.6253 −1.43×104 0.9999 第八级 − 0.1060 0.1383 0.0001 11.8292 − 0.9798 1.33×104 0.9996 第九级 0.9910 − 0.1818 0.0031 − 3.2465 4.1877 2.00×102 0.9729 第十级 5.0740 − 0.12602 0.0113 − 11.8354 15.5496 −6.74×103 0.9385 样本3 第六级 1.8046 − 0.2128 0.0041 − 3.3171 7.1247 1.08×103 0.9997 第七级 4.4131 − 1.2560 0.023 − 8.2726 11.3259 −1.07×103 0.9695 第八级 4.3451 − 1.2319 0.0227 − 8.1738 11.1924 −9.88×102 0.9932 第九级 4.8885 − 1.4043 0.0246 − 8.9494 12.3406 −1.62×103 0.9980 注：带下划线的计算结果为带下划线字母计算值。
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[1] 崔树琴,张远芳,李传镔,等. 突变理论在单桩竖向承载力确定中的应用[J]. 水利与建筑工程学报,2006,4(2):19 − 22. [CUI Shuqin,ZHANG Yuanfang,LI Chuanbin,et al. Application of catastrophe theory in ascertainment of vertical bearing capacity of single pile[J]. Journal of Water Resources and Architectural Engineering,2006,4(2):19 − 22. (in Chinese with English abstract)] doi: 10.3969/j.issn.1672-1144.2006.02.005
CUI Shuqin, ZHANG Yuanfang, LI Chuanbin, et al. Application of catastrophe theory in ascertainment of vertical bearing capacity of single pile[J]. Journal of Water Resources and Architectural Engineering, 2006, 4（2）: 19 − 22. （in Chinese with English abstract） doi: 10.3969/j.issn.1672-1144.2006.02.005
[2] 苏亮,时伟,水伟厚,等. 高能级强夯法处理深厚吹填砂土地基现场试验[J]. 吉林大学学报(地球科学版),2021,51(5):1560 − 1569. [SU Liang,SHI Wei,SHUI Weihou,et al. Field test of high energy dynamic compaction on hydraulic sandy filling[J]. Journal of Jilin University (Earth Science Edition),2021,51(5):1560 − 1569. (in Chinese with English abstract)]
SU Liang, SHI Wei, SHUI Weihou, et al. Field test of high energy dynamic compaction on hydraulic sandy filling[J]. Journal of Jilin University （Earth Science Edition）, 2021, 51（5）: 1560 − 1569. （in Chinese with English abstract）
[3] 陈继彬,李雪梅,罗益斌,等. 侏罗系中等风化泥岩地基承载力试验研究[J]. 水文地质工程地质,2023,50(2):103 − 111. [CHEN Jibin,LI Xuemei,LUO Yibin,et al. A study of bearing capacity of the Jurassic moderately-weathered mudstone foundation[J]. Hydrogeology & Engineering Geology,2023,50(2):103 − 111. (in Chinese with English abstract)]
CHEN Jibin, LI Xuemei, LUO Yibin, et al. A study of bearing capacity of the Jurassic moderately-weathered mudstone foundation[J]. Hydrogeology & Engineering Geology, 2023, 50（2）: 103 − 111. （in Chinese with English abstract）
[4] 张玲,陈金海,欧强. 基于能量法的轴横向荷载作用下单桩受力变形分析[J]. 水文地质工程地质,2020,47(5):81 − 91. [ZHANG Ling,CHEN Jinhai,OU Qiang. Deformation analysis of pile under combined axial and lateral loads by using the energy method[J]. Hydrogeology & Engineering Geology,2020,47(5):81 − 91. (in Chinese with English abstract)]
ZHANG Ling, CHEN Jinhai, OU Qiang. Deformation analysis of pile under combined axial and lateral loads by using the energy method[J]. Hydrogeology & Engineering Geology, 2020, 47（5）: 81 − 91. （in Chinese with English abstract）
[5] 陈飞宇,董利飞,王苗,等. 基于灰色马尔科夫模型的地基承载力预测[J]. 地质科技通报,2022,41(3):222 − 227. [CHEN Feiyu,DONG Lifei,WANG Miao,et al. Prediction of foundation bearing capacity based on grey Markov model[J]. Bulletin of Geological Science and Technology,2022,41(3):222 − 227. (in Chinese with English abstract)]
CHEN Feiyu, DONG Lifei, WANG Miao, et al. Prediction of foundation bearing capacity based on grey Markov model[J]. Bulletin of Geological Science and Technology, 2022, 41（3）: 222 − 227. （in Chinese with English abstract）
[6] 中华人民共和国住房和城乡建设部. 建筑基桩检测技术规范:JGJ 106—2014[S]. 北京:中国建筑工业出版社,2014. [Ministry of Housing and Urban-Rural Development of the People’s Republic of China. Technical code for testing of building foundation piles:JGJ 106—2014[S]. Beijing:China Architecture & Building Press,2014. (in Chinese)]
Ministry of Housing and Urban-Rural Development of the People’s Republic of China. Technical code for testing of building foundation piles: JGJ 106—2014[S]. Beijing: China Architecture & Building Press, 2014. （in Chinese）
[7] 凌复华. 突变理论及其应用[M]. 上海:上海交通大学出版社,1987. [LING Fuhua. Catastrophe theory and its application[M]. Shanghai:Shanghai Jiao Tong University Press,1987. (in Chinese)]
LING Fuhua. Catastrophe theory and its application[M]. Shanghai: Shanghai Jiao Tong University Press, 1987. （in Chinese）
[8] ARNOLD V I. 突变理论[M]. 周燕华,译(trans). 北京:高等教育出版社,1990. [ARNOLD V I. Catastrophe theory [M]. ZHOU Yanhua,trans. Beijing:Higher Education Press,1990. (in Chinese)]
ARNOLD V I. Catastrophe theory [M]. ZHOU Yanhua, trans. Beijing: Higher Education Press, 1990. （in Chinese）
[9] 王新泉,陈永辉,刘汉龙. 基于尖点突变理论的基桩极限承载力判定及预测[J]. 河海大学学报(自然科学版),2008,36(2):248 − 252. [WANG Xinquan,CHEN Yonghui,LIU Hanlong. Determining and forecasting ultimate bearing capacity of pile based on cusp catastrophe theory[J]. Journal of Hohai University (Natural Sciences),2008,36(2):248 − 252. (in Chinese with English abstract)] doi: 10.3876/j.issn.1000-1980.2008.02.022
WANG Xinquan, CHEN Yonghui, LIU Hanlong. Determining and forecasting ultimate bearing capacity of pile based on cusp catastrophe theory[J]. Journal of Hohai University （Natural Sciences）, 2008, 36（2）: 248 − 252. （in Chinese with English abstract） doi: 10.3876/j.issn.1000-1980.2008.02.022
[10] 张远芳,崔树琴. 基于尖点突变理论的端承桩竖向承载力分析[J]. 岩土力学,2007,28(增刊1):901 − 904. [ZHANG Yuanfang,CUI Shuqin. Vertical bearing capacity analysis of end-bearing piles based on cusp catastrophe theory[J]. Rock and Soil Mechanics,2007,28(Sup 1):901 − 904. (in Chinese with English abstract)]
ZHANG Yuanfang, CUI Shuqin. Vertical bearing capacity analysis of end-bearing piles based on cusp catastrophe theory[J]. Rock and Soil Mechanics, 2007, 28（Sup 1）: 901 − 904. （in Chinese with English abstract）
[11] 贺广零. 突变理论新解及其在桩基工程中的应用[J]. 工程力学,2009,26(9):126 − 130. [HE Guangling. New catastrophe theory & its application in pile foundation engineering[J]. Engineering Mechanics,2009,26(9):126 − 130. (in Chinese with English abstract)]
HE Guangling. New catastrophe theory & its application in pile foundation engineering[J]. Engineering Mechanics, 2009, 26（9）: 126 − 130. （in Chinese with English abstract）
[12] 聂珊利,张远芳,赵秀亮. 基于尖点突变理论的摩擦桩竖向承载力分析[J]. 新疆农业大学学报,2010,33(3):264 − 267. [NIE Shanli,ZHANG Yuanfang,ZHAO Xiuliang. An analysis on vertical bearing capacity of friction pile based on cuspidal catastrophe theory[J]. Journal of Xinjiang Agricultural University,2010,33(3):264 − 267. (in Chinese with English abstract)] doi: 10.3969/j.issn.1007-8614.2010.03.017
NIE Shanli, ZHANG Yuanfang, ZHAO Xiuliang. An analysis on vertical bearing capacity of friction pile based on cuspidal catastrophe theory[J]. Journal of Xinjiang Agricultural University, 2010, 33（3）: 264 − 267. （in Chinese with English abstract） doi: 10.3969/j.issn.1007-8614.2010.03.017
[13] 姚文娟,钟倩倩,郭志兴,等. 超长桩竖向极限承载力预测与动力稳定性分析[J]. 力学季刊,2011,32(4):531 − 538. [YAO Wenjuan,ZHONG Qianqian,GUO Zhixing,et al. Prediction of vertical ultimate bearing capacity and dynamic stability analysis of super-long pile[J]. Chinese Quarterly of Mechanics,2011,32(4):531 − 538. (in Chinese with English abstract)]
YAO Wenjuan, ZHONG Qianqian, GUO Zhixing, et al. Prediction of vertical ultimate bearing capacity and dynamic stability analysis of super-long pile[J]. Chinese Quarterly of Mechanics, 2011, 32（4）: 531 − 538. （in Chinese with English abstract）
[14] 姚文娟,郭志兴,程泽坤. 基于突变理论的超长桩横向动力稳定性分析[J]. 水运工程,2011(8):9 − 13. [YAO Wenjuan,GUO Zhixing,CHENG Zekun. Lateral dynamic stability analysis of super-long piles based on catastrophe theory[J]. Port & Waterway Engineering,2011(8):9 − 13. (in Chinese with English abstract)] doi: 10.3969/j.issn.1002-4972.2011.08.002
YAO Wenjuan, GUO Zhixing, CHENG Zekun. Lateral dynamic stability analysis of super-long piles based on catastrophe theory[J]. Port & Waterway Engineering, 2011（8）: 9 − 13. （in Chinese with English abstract） doi: 10.3969/j.issn.1002-4972.2011.08.002
[15] 董天文,郑颖人,唐晓松. 强度折减法判定桩基础极限荷载的尖点突变条件[J]. 西南交通大学学报,2014,49(3):373 − 378. [DONG Tianwen,ZHENG Yingren,TANG Xiaosong. Cusp point condition for estimating ultimate load of pile foundation based on strength reduction method[J]. Journal of Southwest Jiaotong University,2014,49(3):373 − 378. (in Chinese with English abstract)]
DONG Tianwen, ZHENG Yingren, TANG Xiaosong. Cusp point condition for estimating ultimate load of pile foundation based on strength reduction method[J]. Journal of Southwest Jiaotong University, 2014, 49（3）: 373 − 378. （in Chinese with English abstract）
[16] 解志,董天文,谢鹏,等. 超长桩基础极限荷载判定的比能对比法[J]. 地下空间与工程学报,2021,17(2):496 − 502. [XIE Zhi,DONG Tianwen,XIE Peng,et al. Correlation method of specific energy to estimating the ultimate load of super-long pile[J]. Chinese Journal of Underground Space and Engineering,2021,17(2):496 − 502. (in Chinese with English abstract)]
XIE Zhi, DONG Tianwen, XIE Peng, et al. Correlation method of specific energy to estimating the ultimate load of super-long pile[J]. Chinese Journal of Underground Space and Engineering, 2021, 17（2）: 496 − 502. （in Chinese with English abstract）
[17] 刘建飞,高超,周永明. 突变理论与比能对比法推定既有基桩极限承载力的方法与应用[J]. 岩土工程技术,2023,37(4):403 − 407. [LIU Jianfei,GAO Chao,ZHOU Yongming. Method and application of determining ultimate bearing capacity of existing piles based on catastrophe theory and specific energy comparison method[J]. Geotechnical Engineering Technique,2023,37(4):403 − 407. (in Chinese with English abstract)]
LIU Jianfei, GAO Chao, ZHOU Yongming. Method and application of determining ultimate bearing capacity of existing piles based on catastrophe theory and specific energy comparison method[J]. Geotechnical Engineering Technique, 2023, 37（4）: 403 − 407. （in Chinese with English abstract）
[18] 张伟,田新然. 基于突变理论的筒形基础竖向承载力研究[J]. 天津大学学报(自然科学与工程技术版),2021,54(7):704 − 710. [ZHANG Wei,TIAN Xinran. Research on vertical bearing capacity of bucket foundation based on catastrophe theory[J]. Journal of Tianjin University (Science and Technology),2021,54(7):704 − 710. (in Chinese with English abstract)]
ZHANG Wei, TIAN Xinran. Research on vertical bearing capacity of bucket foundation based on catastrophe theory[J]. Journal of Tianjin University （Science and Technology）, 2021, 54（7）: 704 − 710. （in Chinese with English abstract）
[19] 童华炜,周龙翔,钟声. 基坑土钉支护的突变分析[J]. 西安建筑科技大学学报(自然科学版),2007,39(4):485 − 491. [TONG Huawei,ZHOU Longxiang,ZHONG Sheng. Catastrophe analysis of soil nailing support in foundation pit[J]. Journal of Xi’an University of Architecture & Technology (Natural Science Edition),2007,39(4):485 − 491. (in Chinese with English abstract)] doi: 10.3969/j.issn.1006-7930.2007.04.008
TONG Huawei, ZHOU Longxiang, ZHONG Sheng. Catastrophe analysis of soil nailing support in foundation pit[J]. Journal of Xi’an University of Architecture & Technology （Natural Science Edition）, 2007, 39（4）: 485 − 491. （in Chinese with English abstract） doi: 10.3969/j.issn.1006-7930.2007.04.008
[20] 薛晓辉,刘铁骊,周亦涛. 基于尖点突变理论和R/S分析的基坑安全性评价及事故处理措施研究[J]. 工程勘察,2022,50(7):15 − 21. [XUE Xiaohui,LIU Tieli,ZHOU Yitao. Safety evaluation and accident remedy of excavation pit based on cusp catastrophe theory and R/S analysis[J]. Geotechnical Investigation & Surveying,2022,50(7):15 − 21. (in Chinese with English abstract)]
XUE Xiaohui, LIU Tieli, ZHOU Yitao. Safety evaluation and accident remedy of excavation pit based on cusp catastrophe theory and R/S analysis[J]. Geotechnical Investigation & Surveying, 2022, 50（7）: 15 − 21. （in Chinese with English abstract）
[21] 梁冠亭,肖开乾,郑宏伟,等. 基于尖点突变理论的岩溶区嵌岩桩溶洞顶板安全厚度研究[J]. 水文地质工程地质,2018,45(5):67 − 72. [LIANG Guanting,XIAO Kaiqian,ZHENG Hongwei,et al. A study of the safety thickness of cave roof under rock-socketed pile in Karst Area based on the cusp catastrophe theory[J]. Hydrogeology & Engineering Geology,2018,45(5):67 − 72. (in Chinese with English abstract)]
LIANG Guanting, XIAO Kaiqian, ZHENG Hongwei, et al. A study of the safety thickness of cave roof under rock-socketed pile in Karst Area based on the cusp catastrophe theory[J]. Hydrogeology & Engineering Geology, 2018, 45（5）: 67 − 72. （in Chinese with English abstract）
[22] 龚先兵,赵明华,杨明辉,等. 岩溶区桥梁基桩极限承载力的突变求解方法[J]. 公路交通科技,2012,29(11):53 − 57. [GONG Xianbing,ZHAO Minghua,YANG Minghui,et al. Determination of ultimate bearing capacity of pile in Karst Region based on catastrophe theory[J]. Journal of Highway and Transportation Research and Development,2012,29(11):53 − 57. (in Chinese with English abstract)] doi: 10.3969/j.issn.1002-0268.2012.11.010
GONG Xianbing, ZHAO Minghua, YANG Minghui, et al. Determination of ultimate bearing capacity of pile in Karst Region based on catastrophe theory[J]. Journal of Highway and Transportation Research and Development, 2012, 29（11）: 53 − 57. （in Chinese with English abstract） doi: 10.3969/j.issn.1002-0268.2012.11.010
[23] 娄一青,顾冲时,李君. 基于突变理论的有限元强度折减法边坡失稳判据探讨[J]. 西安建筑科技大学学报(自然科学版),2008,40(3):361 − 367. [LOU Yiqing,GU Chongshi,LI Jun. Study on the slope failure criterion in strength reduction finite element method based on catastrophe theory[J]. Journal of Xi’an University of Architecture & Technology (Natural Science Edition),2008,40(3):361 − 367. (in Chinese with English abstract)] doi: 10.3969/j.issn.1006-7930.2008.03.012
LOU Yiqing, GU Chongshi, LI Jun. Study on the slope failure criterion in strength reduction finite element method based on catastrophe theory[J]. Journal of Xi’an University of Architecture & Technology （Natural Science Edition）, 2008, 40（3）: 361 − 367. （in Chinese with English abstract） doi: 10.3969/j.issn.1006-7930.2008.03.012
[24] 夏开宗,刘秀敏,陈从新,等. 考虑突变理论的顺层岩质边坡失稳研究[J]. 岩土力学,2015,36(2):477 − 486. [XIA Kaizong,LIU Xiumin,CHEN Congxin,et al. Analysis of mechanism of bedding rock slope instability with catastrophe theory[J]. Rock and Soil Mechanics,2015,36(2):477 − 486. (in Chinese with English abstract)]
XIA Kaizong, LIU Xiumin, CHEN Congxin, et al. Analysis of mechanism of bedding rock slope instability with catastrophe theory[J]. Rock and Soil Mechanics, 2015, 36（2）: 477 − 486. （in Chinese with English abstract）
[25] 岳建伟,杨光辉,王思远,等. 基于弹性滑体的边坡失稳尖点突变模型研究[J]. 河南大学学报(自然科学版),2019,49(3):354 − 361. [YUE Jianwei,YANG Guanghui,WANG Siyuan,et al. Cusp catastrophe model for slope failure based on elastic slip mass[J]. Journal of Henan University (Natural Science),2019,49(3):354 − 361. (in Chinese with English abstract)]
YUE Jianwei, YANG Guanghui, WANG Siyuan, et al. Cusp catastrophe model for slope failure based on elastic slip mass[J]. Journal of Henan University （Natural Science）, 2019, 49（3）: 354 − 361. （in Chinese with English abstract）
[26] 方汕澳,许强,修德皓,等. 基于斜率模型的突发型黄土滑坡失稳时间预测[J]. 水文地质工程地质,2021,48(4):169 − 179. [FANG Shan’ao,XU Qiang,XIU Dehao,et al. A study of the predicted instability time of sudden loess landslides based on the SLO model[J]. Hydrogeology & Engineering Geology,2021,48(4):169 − 179. (in Chinese with English abstract)]
FANG Shan’ao, XU Qiang, XIU Dehao, et al. A study of the predicted instability time of sudden loess landslides based on the SLO model[J]. Hydrogeology & Engineering Geology, 2021, 48（4）: 169 − 179. （in Chinese with English abstract）
[27] 李彬,周金喜,吴钶桥,等. 基于突变理论的湟水河流域崩滑易发性评价[J]. 中国地质灾害与防治学报,2023,34(6):116 − 126. [LI Bin,ZHOU Jinxi,WU Keqiao,et al. Assessment of landslide susceptibility in the Huangshui River Basin based on catastrophe theory[J]. The Chinese Journal of Geological Hazard and Control,2023,34(6):116 − 126. (in Chinese with English abstract)]
LI Bin, ZHOU Jinxi, WU Keqiao, et al. Assessment of landslide susceptibility in the Huangshui River Basin based on catastrophe theory[J]. The Chinese Journal of Geological Hazard and Control, 2023, 34（6）: 116 − 126. （in Chinese with English abstract）
[28] 于开宁,吴涛,魏爱华,等. 基于AHP-突变理论组合模型的地质灾害危险性评价——以河北平山县为例[J]. 中国地质灾害与防治学报,2023,34(2):146 − 155. [YU Kaining,WU Tao,WEI Aihua,et al. Geological hazard assessment based on the models of AHP,catastrophe theory and their combination:A case study in Pingshan County of Hebei Province[J]. The Chinese Journal of Geological Hazard and Control,2023,34(2):146 − 155. (in Chinese with English abstract)]
YU Kaining, WU Tao, WEI Aihua, et al. Geological hazard assessment based on the models of AHP, catastrophe theory and their combination: A case study in Pingshan County of Hebei Province[J]. The Chinese Journal of Geological Hazard and Control, 2023, 34（2）: 146 − 155. （in Chinese with English abstract）
[29] 徐海清,陈亮,王炜,等. 软岩隧道围岩塌方的尖点突变预测分析[J]. 铁道工程学报,2016,33(11):97 − 101. [XU Haiqing,CHEN Liang,WANG Wei,et al. Prediction analysis of surrounding rock collapse in soft rock tunnel by cusp catastrophe[J]. Journal of Railway Engineering Society,2016,33(11):97 − 101. (in Chinese with English abstract)] doi: 10.3969/j.issn.1006-2106.2016.11.018
XU Haiqing, CHEN Liang, WANG Wei, et al. Prediction analysis of surrounding rock collapse in soft rock tunnel by cusp catastrophe[J]. Journal of Railway Engineering Society, 2016, 33（11）: 97 − 101. （in Chinese with English abstract） doi: 10.3969/j.issn.1006-2106.2016.11.018
[30] 赵延林,吴启红,王卫军,等. 基于突变理论的采空区重叠顶板稳定性强度折减法及应用[J]. 岩石力学与工程学报,2010,29(7):1424 − 1434. [ZHAO Yanlin,WU Qihong,WANG Weijun,et al. Strength reduction method to study stability of goaf overlapping roof based on catastrophe theory[J]. Chinese Journal of Rock Mechanics and Engineering,2010,29(7):1424 − 1434. (in Chinese with English abstract)]
ZHAO Yanlin, WU Qihong, WANG Weijun, et al. Strength reduction method to study stability of goaf overlapping roof based on catastrophe theory[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29（7）: 1424 − 1434. （in Chinese with English abstract）
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