跳到主要內容

臺灣博碩士論文加值系統

(3.87.33.97) 您好!臺灣時間:2022/01/27 17:24
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:曾吉祥
研究生(外文):Chi-shiang Tzeng
論文名稱:彈性常數隨深度呈指數變化之橫向等向性半無限空間承受點荷重後之位移與應力
論文名稱(外文):Displacements and Stresses due to a point load in a Transversely Isotropic half-spaces whose elastic constants vary exponentially with depth
指導教授:廖志中廖志中引用關係王承德
指導教授(外文):Jyh-Jong LiaoCheng-Der Wang
學位類別:碩士
校院名稱:國立交通大學
系所名稱:土木工程系
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:182
中文關鍵詞:異向性異質性橫向等向性半無限空間點荷重
外文關鍵詞:anisotropicnonhomogeneoustransversely isotropichalf spacepoint load
相關次數:
  • 被引用被引用:2
  • 點閱點閱:273
  • 評分評分:
  • 下載下載:31
  • 收藏至我的研究室書目清單書目收藏:1
本文係根據異向性彈性力學理論,解析出有關承受點荷重後,無限與半無限空間之非均質且橫向等向性岩體之位移與應力解;所分析的橫向等向性岩體之彈性對稱面與水平受力面平行,而五個彈性常數(E、 、 、n、 )中的水平楊氏係數(E)、垂直楊氏係數( )及垂直剪力模數( )係假設隨著覆土(岩)深度之增加而呈指數函數增加;其所推導出的解透過數值積分運算,可與水平之均質橫向等向性岩體之特例相互比較,以檢視其異質性與異向性的程度造成橫向等向性岩體內位移與應力分佈之影響。
Based on the theory of anisotropic elasticity, the solutions of displacements and stresses in nonhomogrneous and transversely isotropic full/half spaces subjected to a point load are presented in this thesis. The plane of transversely isotropy is assumed to be parallel to the horizontal loading surface. Three elastic constants 、 、 in the form of exponential increase with the increase of depth. The derved solutions can be simplified to campare with those existed solutions of homogeneous and transversely isotropic full/half spaces. Besides, a series of parametric study was conducted to investigate the degree of nonhomogeneity on the distributions of displacements and stresses induced by the applied point load in the isotropic/transversely isotropic full/half spaces.
目錄
摘要 I
ABSTRACT ii
誌謝 iii
目錄 iv
表目錄 vii
圖目錄 viii
附錄目錄………………………………………………………....xii
符號說明 xii
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究內容 2
1.3 論文架構 3
第二章 文獻回顧 1
2.1 橫向等向性岩體之變形性 6
2.2 非均質且均向性材料之彈性載重問題 9
2.3 非均質且異向性材料 18
2.3.1 Gibson and Kalsi之研究成果 20
2.3.2 Callandine and Greenwood 之研究成果 25
2.3.3 Rowe and Booker之研究成果 29
2.3.4 Erguven之研究成果 32
2.3.5 Tarn and Wang之研究成果 37
2.3.6 Pan之研究成果 44
第三章 研究方法 49
3.1 無限空間之位移與應力 50
3.2 半無限空間之位移與應力 59
3.3 數值逆轉換與積分結果 65
3.3.1高斯積分法 67
3.3.2應力與位移數值解檢驗 70
第四章 研究結果 83
4.1 無限域受點荷重之研究結果 84
4.1.1 無限域位移 : 84
4.1.2 無限域應力 : 92
4.2 半無限域受點荷重之研究結果 107
4.2.1 半無限域位移 : 107
4.2.2 半無限域應力 : 122
第五章 結論與建議 137
5.1 結論 137
5.2 建議 139
參考文獻 141
附錄A 圓形荷重作用於非均質且橫向等向性介質之數值分析.………………………………..…………….A-1
參考文獻
Amadei, B., Rock Anisotropy and the Theory of Stress Measurements. Springer Verlag, Berlin (1983).
Amadei, B., Rogers, J. D. and Goodman, R. E., "Elastic constants and tensile strength of anisotropic rocks", Proc. 5th Congr. Int. Soc. Rock Mech, Melbourne, Australia, 189-196 (1983).
Amadei, B., Savage, W. Z., and Swolfs, H. S., "Gravitational stresses in anisotropic rock masses", Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 24(1):5-14 (1987).
Alexander, L. G., Discussions to "Some results concerning displacements and stresses in a non-homogeneous elastic half-space", Géotechnique, Vol.27:253-254 (1977).
Awojobi, A. O., and Gibson, R.-E., "Plane strain and axially symmetric problems of a linearly nonhomogeneous elastic half-space," Q. J. Mech. Appl. Math., Vol.26(3):285-302 (1973).
Awojobi, A. O. "The invariance of Gibson’s law for a stratum on a frictionless base", Geotechnique, Vol.24(3):359-366 (1974).
Awojobi, A. O., "The settlement of a foundation on Gibson soil of the second kind", Geotechnique, Vol.25(2):221-228 (1975).
Awojobi, A. O., "On the hyperbolic variation of elastic modulus in a non-homogeneous stratum", Int. J. Solids Struct., Vol.12:739-748 (1976).
Bekhterev P., "Analytic investigation of the generalized Hooke’s law", Zh. Russk. Fiz.-khim. Obschestva, Vol.58(3): 415-446 (1926).
Blackmore, M., Evans, A., and Hyslop, J., "Comparison of some methods for evaluating infinite range ocillatory integrals", J. Comp. Phys., Vol.22:352-376 (1976).
Booker, J. R., Balaam, N. P., and Davis, E. H., "The behavior of an elastic non-homogeneous half-space. part I-line and point loads", Int. J. Numer. Anal. Meth. Geomech., Vol.9: 353-367 (1985a).
Booker, J. R., Balaam, N. P., and Davis, E. H., "The behavior of an elastic non-homogeneous half-space. part II-circular and strip footings", Int. J. Numer. Anal. Meth. Geomech., Vol.9:369-381 (1985b).
Booker, J. R., "Analytic methods in geomechanicsl", Proc. 7th Int. Conf. on Computer Meth. Adv. Geomech., Rofferdam, Vol.1:3-14 (1991).
Brown, P. T., and Gibson, R. E., "Rectangular loads on inhomogeneous elastic soil", J. Soil. Mech. Found. Div., ASCE, Vol.99(SM10): 917-920 (1973).
Buchanan, J. L., and Turner, P. R., Numerical Methods and Analysis, McGraw-Hill, Inc. (1992).
Calladine, C. R., and Greenwood, J. A. "Line and point loads on a non-homogeneous incompressible elastic half-space", Q. J. Mech. Appl. Math., Vol.31(4): 507-529 (1978).
Carrier, W. D. III, and Christian, J.-T., "Analysis of an inhomogeneous elastic half-space", J. Soil Mech. Found. Div., ASCE, Vol.99(SM3): 301-306 (1973).
Chen, C. S., Pan, E. and Amadei, B., "Evaluation of properties of anisotropic rocks using Brazilian test", Proc. 2nd NARMS, Montreal, Vol.2:1651-1658 (1996)
Chen, R., and Stimpson B., "Interpretation of indirect tensile strength tests when moduli of defoirmation in compression and in tension are different", Rock Mech. Rock Engng. Vol.26(2):183-189 (1985).
Chow, Y. K., "Vertical deformation of rigid foundations of arbitrary shape on layered soil media", Int. J. Numer. Anal. Meth. Geomech., Vol.11: 1-15 (1987).
Chuaprasert, M. F., and Kassir, M. K., "Torsion of nonhomogeneous solid", J. Engng. Mech. Div., ASCE, Vol.99(EM4): 703-714 (1973).
Cree, M. J., and Bones, P. J., "Alorithms to numerically evaluate Hankel transforms", Comput. Math. Appl., Vol.26: 1-12 (1993).
Cruse, T. A., Snow., D. W., and Wilson, R. B., "Numerical solution in axisymmetric elasticity", Comput. Struct. Vol.7:445-451 (1977).
Davis, P. J., and Rabinowitz, P., Methods of Numerical Integration, Academic Press, NY (1975).
Dempsey, J. P., and Li, H., "A flexible rectangular footing on a Gibson soil: required rigidity for full contact", Int. J. Solids Struct., Vol.32(3/4): 357-373 (1995).
Dhaliwal, R. S., and Singh, B. M. "Torsion by a circular die of a nonhomogeneous elastic layer bonded to a nonhomogeneous half-space", Int. J. Engng. Sci., Vol.16: 649-658 (1978).
Dhaliwal, R. S., and Singh, B. M., "On the theory of elasticity of a nonhomogeneous medium", J. Elasticity, Vol.8(2): 211-219 (1978).
Erguven, M. E., "Torsion of nonhomogeneous and transversely isotropic half-space", J. Engng. Mech. ASCE, Vol.112(10): 1101-1106 (1986a).
Erguven, M. E., "Torsional loading of an elastic transversely isotropic nonhomogeneous semi-infinite solid", Acta Mech., Vol.61: 165-174 (1986b).
Erguven, M. E., "A fundamental solution for transversely isotropic and nonhomogeneous media", Int. J. Engng. Sci., Vol.25(1): 117-122 (1987a).
Erguven, M. E., "The elastic torsion problem for a nonhomogeneous and transversely isotropic half-space", Acta Mech., Vol.67: 151-162 (1987b).
Erguven, M.-E., "An axisymmetric fundamental solution and the Reissner-Sagoci problem for an internally loaded non-homogeneous transversely isotropic half-space", Int. J. Engng. Sci., Vol.26(1): 77-84 (1988).
Evans, G., Practical Numerical Integration, John Wiley and Sons, Chichester (1993).
Gerrard, C. M., "Background to mathematical modeling in geomechanics:The roles of fabric and stress history", Proc. Int. Symp. Numer. Methods, Karlsruhe, 33-120 (1975).
Giannakopoulos, A. E., and Suresh, S., "Indentation of solids with gradients in elastic properties:Part I. Point force", Int. J. Solids Struct., Vol.34(19):2357-2392 (1997a).
Giannakopoulos, A. E., and Suresh, S., "Indentation of solids with gradients in elastic properties:Part II. Axisymmetric indentors", Int. J. Solids Struct., Vol.34(19):2393-2428 (1997b).
Gibson, R. E., "Some results concerning displacements and stresses in a non-homogeneous elastic half-space", Geotechnique, Vol.17(1): 58-67 (1967).
Gibson, R. E., "On the loaded elastic half-space with a depth varying Poisson’s ratio", Z. Angew. Math. Phys., Vol.20: 691-695 (1969).
Gibson, R. E., Brown, P.-T., and Andrews, K.-R.-F., "Some results concerning displacements in a non-homogeneous elastic layer", Z. Angew. Math. Phys., Vol.22: 855-864 (1971).
Gibson, R. E., "The analytical method in soil mechanics", Geotechnique, Vol.24(2): 115-140 (1974).
Gibson, R. E., and Kalsi, G.-S., "The surface settlement of a linearly inhomogeneous cross-anisotropic elastic half-space", Z. Angew. Math. Phys., Vol.25: 843-847 (1974).
Gibson, R. E., and Sills, G.-C., "Settlement of a strip load on a non-homogeneous orthotropic incompressible elastic half-space", Q. J. Mech. Appl. Math., Vol.28(2): 233-243 (1975).
Gladwell, G. M. L., Contact Problems in the Classical Theory of Elasticity, The Netherlands: Sijthoff and Noordhoff (1980).
Hanson, M. T., and Puja, I. W., "Love’s circular patch problem revisited : Closed form solutions for transverse isotropy and shear loading", Q. Appl. Math., Vol.54(2): 359-384 (1996).
Harnpattanapanich, T., and Vardoulakis, I., "Numerical Laplace-Fourier transform inversion technique for layered soil consolidation problems; II, Gibson soil layer", Int. J. Numer. Anal. Meth. Geomech., Vol.11: 103-112 (1987).
Holzlöhner, U., "Strip loads on a non-linear heterogeneous half-space", Geotechnique, Vol.51(8): 655-664 (2001).
Hondros, G., "The evaluation of Poisson’s ratio and modulus of materials of a low tensile resistance by the Brazilian (indirect tensile) test with particular reference to concrete", J. Appl. Sci., Vol.10:243-268 (1959).
Hudson, J. A., "Wave speed and attenuation of elastic waves in material containing rocks", Geophys. J. R. Astr. Soc., Vol.64:133-150 (1981).
Hudson, J. A., and Harrison, J. P., Engineering Rock Mechanics, Oxford (1997).
Kassir, M. K. "The Reissner-Sagoci problem for a non-homogeneous solid", Int. J. Engng. Sci., Vol.8: 875-885 (1970).
Kassir, M. K., "Boussinesq problems for nonhomogeneous solid", J. Engng. Mech. Div., ASCE, Vol.98(EM2): 457-470 (1972).
Kassir, M. K., and Chuaprasert, M. F., "A rigid punch in contact with a nonhomogeneous elastic solid", J. Appl. Mech. ASME, Vol.41: 1019-1024 (1974).
Ko, H. Y., and Gerstle, K. H., "Elastic properties of two coal", Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol.13(13):81-90 (1976).
Kumar, P., "Stress concentration due to underground excavation in cross-anisotropic and nonhomogeneous elastic halfspace", Comput. Struct., Vol.25(5):687-694 (1987).
Kumar, P., "Nonhomogeneous and cross-anisotropic infinite elements", Comput. and Struct., Vol.28(3):327-333 (1988).
Liao, J. J., Yang, M. T., and Hsieh, H. Y., "Direct tensile behavior of a transversely isotropic rock", Int. J. Rock Mech. Min. Sci. Vol.34(5):837-849 (1997).
Liao, J. J., Hu, T. B., and Chang, C. W., "Determination of dynamic elastic constants of transversely isotropic rocks using a single cylindrical specimen", Int. J. Rock Mech. Min. Sci. Vol.34(7):1045-1054 (1997).
Liao, J.-J., and Wang, C.-D., "Elastic solutions for a transversely isotropic half-space subjected to a point load," Int. J. Numer. Anal. Meth. Geomech., Vol.22: 425-447 (1998).
Longman, I. M., "Tables for the rapid and Accurate numerical evaluation of certain infinite integrals involving Bessel functions", Proc. Cambridge Philos. Soc., Vol.52:166-180 (1956a).
Longman, I. M., "Note on a method for computing infinite integrals of ocillatory functions", Proc. Cambridge Philos. Soc., Vol.52:764-768 (1956b).
Mogi, K., "Effect of the traxial stress system on the failure of dolomite and limestone", Tectonophysics, Vol.11(2):111-127 (1971).
Mossakovskii, V. I., "Pressure of circular die (punch) on an elastic half-space, whose modulus of elasticity is an exponential function of depth", PMM, Vol.22(1):123-125 (1958).
Nishimatsu, Y., "The torsion test and elastic constants of the orthotropic rock substance", Proc. 2nd Cong. Int. Soc. Rock Mech., Belgrade, Vol.1:479-484 (1970).
Olszak, W., Non-homogeneity in Elasticity and Plasticity, Pergamon Press, (1959).
Oner, M., "Vertical and horizontal deformation of an inhomogeneous elastic half-space", Int. J. Numer. Anal. Meth. Geomech., Vol.14:613-629 (1990).
Pan, E., "Static response of a transversely isotropic and layered half-space to general dislocation sources", Phys. Earth Plan. Inter., Vol.58:103-117 (1989a).
Pan, E., "Static response of a transversely isotropic and layered half-space to general surface loads", Phys. Earth Plan. Inter., Vol.54:353-363 (1989b).
Pinto, J. L., "Determination of the elastic constants of anisotropic bodies by diametral compression tests", Proc. 4th Cong. Int. Soc. Rock Mech., Montreux, Vol.2:359-363 (1979).
Plevako, V. P., "On the theory of elasticity of inhomogeneous media", PMM, Vol.35(5): 853-860 (1971).
Plevako, V. P., "On the possibility of using harmonic functions for solving problems of the theory of elasticity of nonhomogeneous media", PMM, Vol.36(5): 834-842 (1972).
Popov, G. I., "Bending of an unbounded plate supported by an elastic half-space with a modulus of elasticity varying with depth", PMM, Vol.23(6): 1095-1100 (1959).
Popov, G. I., "The contact problem of the theory of elasticity for the case of a circular area of contact", PMM, Vol.26(1): 152-164 (1962).
Popov, G. I., "Axisymmetric contact problem for an elastic inhomogeneous half-space in the presence of cohesion", PMM, Vol.37(6): 1052-1059 (1973).
Puro, A. E., "Application of Hankel transforms to the solution of axisymmetric problems when the modulus of elasticity is a power function of depth", PMM, Vol.37(5): 896-900 (1973).
Rajapakse, R. K. N. D., "A torsion load transfer problem for a class of nonhomogeneous elastic solids", Int. J. Solids Struct., Vol.24(2): 139-151 (1988).
Rajapakse, R. K. N. D., "A vertical load in the interior of a non-homogeneous incompressible elastic half-space", Q. J. Mech. Appl. Math., Vol.43(1): 1-14 (1990a).
Rajapakse, R. K. N. D., "Rigid inclusion in nonhomogeneous incompressible elastic half-space", J. Engng. Mech. ASCE, Vol.116(2): 399-410 (1990b).
Rajapakse, R. K. N. D., and Selvadurai, A. P. S., "Torsion of foundations embedded in a non-homogeneous soil with a weathered crust", Geotechnique, Vol.39(3): 485-496 (1989).
Rajapakse, R. K. N. D., and Selvadurai, A. P. S., "Response of circular footings and anchor plates in non-homogeneous elastic soils", Int. J. Numer. Anal. Meth Geomech., Vol.15: 457-470 (1991).
Rammamurthy, T., "Strength and modulus responses of anisotropic rocks", Comprehensive Rock Engineering, Principles, Practice & Projects, Pergamon Press, Vol.1:313-329 (1993).
Rostovtsev, N. A., "An integral equation encountered in the problem of a rigid foundation bearing on nonhomogeneous soil", PMM, Vol.25(1): 238-246 (1961).
Rostovtsev, N. A., "On the theory of elasticity of a nonhomogeneous medium", PMM, Vol.28(4): 745-757 (1964).
Rostovtsev, N. A., and Khranevskaia, I. E., "The solution of the Boussinesq problem for a half-space whose modulus of elasticity is a power of the depth", PMM, Vol.35(6): 1000-1009 (1971).
Rowe, R. K., and Booker, J. R., "The behavior of footings resting on a non-homogeneous soil mass with a crust. part I. strip footings", Can. Geotech. J., Vol.18: 250-264 (1981a).
Rowe, R. K., and Booker, J. R., "The behavior of footings resting on a non-homogeneous soil mass with a crust. part II. circular footings", Can. Geotech. J., Vol.18: 265-279 (1981b).
Rowe, R. K., and Booker, J. R., "Finite layer analysis of nonhomogeneous soils", J. Engng. Mech. Div., ASCE, Vol.108(EM1): 115-132 (1982).
Selvadurai, A. P. S., "The settlement of a rigid circular foundation resting on a half-space exhibiting a near surface elastic non-homogenity", Int. J. Numer. Anal. Methods Geomech., Vol.20: 351-364 (1996).
Selvadurai, A. P. S., Singh, B. M., and Vrbik, J., "A Reissner-Sagoci problem for a non-homogeneous elastic solid". J. Elasticity, Vol.16: 383-391 (1986).
Singh, B. M. "A note on Reissner-Sagoci problem for a non-homogeneous solid", Z. Angew. Math. Mech., Vol.53: 419-420 (1973).
Stark, R. F., and Booker, J. R., "Surface displacements of a non-homogeneous elastic half-space subjected to uniform surface tractions. part I-loading on arbitrarily shaped areas", Int. J. Numer. Anal. Meth. Geomech., Vol.21: 361-378 (1997a).
Stark, R. F., and Booker, J. R., "Surface displacements of a non-homogeneous elastic half-space subjected to uniform surface tractions. Part II-loading on rectangular shaped areas", Int. J. Numer. Anal. Meth. Geomech., Vol.21: 379-395 (1997b).
Stroud, A. H., Gaussian Quadrature Formulas, Prentice-Hall, Inc., Englewood Cliffs, N.J. (1966).
Talesnick, M. L., Lee, M. Y., and Haimson, B. C., "On the determination of elastic material parameters for transverse isotropic rocks from a single test specimen", Rock Mech. Rock Eng., Vol.28(1): 17-36 (1995).
Talexnick, M. L., and Ringel, M., "Completing the hollow cylinder methodology for testing of transversely isotropic rock:torsion testing", Int J. Rock Mech. Min. Sci., Vol.36:627-639 (1999).
Tarn. J. Q., and Wang. Y. M., "Fundamental solutions for torsional problems of cylindrical anisotropic elastic medium", J. Chin. Inst. Eng., Vol.9(2):1-8 (1986a).
Tarn, J. Q., and Wang, Y.-M., "Fundamental solutions for torsional problems of nonhomogeneous transversely isotropic media", J. Chin. Inst. Eng., Vol.9(2): 187-194 (1986b).
Ter-mkrtich’ian, L. N., "Some problems in the theory of elasticity of nonhomogeneous elastic media", PMM, Vol.25(6): 1667-1675 (1961).
Vrettos, C., "In-plane vibrations of soil deposits with variable shear modulus: I. surface wave", Int. J. Numer. Anal. Meth. Geomech., Vol.14: 209-222 (1990).
Vrettos, C., "Time-harmonic Boussinesq problem for a continuously non-homogeneous soil", Earth. Engng. Struct. Dyn., Vol.20: 961-977 (1991a).
Vrettos, C., "Surface Green’s functions for continuously nonhomogeneous soil", Proc. 7th Int. Conf. Computer Meth. Adv. Geomech., Vol.1: 801-804 (1991b).
Vrettos, C., "The Boussinesq problem for soils with bounded non-homogenity", Int. J. Numer. Anal. Meth. Geomech., Vol.22: 655-669 (1998).
Watson, G. N., A Treatise on the Theory of Bessel Functions, Cambridge University Press (1966).
Youash, Y. Y., "Dynamic physical properties of rock:part, theory and procedure", Proc. 2nd Cong. Int. Soc. Rock Mech., Belgrade, Vol.1:171-183 (1970).
Yue, Z. Q., Yin, J. H., and Zhang, S. Y., "Computation of point load solutions for geo-materials exhibiting elastic non-homogeneity with depth", Comput Geotech., Vol.25: 75-105 (1999).
呂志宗、彭清源, "牽涉Bessel函數之壓密問題數值解析", 第七屆大地工程學術研討會,金山,第819-826頁 (1997).
秦滿傑,結合巴西試驗與邊界元素法分析求取異向性岩石之彈性係數與張力強度,國立成功大學資源工程研究所碩士論文 (2001).
彭清源,抽水引致壓密問題數值解析與近似展開理論之應用,私立中華大學土木工程研究所碩士論文 (1999).
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top