ارايه مفهوم "تخلخل متغير" براي افزايش دقت تحليل جريا نهاي غيرخطي غيرماندگار در ساز ههاي توده سنگي دريايي

Concept of “Variable Porosity” In Nonlinear Analysis of Unsteady Flow within Marine Rubble Mound Structures

چكيده- امروزه به سازه هاي توده سنگي به علت سادگي ساخت در محيط هاي دريايي و هزينه ي نسبتاً كم، بين سازه هاي ساحلي بيش از سايرين توجه شده است. طراحي صحيح اين سازه هاي حجيم و سنگين مستلزم درك جريان هاي غيرخطي غيرماندگار در محيط هاي نسبتاً درشت دانه است. از طرفي يكي از مهم ترين نكات مبهم در مطالعه ي هيدروليك تغييرات فشار حفره اي در محيط هاي متخلخل، مسيله ي چگونگي براورد دقيق مقدار تخلخل است. براي درك مطلب با توجه به تحقيقات محدودي كه در سال هاي اخير پيرامون اين موضوع انجام شده، جريان غيرخطي غيرماندگار در محيط هاي توده سنگي نسبتاً درشت دانه طي پژوهشي جامع در دانشگاه صنعتي اميركبير بررسي شده است. اين مقاله ، پس از مرور يافته هاي پژوهش ياد شده، نشان مي دهد كه روابط رياضي معمول استفاده شده براي تحليل غيرخطي جريان قادر به تخمين دقيق شيب هيدروليكي جريان در توده هاي سنگ ريز نيست . با قبول تخلخل به عنوان مهم ترين پارامتر موثر بر اين مدل هاي رياضي، در يك نتيجه گيري كلي تخلخل به صورت تابعي از رژيم جريان بيان شده است. به طوري كه بر خلاف نظريه ي غالب كه تخلخل را يك پارامتر كاملاً ژيوتكنيكي معرفي مي كند، مقدار اين پارامتر در نتيجه ي تغييرات حجم موثر حفرات و ضريب شكل موثر در هر رژيم جريان متفاوت خواهد بود . سرانجام مطالعات عددي كه براي تاييد يافته ها انجام شده نشان مي دهد نتايج نامعتبري كه از روابط رياضي غيرخطي حاكم بر جريان هاي غيرماندگار به دست آمده، ممكن است ناشي از تخمين نادرست مقدار تخلخل باشد.

Nowadays, several investigators pay attention to the rubble mounds among coastal structures due to their economic superiority over other types of in-shore structures and ease of construction in the marine environment. However, in order to guarantee a reliable design for such heavy structures, it is certainly necessary to have a sound understanding of the hydraulic nature of the unsteady- nonlinear flowʹs parameters controlling the rubble mounds response to the wave loadings. One of the basic uncertainties in determining hydraulic pressure gradient variations is known to be porosity of the media that should be estimated reliably. To cast light on the aforementioned issue, in the absence of up-to-date research works in the literature, a comprehensive investigation has been carried out in the Civil Engineering Department, Amirkabir University of Technology (Tehran, Iran). This paper reviews part of our research findings and points out that the conventional mathematical models for non-linear analysis of unsteady flow through coarse porous media are unable in precisely predicting the hydraulic gradient of flow within rubble mounds. The purpose of this paper is four folds: a. To study the state-of-the-art of mathematical modeling of the flow in coarse porous media: - Firstly, Carman-Kozeny mathematical model is investigated in the steady transient flow; - Secondly, the Forschheimer equation is investigated, where the second term shows the effect of turbulence (still) in steady flow; - Thirdly, a sound literature review is carried out to show the investigators’ view point on the third term that should be added to the Forschheimer equation to represent the impact of unsteadiness in unsteady non-transient flow in coarse porous media. b. To show the determining role of porosity in calculating the value of hydraulic pressure gradient: - After studying the distribution of errors amongst the parameters of the currently used mathematical models, it is shown that, to a large extent, an error in the value of hydraulic pressure gradient stems from the error in porosity. c. To show that mathematical models fail to determine correct values of Forschheimer coefficients: - The calculated values of Forschheimer coefficients are compared with the experimental results. - Discrepancies between the two values are shown on diagrams. d. To introduce the novel concept of effective porosity: - Effective porosity is introduced as the available space for the flow; - - In that sense, porosity should be determined not only based on geotechnical parameters but also it has to be regarded as a function of flow regime. It is also shown that contrary to the dominant opinion, which introduces porosity as a geotechnical property, it may be affected by flow regime through variations in the effective pore volume and effective shape factor. In a numerical justification of findings, it is shown that unsatisfactory results, obtained from non-linear mathematical models of unsteady flow, may be due to unreliable porosity estimates.