本文主旨係於二度空間裡，針對前進在平緩坡度( )底床上的週期性規則表面重力波，產生連續時空變形至碎波(breaker)時，探討其碎波特性及產生之衝量。
對此問題，首先引用陳等(1992~2005)以底床坡度 及深海波浪
振幅 為雙攝動參數，所得之至 階的Eulerian與Lagrangian形式解。然後，由波峯處水粒子之水平速度分量 恰等於波速 之碎波條件的引入，本文解析描述出至 階的非線性量下，波動流場隨波浪前進之時空連續演變至碎波的發生，包括波形的變形、水粒子運動軌跡、波壓等，並由之定出碎波波長、碎波波高、碎波水深、碎波時之波浪尖銳度等碎波特性；接著，再藉由自平均靜水位以上至自由表面的波壓積分，求出碎波衝量的理論模式，來彌補歷來對碎波衝量多以半經驗公式來行之之不足。最後，引入往昔對此問題相關試驗與現場結果，以及本研究再行試驗之結果，尤其對水粒子運動軌跡與碎波時之波力及碎波衝量之量測，來具體印證本文解析所得之碎波特性及碎波衝量的理論結果的吻合一致性；且由之確認的是，對碎波問題的研究，其非線量是不可遺缺的。

The major purpose of this study is focused on the characteristics of the breaker and the impulse caused by wave breaking. Two-dimensional surface regular gravity water waves propagating on a gentle sloping bottom are considered and the consecutively temporal-spatial evolution of wave traveling form deep water to shallow water is also investigated.
Two perturbation parameters, bottom slope and the deep water wave amplitude , proposed by Chen et al.(1992~2005), are introduced in this problem. Also, two different systems in fluid mechanics are used and the theoretical results are corrected to order , including nonlinear quantities, in both of Eulerian and Lagrangian systems. Considering the point of view that the horizontal velocity of a specified fluid particle is equal to the wave celerity while the wave begins to break, some important physical phenomena, such as the evolution of wave profile, the trajectory of fluid particle, and the water wave pressure, are described in this analytical analysis. Furthermore, the wave length, wave height, water depth and wave steepness of breaking wave are solved. To modify the insufficiency of former semi-empirical formula for the impulse due to wave breaking, a theoretical formula is proposed by integrating the resulting water wave pressure form mean still water level to free surface.
Previous experimental studies are employed to verify the theoretical results. For wave for a further verification on the characteristics of wave breaking, some measurements on the movement of fluid particle, wave force and impulse wave conducted. Reasonable agreements can be found from the comparisons. It is concluded that consideration of wave nonlinearity is necessary while dealing with wave breaking problem.

目錄

中文摘要……………………………………………………………. I
英文摘要……………………………………………………………. II
目錄…………………………………………………………………. IV
圖目錄………………………………………………………………. VII
表目錄………………………………………………………………. XI
符號說明……………………………………………………………. XII
第一章 緒論………………………………………………………... 1
1-1 前言………………………………………………………... 1
1-2 往昔研究…………………………………………………... 2
1-3 研究目的及方法…………………………………………... 14
1-4本文組織……………………………………………………. 15
第二章 至 階的Lagrangian與Eulerian方式之結果與比較..
18
2-1 Lagrangian方式之線性理論解析……………………………… 18
2-1-1座標系統之描述……………………………………... 19
　　　2-1-2控制方程式及邊界條件……………………………... 20
2-1-3波動系統之攝動展開及至 階之解……………..
22
2-1-4波浪變形及碎波特性之探討………………………... 27
2-1-4-1波浪之變形………………………………….. 27
2-1-4-2碎波特性之探討…………………………….. 28
2-2 Eulerian方式之線性理論解析…………………………….. 34
2-2-1座標系統之描述……………………………………... 34
2-2-2控制方程式及邊界條件……………………………... 35
2-2-3波動系統之攝動展開及至 階之解……………..
36
2-2-4波浪變形及碎波特性之探討………………………... 40
2-2-4-1波浪之變形………………………………….. 40
2-2-4-2碎波特性之探討…………………………….. 44
2-3兩種描述方式所得之碎波特性解析結果的比較…………………… 47
第三章 Eulerian方式的非線性結果與轉換至Lagrangian形式… 49
3-1至 階之Eulerian方式的非線性量解…………………
50
3-2波浪變形及碎波特性的探討……………………………….. 55
3-2-1波浪之變形…………………………………………... 55
3-2-2碎波特性之探討…………………………………….... 59
3-3碎波特性之結果分析與討論……………………………….. 65
第四章 碎波衝量之探討…………………………………………... 81
4-1碎波衝量往昔之探討方式……………………………….... 83
4-2碎波衝量理論解析…………………………………………….... 84
4-2-1波浪於緩坡上之波力………………………………... 85
4-2-2波浪於緩坡上碎波處之正衝量…………………....... 89
第五章 水工模型試驗……………………………………………... 93
5-1實驗設備與儀器…………………………............................. 93
5-2實驗設計、佈置及條件……………………………………. 102
5-3試驗量測資料之處理………………………………………. 108
5-4臨碎波點在自由表面處質點的運動軌跡量測分析與理論印證…. 109
5-5碎波衝量之試驗結果分析與理論印證……………………. 109
第六章 結論與建議………………………………………………... 126
6-1結論…………………………………………………………. 126
6-2建議…………………………………………………………. 128
參考文獻……………………………………………………………. 130
附錄…………………………………………………………………. 145
附錄A1：Lagrangian方式下 各階解之導述過程…….
145
附錄A2：Eulerian方式下 各階解之導述過程………
156
附錄A3：Eulerian方式下 各階解之導述過程……..
168
簡歷及著作………………………………………………………… 174

參考文獻
1. Asu, I. and Lale, B. (2002) Applications of A Numerical Model to Wave Propagation on mild slopes, China Ocean Engineering, Vol. 16(4), pp.569-576.
2. Bagnold, R. A. (1939) Interim Report on Wave-Pressure Research. J. Inst. Civil Engineers, Vol. 12, pp. 202-226.
3. Battjes, J. A. and Groenendijk, H. W. (2000) Wave height distributions on shallow foreshores. Coastal Engineering, Vol. 40(3), pp. 161-182.
4. Biesel, F. (1952) Study of propagation in water of gradually varying depth. U.S. National Bureau of Standards, Gravity Waves, NBS Circular 521, pp. 243~253.
5. Blackmore, P. A. and Hewson, P. J. (1984) Experiments on Full-scale Wave Impact Pressures. Coastal Engineering, 8, pp. 331-346.
6. Bodge, K. R. and Creed, C. G. (1966) Improving Input Wave Data For Use With Shoreline Change Models. Journal Of Waterway, port Coastal, And Ocean Engineering, Vol. 121(5), pp. 259-263.
7. Camfield, F. E. and Street, R. L. (1968) The effects of bottom configuration on the deformation, breaking and run-up of solitary waves. Coastal Engineering, Chapter II, pp. 173-189.
8. Chen, Y. Y., Yang, B. D., Tang, L. W., Ou, S. H. and Hsu, H. C. (2004) Transformation of Progressive waves Propagation Obliquely on Gentle Slope, Journal of Waterway, Port, Coastal and Ocean Engineering., Vol. 130(4), pp. 162~169.
9. Cox, S.J. and Cooker, M.J. (2001) The pressure impulse in a fluid saturated crack in a sea wall. Coastal Engineering, Vol. 42, pp.241-256.
10. Cox, S. J. and Cooker, M. J. (1999) The motion of a rigid body impelled by sea-wave impact. Applied Ocean Research, Vol. 22, pp. 113-125.
11. Deo, M. C. and Jagdale, S. S. (2003) Prediction of breaking waves with neural networks, Ocean Engineering, Vol. 30(9), pp. 1163-1178.
12. Doering, J. C. and Donelan, M. A. (1997) Acoustic measurements of the velocity fined beneath shoaling and breaking waves. Coastal Engineering, Vol. 32(4), pp. 321-330.
13. Eldeberky, Y. and Battjes, J. A. (1996) Spectral modeling of wave breaking：application to Boussinesq equations. Ouanographic Liternature Review, Vol. 43(9), pp. 852.
14. Fuhrboter, A. (1986) Model and prototype tests for wave impact and run-up on a uniform 1:4 slope. Coastal Engineering, Vol. 10, pp.49-84.
15. Franco, L. (1994) Vertical breakwaters: the Italian experience. Coastal Engineering, Elsevier, Amsterdam, Vol. 22, pp.30-35.
16. Gaillard, D. D. (1904) Wave action in relation to engineering structure, U.S. Army, Corps of Engineers, Beach Erosion Board, Technical Report, No. 13.
17. Galvin, C. J. (1968) Breaker type classifications of three laboratory beaches, J. Geophysics Res., Vol. 73(12), pp. 3651-3659.
18. Gerstner, F. (1802) Theories der wellen, Abhandlungen der Koniglichen Bohmischen Gesellschaft der Wissenschaften, Prague.
19. Goda, Y. (2004) A 2-D Random Wave Transformation Model With Gradational Breaker Index, Coastal Engineering Journal, Vol. 46(1), pp. 1-38.
20. Goda, Y., and Morinobu, K. (1998) Breaking wave heights on horizontal bed affected by approach slope, Coastal Engineering Journal, Vol. 40(4), pp. 307-326.
21. Goda, Y. (1975) Irregular wave deformation in the surf zone, Coastal Eng. in Japan, Vol. 18, pp. 13-26.
22. Goda, Y. (1974) New wave pressure formula for composite breakwater, Proc.14th Int. Conf. on Coastal Eng., ASCE, pp. 1702-1720.
23. Goda, Y. (1970) A synthesis of breaker indices, Trans. of JSCE, Vol. 2, Part 2, pp. 227-230.
24. Gotoh, H. and Sakai, T. (1999) Lagrangian simulation of breaking waves using particle method, Coastal Engineering Journal, Vol. 41(3~4), pp. 303-326.
25. Grill, S. T. and Svendsen, I.A. (1997) Breaking criterion and Characteristics of solitary wave on slops. Journal of Waterway Port. Coastal and Ocean Engineering, Vol. 123(3), pp. 101-112.
26. Hamada, T. (1951) Breakers and beach erosion, Port and Harbor Research Institute, Ministry of Transportation, Japan, pp. 165.
27. Hansen, J. B. (1990) Periodic waves in the surf zone: Analysis of experimental data, Coastal Eng., Vol. 14(1), pp. 19-41.
28. Hattori, M. and Arami, A. (1992) Impact breaking wave pressures on vertical walls. Proceeding of 23th Coastal Engineering Conference, pp. 1785-1798.
29. Hitachi, S. (1994) Case study of breakwater damage – Mutsu-Ogawara Port. Proceeding of International Workshop on Wave Barriers in Deepwaters, Port and Harbour Research Institute, Yokosuka, Japan, pp. 308-331.
30. Hsu, H. C., Chen, Y. Y., Hwung, H. H. (2001) Surface wave propagation on a gentle sloping bottom, Proc. of the 23rd Ocean Engineering Conf. in Taiwan, pp. 33-40. (in Chinese)
31. Hull Philip and Muller Gerald (2002) An investigation of breaker heights, shapes and pressures. Ocean Engineering, Vol. 29(1), pp. 59-79.
32. Hwang, P. A. Wright, W. Krabill, W. B. and Swift, R.N. (2002) Airborne remote sensing of breaking waves. Vol. 80(1), pp. 65-75
33. Ito, Y. (1971) Stability of mix-type breakwater-a method of probable sliding distance. Coastal Engineering in Japan, Vol. 14, pp. 53-61.
34. Iversen, H. W. (1952) Waves and breakers in shoaling water, Proc. 3rd Int. Conf. on Coastal Eng., ASCE, pp. 1-12.
35. Iwagaki, Y., Sakai, T., Tsukioka, K. and Sawai, N. (1974) Relationship Between Vertical Distribution of Water Particle Velocity and Type of Breakers on Beaches, Coastal Eng. in Japan, Vol. 17, pp. 51-58.
36. Kamel, M. A. (1970) Shock pressure on coastal structures. Proceeding of ASCE, Waterways, Harbors Coastal Engineering Division 96, pp. 689-699.
37. Keller, K. B. (1958) Surface waves on water of non-uniform depth, J. Fulid Mech. Vol.4, pp. 607-614.
38. Kirkgoz, M. S. and Akoz, M. S. (2005) Geometrical properties of perfect breaking wave on composite breakwaters. Ocean Engineering, Vol. 32(16), pp. 1994-200.
39. Kirkgoz, M. S., Tanrikulu, A. K. and Dundar, C. (2004) Dynamic analysis of a vertical plate exposed to breaking wave impact. Ocean Engineering, Vol. 29(13), pp. 1623-1635.
40. Kirkgoz, M. S. (1995) Breaking Wave Impact on Vertical and Sloping Coastal Structures. Vol. 22(1), pp. 35-48.
41. Klammer, P., Kortenhaus, A., and Oumeraci, H. (1996) Wave impact loading of vertical face structure for dynamic stability analysis-prediction formula. Proceeding of 25th Coastal Engineering Conference, pp. 2534-2547.
42. Komar, P. D. and Gaughan M. K. (1972) Airy wave theory and breaker height prediction. Porc. 13th Conf. on Coastal Engineering, pp. 405-418.
43. Koshizuka, S., A. Nobe and Oka Y. (1998) Numerical analysis of breaking waves using the moving particle semi-implicit method. Int. J. Numer. Math. Fluids, Vol.26, pp. 751-769.
44. Kotner and Apel, C. J. (1999) Application of a Boussinesq model for the Computation of breaking waves（part 1）.Ocean Engineering, Vol. 26(10), pp. 905-925.
45. Kotner and Apel, C. J. (1999) Application of a Boussinesq model for the Computation of breaking waves（part 2）.Ocean Engineering, Vol. 26(10), pp. 927-947.
46. Le M´ehaut´e, B. and Koh, R. C. Y. (1967) On the Breaking of waves arriving at an angle to the shore, J. Hydraul. Res., Vol. 5(1), pp. 67-88.
47. Le M´ehaut´e, B. and Webb, L. (1964) Periodic gravity wave over a gentle slope at a third order of approximation. Proceedings of the 9th International Conference on Coastal Engineering, ASCE, pp. 23-40.
48. Li, R. and Wang, H. (1999) Nonlinear Effect of Wave Propagation in Shallow Water, China Ocean Engineering, Vol. 13(1), pp. 109-114.
49. Martin, G. (1989) A probability distribution of breaking wave crest height based on a crest-acceleration threshold method. Ocean Engineering, Vol. 16(5), pp. 537-544.
50. Mason, M. A. (1941) A study of progressive oscillatory waves in water, U.S. Army, Corps of Engineers, Beach Erosion Board, Technical Report, No. 1.
51. Mitsuyasu, H. (1966) Shock pressure of breaking wave. Proceeding of 10th Coastal Engineering Conference, ASCE, Vol. 2, pp. 268-283.
52. Mitsuyasu, H. (1962) Experimental study on wave force against sea wall. Coastal Engineering in Japan, Vol. 5, pp. 23-47.
53. Ogawa, Y. and Shuto, N. (1984) Run-up of periodic waves on beaches of non-uniform slope, Proc. 19th Int. Conf. on Coastal Eng., ASCE, pp. 328-334.
54. Oumeraci, H. (1994) Review and analysis of vertical breakwater failures-lessons learned. Coastal Engineering, Elsevier, Amstordam, Vol. 22, pp. 3-29.
55. Partenscky, H. W. (1988) Dynamic forces due to waves breaking at vertival coastal structures. Proceeding of 21th Coastal Engineering Conference, pp. 2504-2518.
56. Pierson, W. J., Jr. (1962) Perturbation analysis of the Navier-Stokes equations in Lagrangian form with selected linear solution. J. Geophys Res. Vol. 67(8), pp. 3181-3160.
57. Rakine, W. J. M. (1863) On the exact form of waves near the surface of deep water, Philosophical Transactions of the Royal Society of London, pp.127-138.
58. Rattanapitikon, W. and Shibayama, T. (2000) Verification and modification of breaker height formulas, Coastal Engineering Journal, Vol. 42(4), pp. 389-406.
59. Saeki, H. S. Hanayasu, A. O. and Takgi, K. (1971) The shoaling and run-up height of the solitary wave, Coastal Engineering in Japan, Vol. 14, 25-42.
60. Seyama, A. and Kimura, A. (1988) The measured properties of irregular wave breaking and wave height change after breaking on slope, Proc. 21st Int. Conf. on Coastal Eng. Malaga, ASCE, pp. 419-432.
61. Smith, J. M. and Kraus, N. C. (1990) Laboratory study on macro-features of wave breaking over bars and artificial reefs, Technical Report CERC-90-12, WES, US Army Corps of Engineers, p 232 p..
62. Stokes, G. G. (1847) On the theory of oscillatory waves, Transactions of the Cambridge Philosophical Society, Vol. 8, pp. 441-445.
63. Street, R. L. and Camfield F. E. (1966) Observations and experiments on solitary wave deformation, Proc. 10th Int. Conf. on Coastal Eng., ASCE, pp. 284-301.
64. Sunamura, T. (1983) Determination of breaker height and depth in the field, Ann. Rep., Inst. Geosci., Univ. Tsukuba, No. 8, pp. 53-54.
65. Sunamura, T. (1980) A laboratory study of offshore transport of sediment and a model for eroding beaches, Proc. 17th Int. Conf. on Coastal Eng., ASCE, pp. 1051-1070.
66. Sunamura, T. and Horikawa, K. (1974) Two-dimensional beach transformation due to waves, Proc. 14th Int. Conf. on Coastal Eng., ASCE, Copenhagen, pp. 920-938.
67. Suquet, F. (1950) Experimental study on the breaking of waves, La Houille Blancha, No. 3, May to June.
68. Sverdrup, H. U. and Munk, W. H. (1944) Breaker and surf, U.S. Navy Hydrographic Office, Technical Report, No. 234.
69. Takahashi, S. and Tsuda, M. etc. (1998) Experiment and FEM Simulation on dynamic response of a caisson against breaking impulsive pressure. Proceeding of 26th Coastal Engineering Conference.
70. Tang, L. W. (1966) Coastal Engineering researches on the western coast of Taiwan, Proc. 10th Conference on Coastal Engineering.
71. Tanimoto, K., and Takahashi, S. (1994) Japanese experience on composite breakwaters. Proceeding of International Workshop on Wave Barriers in Deepwaters, Port and Harbour Research Institute, Yokosuka, Japan, pp.1-24.
72. Tsai, C. P., Chen, H. B., Hwung, H. H. and Huang, M. J. (2005) Examination of empirical formulas for wave shoaling and breaking on steep slopes, Ocean Engineering, Vol. 32(4), pp. 469-483.
73. Tseng, W. J. Chen, Y.Y. and Chen, G. Y. (2005) Nonlinear lagrangian breaker characteristic for waves propagating normally toward a mild slope, China Ocean Engineering, Vol. 19(4).
74. Wood, D. J. and Peregrine, D. H. (2000) Wave Impact on A Wall Using Pressure-Impulse Theory, Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 126(4), pp.182-190.
75. Wu, Y. H. and Tian, J. W. (2000) Mathematical analysis of long-wave breaking on open channels with bottom friction, Ocean Engineering, Vol. 27(2), pp. 187-202.
76. Zhang, H., Hong, G., Ding, P. and Cao, Z. (2001) Numerical Simulation of Non-Linear Wave Propagation in Waters of Mildly Varying Topography with Complicated Boundary, China Ocean
Engineering, Vol. 15(1), pp. 37-52.
77. 許弘莒(2005)，斜坡底床上前進波的非線性解析，國立成功大學水利及海洋工程研究所博士論文。
78. 李忠潘、廖亦鈞、魏文俊(2005)，碎波於斜波後平台上水位抬升之試驗研究，第27屆海洋工程研討會論文集第，445頁-452頁。
79. 曾文哲、陳陽益、陳冠宇(2005)，Lagrangian 系統下碎波衝量之研
究，第27屆海洋工程研討會論文集，第589頁-597頁。
80. 楊炳達(2004)，緩坡底床上斜向波列變形之理論解析，國立成功大學水利及海洋工程研究所博士論文。
81. 曾文哲、陳陽益(2004)，碎波衝量之研究，第26屆海洋工程研討
會論文集，第329頁-337頁。
82. 林銘崇、丁肇隆、胡惟鈞(2003)，碎波拍擊直立壁之流場試驗量測
，第25屆海洋工程研討會論文集，第547頁-553頁。
83. 陳陽益(2003a)，非陡坡底床上前進波的非線性解析：.I. 系統化攝
動展開模式，第二十五屆海洋工程研討會論文集，第39頁-48頁。
84. 陳陽益(2003b)，非陡坡底床上前進波的非線性解析：II. 至
階的解析解及印證，第二十五屆海洋工程研討會論文集，第49頁-58頁。
85. 曾文哲、陳陽益(2003)，Lagrangian系統下平緩坡度底床上碎波的
特性研究，第25屆海洋工程研討會論文集，第79頁-88頁。
86. 許泰文、藍元志、蔡金晏 (2002)，有限元素法波場模式之延伸，第24屆海洋工程研討會論文集，第34頁-41頁。
87. 丁肇隆、林銘崇、胡惟鈞、謝有信(2002)，陡坡地形碎波後之波浪特性研究，第24屆海洋工程研討會論文集，第51頁-62頁。
88. 廖奕鈞、王兆璋、李忠潘、柯文貴(2002)，人工沙洲碎波條件及
特性研究，第二十四屆海洋工程研討會論文集，第541頁-547頁。
89. 邱耀達(2002)，直立堤面衝擊波力與衝升時間聯合機率分布特性
之研究，國立成功大學水利及海洋研究所博士論文。
90. 曾文哲、陳陽益(2002)，平緩坡度底床上碎波的特性研究，第24
屆海洋工程研討會論文集，第42頁-50頁。
91. 周宗仁、石瑞祥，尹彰、歐陽寬(2001)，孤立波碎波指標之數值研
究，第23屆海洋工程研討會論文集，第41頁-48頁。
92. 林朝福、施佳利、杜旻儒(2001)，碎波型態特性之探討,第23屆海
洋工程研討會論文集，第64頁-72頁。
93. 楊炳達、陳陽益、湯麟武、歐善惠(2001)，前進波列斜向傳遞於
等緩坡度上之研究(Ⅱ)，第23屆海洋工程研討會論文集，第6頁-15頁。
94. 許弘莒、陳陽益、黃煌煇(2001)，平緩坡度底床上非線性表面波
之演變，第23屆海洋工程研討會論文集，第33頁-40頁。
95. 謝榮華 (2001)，波浪作用下垂直與水平柱體受力行為及減力設施
之試驗研究，國立中山大學海洋環境及工程研究所碩士論文。
96. 郭一羽等(2001)，海岸工程學，文山書局。
97. 楊炳達、陳陽益、湯麟武、歐善惠(2000)，前進波列斜向傳遞於
等緩坡度底床之研究，第22屆海洋工程研討會論文集，第1頁-8頁。
98. 陳陽益、黃啟暘(2000)，Lagrangian方式下緩底床上之前進波， 第
22屆海洋工程研討會論文集，第79頁-88頁。
99. 陳陽益、湯麟武(1999)，波浪像岸上前進之折射：I.通式與等緩
坡度底床情況，第21屆海洋工程研討會論文集，第147頁-156
頁。
100. 陳陽益、張富東(1999)，平緩坡度底床上前進波的試驗研究，第
21屆海洋工程研討會論文集，第165頁-174頁。
101. 湯麟武(1999)，港灣及海域工程，中國工程師手冊水利類第十一
　　篇。
102. 蕭豐格 林銘崇 丁肇隆(1997)，深水碎波在直立壁上之衝擊壓力
量測分析國立臺灣大學造船及海洋工程學研究所碩士論文。
103. 陳陽益(1997)，平緩坡度底床上前進的表面波，第19屆海洋工程
研討會論文集，第112頁-121頁。
104. 陳陽益(1996)，非旋轉性前進波的Eulerian與Lagrangian解間的 轉換性，第十八屆海洋工程研討會論文集，第1頁-13頁。
105. 陳陽益 (1995)， Lagrangian 與 Eulerian 解下前進重力波與重力
駐波之Lagrangian方式的攝動解析，第十六屆海洋工程研討會論
文集，第A30-A59頁。
106. 陳陽益(1994a)，等深水中非旋轉性的自由表面前進重力波之 Lagrangian方式的攝動解析，第十六屆海洋工程研討會論文集，
A21頁-A29頁。
107. 陳陽益(1994b)，等深水中非旋轉性的自由表面前進重力波之
Lagrangian方式的攝動解析，第十六屆海洋工程研討會論文集，A30頁-A59頁。
108.陳陽益、湯麟武(1992)，平緩坡度底床上前進的表面波，第14屆海洋工程研討會論文集，第1頁-22頁。
109.黃正欣、林西川(1986)，通用模式波浪理論之應用-波浪變形及平均水位之變化. 第三屆水利工程研討會論文集，第343頁-362頁。
110.楊春生(1980)，沈箱式防波堤受衝擊碎波壓力之動力分析。土木
水利彙刊第11卷，第46頁-62頁。
111.合田良實(1973)， 衝擊碎波波壓ける混成防波堤の舉動に關する
考察，運輸省港灣技術研究所報告第12卷，第3頁-29頁。
112.堀川清司、野口雄二(1970)，直立壁に作用すゐ碎波の波力と波面との關係，第19回海岸工學講演會講演集，第177頁-184頁。
113.合田良實(1967)，構造物に動く波力，運輸省港灣技術研究所報告第6卷，第1頁-34頁。
114.光易??(1959)，直立壁に働く全波利働にっいて，第六回海岸工學講演會講演集，第107頁-113頁。
115.林泰造、服部昌太郎、林憲吉(1958)，碎波の波壓と力積。第5回海岸工學講演會講演集，第21頁-27頁。
116.永井莊七郎(1958)，防波堤に働りく碎波の壓力に關すゐ研究，第五回海岸工學講演會講演集，第29頁-29頁。