人工冻土冻胀数值模拟分析
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摘要
人工冻结法施工产生冻胀会影响地表建筑物，使之产生各种破坏现象，因此，预报冻土冻胀对周围环境的影响非常重要，但目前关于这方面的研究还十分欠缺。本文总结了当前冻胀机理、数值预报模型和防冻害措施的研究成果。建立了冻土中的热传导模型，在计算冻胀时，利用水分人流量和时间关系计算水分迁移引起的冻胀应变；利用已冻土中未冻含水量和温度关系，求原位水的冻胀应变，将冻结引起的体积膨胀系数作为负的热膨胀系数，利用MARC程序中热应力的计算程序计算外界迁移水和原位水的冻胀位移；两项位移之和为总冻胀位移，并利用冻胀率和荷载的实验经验公式来考虑荷载对冻胀的影响。采用有限单元法对一维冻结和二维水平冻结模型进行数值模拟分析，经比较模拟计算和实测结果，其误差在10％～15％之间，说明本文所提模型和计算方法是正确可行的。探讨了在水平冻结情况下覆盖厚度(埋深)、冻土壁厚度、开挖半径、含水量和盐水温度对冻胀位移的影响。经计算得出如下结论：地表竖向位移在靠近对称面处最大，随距对称面距离的增大而呈波浪形减小，而地表水平位移则在距对称面一定距离才达到最大值，其最大值的位置和覆盖厚度成正比，受其它因素的影响不大。地表最大竖向冻胀位移随荷载增大按指数规律减少，且有最终趋于不变的趋势；随冻土壁厚度增大，其前期增大得较快，中期增大得较慢，但后期增大又渐渐变快；地表最大竖向位移和开挖半径及含水量均成正比关系；和盐水温度呈开口向下的抛物线关系，在抛物线峰值左边，其随盐水温度变化的剧烈程度比峰值右边的小。地表最大水平位移和最大竖向位移随上述各因素的变化规律相同，但水平位移均比竖向位移小，且变化剧烈程度也较小。对称面处，冻结壁以上和以下的地层中竖向位移随深度增加而增大，而在冻结壁范围内随深度增加而减小。根据计算分析结果提出了抑制冻胀的建议，对人工冻结法在城市地下工程中推广应用具有理论意义和实用参考价值。
Frost displacement is very important to predict the influence to the environment during the article frost construction because it may affect buildings on the earth due to the frost heave by water migration, thus cause a variety of destructions. Yet relative study is quite short. The research results of frost heave mechanisms, numerical predication models and the frost precaution method are summarized in this paper, and the heat transfer model in the frozen soil is formulated. On calculating the frost heave, the water migration content is determined by the relationship between the water influx content and the time, the original water frost displacement is determined by the relationship between the unfrozen water content and the temperature, thus, the emigrant and original water frost displacement is calculated by the thermal stress computing program of MARC in which the volume expantion coefficient induced by freezing is considered as negative thermal expansion coefficient; the total frost heave displacement is the sum of the two displacements, and the influence of the load to the frost heave is taken into consideration by the frost coefficient and load experiential formula. The Finite Element Method is used modelling one-dimension freezing and two-dimension model of artificial horizontal freezing method. Comparing the results of simulation and experimental and field measurements, the error ranges from 10% to 15%, which indicates the method of computing modelling in the paper is feasible. The influence of different covered depths, thickness of frozen wall, excavating radius, original water content and brine temperature on frost displacement are discussed for horizontal freezing model. The results are: The vertical frost displacements of earth surface is maximal at the plane of symmetry, and minish wavely with the increasing of distanace from symmetry plane. While the horizontal frost displacements of earth surface reaches the maximum at a certain distance from symmetry plane, which is direct proportional to the covered depth and weekly influenced by the other factors. The maximal earth surface vertical frost displacements decrease exponentially with the decreasing of the load, and ultimately are constants, and increase more quickly at the beginning with the increasing of frost wall width, then slowe, and expedite again later, and are direct proportional to the excavating radius and original water content, and the curve of them and brine temperatures is a parabola with a downwards hatch, that the slop on the right side is more precipitous than the left. Under the same conditions as above, the maximal earth surface horizontal displacements have the same varying laws as the maximal vertical displacements, but are smaller than them and vary more gently. At the plane of symmetry, the vertical displacements increase with the depth's increasing in the earth outside the frozen wall while decrease inside. According to the results, the suggestions about restraining the frost heave are brought forward. The results have theoretical significance and reference value to the application of the artificial freezing project in the underground engineerings of city.
Frost displacement is very important to predict the influence to the environment during the article frost construction because it may affect buildings on the earth due to the frost heave by water migration, thus cause a variety of destructions. Yet relative study is quite short. The research results of frost heave mechanisms, numerical predication models and the frost precaution method are summarized in this paper, and the heat transfer model in the frozen soil is formulated. On calculating the frost heave, the water migration content is determined by the relationship between the water influx content and the time, the original water frost displacement is determined by the relationship between the unfrozen water content and the temperature, thus, the emigrant and original water frost displacement is calculated by the thermal stress computing program of MARC in which the volume expantion coefficient induced by freezing is considered as negative thermal expansion coefficient; the total frost heave displacement is the sum of the two displacements, and the influence of the load to the frost heave is taken into consideration by the frost coefficient and load experiential formula. The Finite Element Method is used modelling one-dimension freezing and two-dimension model of artificial horizontal freezing method. Comparing the results of simulation and experimental and field measurements, the error ranges from 10% to 15%, which indicates the method of computing modelling in the paper is feasible. The influence of different covered depths, thickness of frozen wall, excavating radius, original water content and brine temperature on frost displacement are discussed for horizontal freezing model. The results are: The vertical frost displacements of earth surface is maximal at the plane of symmetry, and minish wavely with the increasing of distanace from symmetry plane. While the horizontal frost displacements of earth surface reaches the maximum at a certain distance from symmetry plane, which is direct proportional to the covered depth and weekly influenced by the other factors. The maximal earth surface vertical frost displacements decrease exponentially with the decreasing of the load, and ultimately are constants, and increase more quickly at the beginning with the increasing of frost wall width, then slowe, and expedite again later, and are direct proportional to the excavating radius and original water content, and the curve of them and brine temperatures is a parabola with a downwards hatch, that the slop on the right side is more precipitous than the left. Under the same conditions as above, the maximal earth surface horizontal displacements have the same varying laws as the maximal vertical displacements, but are smaller than them and vary more gently. At the plane of symmetry, the vertical displacements increase with the depth's increasing in the earth outside the frozen wall while decrease inside. According to the results, the suggestions about restraining the frost heave are brought forward. The results have theoretical significance and reference value to the application of the artificial freezing project in the underground engineerings of city.
引文
1 徐学祖，王家澄，张立新著．冻土物理学．北京．科学出版社．2001．ISBN 7-03-006555-7
2 徐兵壮，崔海涛．地层冻结技术在地铁建设中的应用．铁道建筑技术，2001(2)：6-9
3 汪崇鲜，楼根达，马玉峰．繁华市区含水地层水平冻结及暗挖法施工．冰川冻土，2000，VOL22，NO．3：278-281
4 杨平，佘才高，董朝文等．人工冻结法在南京地铁张府园车站的应用．岩土力学，2003，Vol．24，SUPP．：388-391
5 李萍、徐学祖、陈峰峰．冻结缘和冻胀模型的研究现状与进展．冰川冻土．2000，22(1)：90-95
6 Everett D H. The thermodynamics of frost damage to porous solids [J]. Trans. Faraday Soc., 1961, 57: 1541-1551.
7 Miller R D. Freezing and heaving of saturated and unsaturated soils [J]. Highway Research Record, 1972, (393): 1-11
8 周国庆．饱水砂层中结构的融沉附加力研究．冰川冻土，1998，20(2)：11-14
9 陈湘生、濮家骝等．土壤冻胀离心模拟试验．煤炭学报，1999，24(6)：615-619
10 罗小刚、陈湘生、吴成义．冻融对土工参数影响的试验研究．建井技术，2000，21(2)：24-26
11 杨平、张婷．人工冻融土物理力学性能研究．冰川冻土，2002-10，24(5)：665-667
12 周希圣、郑宜枫．高含水粘土层隧道冻结位移场模型试验研究．同济大学学报，2000，28(4)：472-476
13 陈明雄、翁家杰．软土盾构隧道冻结施工试验研究．石家庄铁道学院学报，2000，13(增刊)：37-39
14 程国栋．冻土力学与工程的国际研究新进展——2000年国际地层冻结和土冻结作用会议综述．Inter．
15 Jessberger H L. Opening address [A]. In: Jones and Hotden, eds. Ground Freezing 88, Proceedings of 5th International Symposium on Ground Freezing[C]. Rotterdam: Balke ma A A, 1989, 407-411
16 王建平、王文顺等．人工冻结土体冻胀融沉的模型试验．中国矿业大学学报，1999，28(4)：303-306
17 Taylor G S, Luthin J N. A model for coupled heat and moisture transfer during soil freezing [J]. Can. Geotech. J., 1978, 15:548-555.
18 王正中、沙际德等．正交各向异性冻土与建筑物相互作用的非线性有限元分析．土木工程学报，1999，32(3)：55-60
19 李洪升、张斌等．一维冻结土体冻胀量的水热力耦合计算．大连理工大学学报，1999，39(5)：621-624
20 李洪升等．基于冻土水分温度和外荷载相互作用的冻胀模式．大连理工大学学报，1998，38(1)：29-33
21 赖远明，吴紫汪，朱元林等．寒区隧道温度场、渗流场和应力场耦合问题的非线性分析．岩土工程学报，1999，VOL．21，NO．5：429-533
22 侯芸，田波等．季节性冰冻地区路基内温度场、湿度场耦合计算．同济大学学报，2002-3，Vol．30，No．3：297-301
23 王铁行．多年冻土地区路基计算原理及临界高度研究．长安大学博士论文，2001．1
24 程桦．城市地下工程人工地层冻结技术现状及展望．淮南工业学院学报，2000，20(2)
25 A. P. S. Selvadurai, J. Hu, I. Konuk. Computational modeling of frost heave induced soil-pipeline
interaction-I. Modelling of frost heave. Cold Regions Science and Technology 29(1999)215-228
26李述训、南卓铜等．冻融作用对系统与环境间能量交换的影响．冰川冻土，2002，24(2)：109-115
27吴国侯．土的冻胀理论及其应用．勘察科学技术，1997，3：12-14
28徐学祖、何平等．土体冻结和冻胀研究的新进展——“国际地层冻结和冻结作用研讨会”论文综述．冰川冻土，1997，19(3)：280-283
29Ma Wei (Lanzhou Gansu). Review and Prospect of the Studies of Ground Freezing Technology in China. Journal of Glaciology and Geocryology, 2001, 23(3): 218-224
30陈瑞杰、程国栋等．人工地层冻结应用研究进展和展望．岩土工程学报，2000，22(1)：40-44
31徐干成，白洪才，郑颖人，刘朝编．地下工程支护结构．北京：中国水利水电出版社，2001，ISBN 7-5084-0816-0
32龙驭球编．有限元法概论．人民教育出版社，1978
33陆君安，尚涛等编．偏微分方程的MATLAB解法．武汉大学出版社，2001，ISBN 7-307-03256-2
34林群编．微分方程数值解法基础教程．北京：科学出版社，2001，ISBN 7-03-009056-X
35龚晓南编．土工计算机分析．北京：中国建筑工业出版社，2000，ISBN 7-112-04330-1
36孟凡中编．弹塑性有限变形理论和有限元方法．北京：清华大学出版社，1985
37朱伯芳编．有限单元法原理与应用．北京：中国水利水电出版社，1998，ISBN 7-80124-701-9
38朱梅生主编．软土地基．北京：中国铁道出版社，1989
39钱家欢，殷宗泽主编．土工原理与计算．中国水利水电出版社，1996，ISBN 7-80124-142-8
40陈火红编．MARC有限元实例分析教程．机械工业出版社，2002，ISBN 7-111．10054-9
41I．M．Smith, D．V．Griffiths著．有限元方法编程．电子工业出版社，2003，ISBN 7-5053-9115-1
42邓巍巍，王越男著．Visual FORTRAN编程指南．人民邮电出版社，2000，ISBN 7-115-08530-7
43王勖成，邵敏编著．有限单元法基本原理和数值方法．清华大学出版社，1996，ISBN 7-302-02421-9
44中国科学院兰州冰川冻土研究所，煤炭工业部特殊凿井公司冻土壁研究组编著．冻结凿井冻土壁的工程性质．兰州大学出版社，1988
45徐芝纶编．弹性力学简明教程．高等教育出版社，1983，ISBN 7-04-001483-1
46H．A．崔托维奇(苏)著．张长庆，朱元林译．冻土力学[M]．北京：科学出版社，1985
47李相然，岳同助编著．城市地下工程实用技术．北京：中国建材工业出版社，2000，ISBN 7-80159-018-X
48黄成光主编．公路隧道施工．人民交通出版社．
49杨桂通，树学锋编著．塑性力学．中国建材出版社，1999，ISBN 7-80090-971-9
50熊祝华编．塑性力学基础知识．高等教育出版社，1986
51王仁等编．塑性力学基础知识
52MARC培训手册
53MARC实例教程
54夸克工作室编．有限元分析基础篇：ANSYS与MATLAB．清华大学出版社，2002，ISBN 7-302-05154-2
55中国土木工程学会第四届土力学及基础工程学术会议论文选集．北京：中国建筑工业出版社
56张道宽，王显义．软基变形问题的弹塑性有限元分析
2 徐兵壮，崔海涛．地层冻结技术在地铁建设中的应用．铁道建筑技术，2001(2)：6-9
3 汪崇鲜，楼根达，马玉峰．繁华市区含水地层水平冻结及暗挖法施工．冰川冻土，2000，VOL22，NO．3：278-281
4 杨平，佘才高，董朝文等．人工冻结法在南京地铁张府园车站的应用．岩土力学，2003，Vol．24，SUPP．：388-391
5 李萍、徐学祖、陈峰峰．冻结缘和冻胀模型的研究现状与进展．冰川冻土．2000，22(1)：90-95
6 Everett D H. The thermodynamics of frost damage to porous solids [J]. Trans. Faraday Soc., 1961, 57: 1541-1551.
7 Miller R D. Freezing and heaving of saturated and unsaturated soils [J]. Highway Research Record, 1972, (393): 1-11
8 周国庆．饱水砂层中结构的融沉附加力研究．冰川冻土，1998，20(2)：11-14
9 陈湘生、濮家骝等．土壤冻胀离心模拟试验．煤炭学报，1999，24(6)：615-619
10 罗小刚、陈湘生、吴成义．冻融对土工参数影响的试验研究．建井技术，2000，21(2)：24-26
11 杨平、张婷．人工冻融土物理力学性能研究．冰川冻土，2002-10，24(5)：665-667
12 周希圣、郑宜枫．高含水粘土层隧道冻结位移场模型试验研究．同济大学学报，2000，28(4)：472-476
13 陈明雄、翁家杰．软土盾构隧道冻结施工试验研究．石家庄铁道学院学报，2000，13(增刊)：37-39
14 程国栋．冻土力学与工程的国际研究新进展——2000年国际地层冻结和土冻结作用会议综述．Inter．
15 Jessberger H L. Opening address [A]. In: Jones and Hotden, eds. Ground Freezing 88, Proceedings of 5th International Symposium on Ground Freezing[C]. Rotterdam: Balke ma A A, 1989, 407-411
16 王建平、王文顺等．人工冻结土体冻胀融沉的模型试验．中国矿业大学学报，1999，28(4)：303-306
17 Taylor G S, Luthin J N. A model for coupled heat and moisture transfer during soil freezing [J]. Can. Geotech. J., 1978, 15:548-555.
18 王正中、沙际德等．正交各向异性冻土与建筑物相互作用的非线性有限元分析．土木工程学报，1999，32(3)：55-60
19 李洪升、张斌等．一维冻结土体冻胀量的水热力耦合计算．大连理工大学学报，1999，39(5)：621-624
20 李洪升等．基于冻土水分温度和外荷载相互作用的冻胀模式．大连理工大学学报，1998，38(1)：29-33
21 赖远明，吴紫汪，朱元林等．寒区隧道温度场、渗流场和应力场耦合问题的非线性分析．岩土工程学报，1999，VOL．21，NO．5：429-533
22 侯芸，田波等．季节性冰冻地区路基内温度场、湿度场耦合计算．同济大学学报，2002-3，Vol．30，No．3：297-301
23 王铁行．多年冻土地区路基计算原理及临界高度研究．长安大学博士论文，2001．1
24 程桦．城市地下工程人工地层冻结技术现状及展望．淮南工业学院学报，2000，20(2)
25 A. P. S. Selvadurai, J. Hu, I. Konuk. Computational modeling of frost heave induced soil-pipeline
interaction-I. Modelling of frost heave. Cold Regions Science and Technology 29(1999)215-228
26李述训、南卓铜等．冻融作用对系统与环境间能量交换的影响．冰川冻土，2002，24(2)：109-115
27吴国侯．土的冻胀理论及其应用．勘察科学技术，1997，3：12-14
28徐学祖、何平等．土体冻结和冻胀研究的新进展——“国际地层冻结和冻结作用研讨会”论文综述．冰川冻土，1997，19(3)：280-283
29Ma Wei (Lanzhou Gansu). Review and Prospect of the Studies of Ground Freezing Technology in China. Journal of Glaciology and Geocryology, 2001, 23(3): 218-224
30陈瑞杰、程国栋等．人工地层冻结应用研究进展和展望．岩土工程学报，2000，22(1)：40-44
31徐干成，白洪才，郑颖人，刘朝编．地下工程支护结构．北京：中国水利水电出版社，2001，ISBN 7-5084-0816-0
32龙驭球编．有限元法概论．人民教育出版社，1978
33陆君安，尚涛等编．偏微分方程的MATLAB解法．武汉大学出版社，2001，ISBN 7-307-03256-2
34林群编．微分方程数值解法基础教程．北京：科学出版社，2001，ISBN 7-03-009056-X
35龚晓南编．土工计算机分析．北京：中国建筑工业出版社，2000，ISBN 7-112-04330-1
36孟凡中编．弹塑性有限变形理论和有限元方法．北京：清华大学出版社，1985
37朱伯芳编．有限单元法原理与应用．北京：中国水利水电出版社，1998，ISBN 7-80124-701-9
38朱梅生主编．软土地基．北京：中国铁道出版社，1989
39钱家欢，殷宗泽主编．土工原理与计算．中国水利水电出版社，1996，ISBN 7-80124-142-8
40陈火红编．MARC有限元实例分析教程．机械工业出版社，2002，ISBN 7-111．10054-9
41I．M．Smith, D．V．Griffiths著．有限元方法编程．电子工业出版社，2003，ISBN 7-5053-9115-1
42邓巍巍，王越男著．Visual FORTRAN编程指南．人民邮电出版社，2000，ISBN 7-115-08530-7
43王勖成，邵敏编著．有限单元法基本原理和数值方法．清华大学出版社，1996，ISBN 7-302-02421-9
44中国科学院兰州冰川冻土研究所，煤炭工业部特殊凿井公司冻土壁研究组编著．冻结凿井冻土壁的工程性质．兰州大学出版社，1988
45徐芝纶编．弹性力学简明教程．高等教育出版社，1983，ISBN 7-04-001483-1
46H．A．崔托维奇(苏)著．张长庆，朱元林译．冻土力学[M]．北京：科学出版社，1985
47李相然，岳同助编著．城市地下工程实用技术．北京：中国建材工业出版社，2000，ISBN 7-80159-018-X
48黄成光主编．公路隧道施工．人民交通出版社．
49杨桂通，树学锋编著．塑性力学．中国建材出版社，1999，ISBN 7-80090-971-9
50熊祝华编．塑性力学基础知识．高等教育出版社，1986
51王仁等编．塑性力学基础知识
52MARC培训手册
53MARC实例教程
54夸克工作室编．有限元分析基础篇：ANSYS与MATLAB．清华大学出版社，2002，ISBN 7-302-05154-2
55中国土木工程学会第四届土力学及基础工程学术会议论文选集．北京：中国建筑工业出版社
56张道宽，王显义．软基变形问题的弹塑性有限元分析
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