本文係以規則波模型實驗，於斷面水槽中拍打七種相對水深d/Lo之碎波波浪條件；碎波型態涵蓋捲波型（plunging）、過渡型（transitional）及溢出型（spilling）。實驗以直接擷取波力資料之方式，探討碎波作用於緩坡上直立堤時，衝擊波力（impulsive wave force）與衝升時間（rising time）之聯合機率分佈特性。
實驗之前，首先以40,000Hz擷取速率獲得捲波型碎波衝擊波力之時系列數據，進行一系列之隨機擷取模擬，以檢定最大衝擊波力偏差與擷取頻率之相關性；結果顯示，高於400Hz擷取頻率所擷取之波力較具有代表性，本文則以2,500Hz作為所有波力實驗之擷取頻率，其擷取最大衝擊波力之偏差經檢定已小於0.3%。
各試驗所擷取之衝擊波力經以波力形狀量化定義及其相關統計參數之信賴度區間檢定；同時考量Goda(1985)建議有關樣本數大小限制之下，選定衝擊波力波形中第一峰值對第二峰值之比F1/F2=1.5作為閥值（threshold），各衝擊波力波形大於此一閥值者始通過檢定，用於後續衝擊波力與衝升時間之聯合機率分佈分析。
經一系列實驗值與理論聯合機率分佈之比較分析，結果顯示雙常態密度函數頗適於無因次衝擊波力與衝升時間聯合機率分佈型態之描述；本文並據以迴歸出雙常態密度函數中各機率參數與相對水深d/Lo、波浪尖銳度 之關係式；同時，提擬以此聯合機率分佈函數用予推估衝擊波力之流程，經以現場設計條件作為應用例，實際說明不同發生機率衝擊波力之推估方式，並與Hiroi(1920)、Minikin(1950)、Nagai(1960)、Mitsuyasu(1962)、Goda(1985)等衝擊波壓公式計算值作比較，結果顯示本文有關衝擊波力與衝升時間聯合機率分佈之研究成果頗為合理。

Regular wave model tests are carried out with 7 kinds of relative depth d/Lo to investigate the joint probability distribution of impulsive forces and rising time for plunging, transitional and spilling breakers on vertical breakwater.
In the model tests, the acquisition rate in model tests was set as 2,500Hz, from which an estimated maximum deviation of impulsive force was below 0.3%. Through a sequence of investigations on deviation of maximum force via acquisition rate for a time series of impulsive forces obtained in a rate of 40,000Hz.
Morover, with confidence interval tests on waveform and statistic parameters of impulsive force data and sample size limitation of data suggested by Goda(1985), impulsive force data were collected to perform the probability analysis by setting a threshold of 1.5 on F1/F2, ratio of first peak to second peak in a waveform of impulsive force.
Based on a series of comparisons of the theoretic and experimental distribution, it was found that the bivariate normal density function could present the joint probability distribution of dimensionless impulsive force and rising time quite well. Meanwhile, parametric formula was regressed with relative water depth d/Lo and wave steepness to estimate the statistic parameters of bi-variate normal density function. Furthermore, a design process on the basis of joint probability distribution was suggested to estimate the impulsive force of plunging wave on breakwaters. The illustrative examples were presented and the results were compared with the formulas presented in Hiroi(1920), Minikin(1950), Nagai(1960), Mitsuyasu(1962) and Goda(1985). It was shown that the design process on the basis of joint probability distribution is quite reasonable.

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