بررسی تغییرات ضرایب رابطه‌ی نمایی جریان غیردارسی درون مصالح سنگریزه‌ای تحت شرایط مختلف جریان

محاسبه‌ی‌ گرادیان هیدرولیکی در تحلیل جریان ماندگار درون مصالح سنگریزه‌ای اهمیت بالایی دارد. برای محاسبه‌ی گرادیان هیدرولیکی بر اساس سرعت جریان غیردارسی از روابط دوجمله‌ای و نمایی استفاده می‌شود که رابطه‌ی دوجمله‌ای نسبت به نمایی از دقت و کارایی بالاتری برخوردار است. از آنجا که در تحلیل دو‌بُعدی جریان غیردارسی در محیط‌های متخلخل درشت استفاده از رابطه‌ی نمایی ضرورت دارد، محققین در گذشته روابطی را جهت محاسبه‌ی ضرایب m و n رابطه‌ی نمایی بر اساس ضرایب a و b رابطه‌ی دو جمله‌ای ارائه داده‌اند. در برخی از پژوهش‌های قبلی vmax=1 در نظر گرفته شده است، این در حالی است که حداکثر سرعت جریان به خصوصیات فیزیکی سنگریزه‌ها و ویژگی‌های جریان بستگی داشته و لزوماً معادل واحد نیست. در پژوهش حاضر محاسبه‌ی سرعت حداکثر بر مبنای مقادیر a و b و re مدل تحلیلی احمد و سونادا پیشنهاد شده است. نتایج نشان می‌دهد که برای محاسبه‌ی ضرایب m و n رابطه‌ی نمایی با استفاده از ضرایب a و b و با فرض vmax=1، اختلاف بین متوسط میانگین خطای نسبی گرادیان هیدرولیکی محاسباتی و ثبت شده در آزمایشگاه برای مصالح ریز، متوسط و درشت‌ به ترتیب برابر با 21.95، 22.98 و 21.97 درصد به دست آمده است. در حالی که بر مبنای رابطه‌ی پیشنهادی، مقادیر میانگین خطای نسبی در مصالح ریز، متوسط و درشت به ترتیب برابر با 11.39، 14.69 و 19.72 درصد محاسبه شده است. به بیان دیگر، راهکار پیشنهادی باعث افزایش دقت محاسبه‌ی گرادیان هیدرولیکی با استفاده از مقادیر a و b، در برآورد ضرایب m و n شده است.

studying changes in coefficients of the non-darcy flow exponential relationship within rockfill materials under different flow conditions

as we know, the calculation of hydraulic gradient is highly important in the analysis of steady flow inside rockfill materials. binomial and exponential relationships are used to calculate the hydraulic gradient based on the non-darcy flow velocity, and the binomial relationship is more accurate and efficient than the exponential relationship. since it is necessary to use an exponential relationship in the two-dimensional analysis of non-darcy flow in coarse porous media, in the past, researchers have provided relationships to calculate the coefficients m and n of the exponential relationship based on the coefficients a and b of the binomial relationship. in some previous studies, vmax= 1 has been considered, even though the maximum flow velocity depends on the physical characteristics of the pebbles and the characteristics of the flow and is not necessarily equal to one. for this reason, in this research, by designing and equipping the laboratory and recording the laboratory data, the maximum velocity based on the values of a, b and re of the analytical model of ahmed and sunada(1969) is proposed.as mentioned above, various researchers tried to calculate the coefficients of the exponential relationship using the values of a and b in the binomial relationship. one of the most important relationships is presented by george and hansen (1992) as follows.n=(5a+6bv_max)/(5a+3bv_max ) (1)m=(5a+4bv_max )(4a+3bv_max )/(4(5a+3bv_max ) (v_max )^(n-1) ) (2)further, by stating that in the coarse-grained porous medium, the slope of the energy line (sf) is equal to the hydraulic gradient (i), it can be stated that one of the most important parameters in the investigation of the flow in the gravel medium in free flow and under pressure is the calculation of it is a hydraulic gradient. in this research, using the coefficients of the binomial relationship, we presented a solution to calculate the values of m and n in the exponential relationship with better accuracy. therefore, considering that the exponential relationship is used in the two-dimensional analysis of the non-darcy flow in porous gravel media, this can play a significant role in reduction of the error of hydraulic gradient calculation.methodologyin the current research, the laboratory data recorded in the hydraulic laboratory of the faculty of civil engineering of zanjan university were used. for this purpose, an attempt was made to design and set up a test device and perform tests on different gravel materials. experiments were carried out in a laboratory flume with the ability to tilt, with dimensions of 1m×1m and a length of 15m, and the length of 2.2m of the mentioned flume is filled with rockfill. the walls of the flume are made of plexiglass, and to measure the piezometric height along the porous media, 23 piezometers are used on the bottom of the channel, which are arranged at certain distances from each other and along them. the water flow in the channel is created by a pump with a maximum flow capacity of 90 liters per second. in order to create a porous media, three types of rockfill materials with small, medium and large diameters have been used in the experiments. during the tests, to ensure a stable flow, the pump was working for about 10 minutes with the desired flow and after the stability of the flow, the desired parameters were measured. these parameters include the piezometric height at the location of 23 piezometers as well as the water depth at the location of each piezometer. piezometric values are read using a calibrated table.