基于二维浅水方程的直线段沥青路面径流特性
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摘要
基于二维浅水方程的水动力学方法建立了直线段沥青路面径流的数值模型,根据实际降雨条件下沥青路面径流变化过程的监测结果验证了模型参数,研究了路面宽度、组合坡度等几何参数与路侧排水方式对路面径流时空分布特性的影响。研究结果表明:设计降雨条件下,路面径流在空间分布上呈较强的二维特性,沥青路面径流深度变化依次经历增加、稳态径流与退水3个过程;漫排水条件下,路面宽度分别为11、15、20、25、30 m时,路面径流最大深度分别为11.87、14.39、17.08、19.69、21.98 mm,退水时间分别为1.4、1.4、2.4、2.9、3.4 min;路面径流深度增幅随路面宽度的增加而降低,退水时间随路面宽度的增加而增加;相比于行车道,硬路肩路面径流的退水时间延长约20%;较大的坡度组合(横坡为3%,纵坡为2%)有利于排水;当采用集中排水时,路缘石的阻拦使路侧产生壅水,壅水区宽度为6～8 m,壅水区范围占路面宽度的比例随路面宽度的增加而逐渐缩小,非壅水区内的路面径流深度变化与漫排水条件下基本相同;为保证行车安全,可通过改变路面坡度来减少路面径流的汇流时间;路缘石对路面径流的阻拦效应明显,在排水设计中应合理设置路缘石高度与开口间隔,避免行车道出现壅水现象。
Based on the hydrodynamic method of two-dimensional shallow water equations, a numerical model of straightline segment asphalt pavement runoff was proposed. According to the monitoring result of asphalt pavement runoff variation under the actual rainfall conditions, the model parameters were validated. The influences of geometric parameters such as the pavement width, slope combination, and drainage method on the temporal and spatial variations in the pavement runoff were analyzed. Research result shows that under the designed rainfall conditions, the pavement runoff exhibits strong two-dimensional characteristics in the spatial distribution. The runoff depth variation process includes the increasing period, steady-state runoff and retreat. Under the condition of decentralized drainage, when the pavement width is 11, 15, 20, 25 and 30 m, respectively, the maximum pavement runoff depth is 11.87, 14.39, 17.08, 19.69 and 21.98 mm, respectively, and the retreat time is 1.4, 1.4, 2.4, 2.9 and 3.4 min, correspondingly. The increment of pavement runoff depth decreases as the pavement width increases. The retreat time of pavement runoff increases with the addition of pavement width. Comparing with the carriageway, the retreat time in shoulder area increases by approximately 20%. A larger slope combination(the cross slope is 3% and the longitudinal slope is 2%) is beneficial to the drainage. When adopting the central drainage, the block of curbs leads to the formation of backwater on the roadside. The width of backwater area is 6-8 m, and its proportion decreases with the increase of pavement width. In the no-backwater area, the pavement runoff depth shows a similar change to that when using the decentralized drainage. To ensure the driving safety, a reasonable pavement slope should be set to reduce the confluence time of pavement runoff. The blocking effect of curbs on the pavement runoff is obvious, thus, the height of curbs and outlets interval should be set reasonably in the drainage design to avoid the formation of backwater in the carriageway.
Based on the hydrodynamic method of two-dimensional shallow water equations, a numerical model of straightline segment asphalt pavement runoff was proposed. According to the monitoring result of asphalt pavement runoff variation under the actual rainfall conditions, the model parameters were validated. The influences of geometric parameters such as the pavement width, slope combination, and drainage method on the temporal and spatial variations in the pavement runoff were analyzed. Research result shows that under the designed rainfall conditions, the pavement runoff exhibits strong two-dimensional characteristics in the spatial distribution. The runoff depth variation process includes the increasing period, steady-state runoff and retreat. Under the condition of decentralized drainage, when the pavement width is 11, 15, 20, 25 and 30 m, respectively, the maximum pavement runoff depth is 11.87, 14.39, 17.08, 19.69 and 21.98 mm, respectively, and the retreat time is 1.4, 1.4, 2.4, 2.9 and 3.4 min, correspondingly. The increment of pavement runoff depth decreases as the pavement width increases. The retreat time of pavement runoff increases with the addition of pavement width. Comparing with the carriageway, the retreat time in shoulder area increases by approximately 20%. A larger slope combination(the cross slope is 3% and the longitudinal slope is 2%) is beneficial to the drainage. When adopting the central drainage, the block of curbs leads to the formation of backwater on the roadside. The width of backwater area is 6-8 m, and its proportion decreases with the increase of pavement width. In the no-backwater area, the pavement runoff depth shows a similar change to that when using the decentralized drainage. To ensure the driving safety, a reasonable pavement slope should be set to reduce the confluence time of pavement runoff. The blocking effect of curbs on the pavement runoff is obvious, thus, the height of curbs and outlets interval should be set reasonably in the drainage design to avoid the formation of backwater in the carriageway.
引文
[1] 张明珠,曾娇娇,黄国如,等.市政排水与水利排涝设计暴雨重现期衔接关系的分析[J].水资源与水工程学报,2015,26(1):131-135.ZHANG Ming-zhu, ZENG Jiao-jiao, HUANG Guo-ru, et al. Analysis of cohesive relationship for return period of design rainstorm between municipal sewerage and waterlogging drainage[J]. Journal of Water Resources and Water Engineering, 2015, 26(1): 131-135. (in Chinese)
[2] DAN Han-cheng, TAN Jia-wei, ZHANG Zhi, et al. Modelling and estimation of water infiltration into cracked asphalt pavement[J]. Road Materials and Pavement Design, 2017, 18(3): 1-22.
[3] MORITA M. Flood risk impact factor for comparatively evaluating the main causes that contribute to flood risk in urban drainage areas[J]. Water, 2014, 6: 253-270.
[4] 张驰,郭鑫鑫,崔卜心.不均匀积水条件对路面行车安全的影响[J].公路交通科技,2014,31(10):104-111.ZHANG Chi, GUO Xin-xin, CUI Bu-xin. Influence of uneven wet pavement surface condition on driving safety[J]. Journal of Highway and Transportation Research and Development, 2014, 31(10): 104-111. (in Chinese)
[5] 赵鸿铎,伍梦竹,吴世涛.沥青道面摩擦系数随水膜厚度的变化规律[J].中国民航大学学报,2015,33(2):47-52.ZHAO Hong-duo, WU Meng-zhu, WU Shi-tao. Variation of asphalt pavement friction coefficient with change of water film thickness[J]. Journal of Civil Aviation University of China, 2015, 33(2): 47-52. (in Chinese)
[6] 滕旭秋,王海峰,文华.基于动量原理的大坡度沥青路面动水压力计算及影响因素分析[J].计算力学学报,2016,33(2):257-261.TENG Xu-qiu, WANG Hai-feng, WEN Hua. Calculation and influence factors analysis for hydrodynamic pressure of asphalt pavement with large slope based on momentum theorem[J]. Chinese Journal of Computational Mechanics, 2016, 33(2): 257-261. (in Chinese)
[7] COMPORT B C, THORNTON C I. Hydraulic efficiency of grate and curb inlets for urban storm drainage[J]. Journal of Hydraulic Engineering, 2012, 138(10): 878-884.
[8] 李家春,田伟平,吕亚莉.高等级公路路面集中排水水力计算[J].重庆交通学院学报,2002,21(4):54-56.LI Jia-chun,TIAN Wei-ping,LYU Ya-li. Hydraulic calculation for expressway pavement surface drainage[J]. Journal of Chongqing Jiaotong University, 2002, 21(4): 54-56. (in Chinese)
[9] 梁小光,程松青.道路坡度对路面排水的影响研究[J].给水排水,2018,44(3):9-15.LIANG Xiao-guang, CHENG Song-qing. Study on the influence of roadway slope on pavement drainage[J]. Water and Wastewater Engineering, 2018, 44(3): 9-15. (in Chinese)
[10] 刘毓氚,缪宏杰.降雨入渗条件下新型路面排水系统性能研究[J].中国公路学报,2017,30(5):1-9.LIU Yu-chuan, MIAO Hong-jie. Research on performance of new pavement drainage system under rainfall infiltration[J]. China Journal of Highway and Transport, 2017, 30(5): 1-9. (in Chinese)
[11] 季天剑,黄晓明,刘清泉,等.沥青路面表面水膜厚度试验[J].公路交通科技,2004,21(12):14-17.JI Tian-jian, HUANG Xiao-ming, LIU Qing-quan, et al. Test depth of water film on asphalt pavement surface[J]. Journal of Highway and Transportation Research and Development, 2004, 21(12): 14-17. (in Chinese)
[12] CRISTINA C M, SANSALONE J J. Kinematic wave model of urban pavement rainfall-runoff subject to traffic loadings[J]. Journal of Environmental Engineering, 2003, 129(7): 629-636.
[13] BRUFAU P, GARCíA-NAVARRO P, VáZQUEZ-CENDóN M E. Zero mass error using unsteady wetting-drying conditions in shallow flows over dry irregular topography[J]. International Journal for Numerical Methods in Fluids, 2004, 45(10): 1047-1082.
[14] 张大伟,权锦,何晓燕,等.基于一维运动波理论的坡面汇流和沟道汇流数学模型研究[J].中国防汛抗旱,2014,24(5):33-35,47.ZHANG Da-wei, QUAN Jin, HE Xiao-yan, et al. Numerical modeling of overland flow and channel flow based on 1D kinematic wave theory[J]. China Flood and Drought Management, 2014, 24(5): 33-35, 47. (in Chinese)
[15] CEA L, GARRIDO M, PUERTAS J. Experimental validation of two-dimensional depth-averaged models for forecasting rainfall-runoff from precipitation data in urban areas[J]. Journal of Hydrology, 2010, 382(1-4): 88-102.
[16] STAUFER P, SIEKMANN M, LOOS S, et al. Numerical modeling of water levels on pavements under extreme rainfall[J]. Journal of Transportation Engineering, 2012, 138(6): 732-740.
[17] ESCARAMEIA M, GASOWSKI Y, MAY R W P, et al. Estimation of runoff depths on paved areas[J]. Urban Water Journal, 2006, 3(4): 185-197.
[18] MA Yao-lu, GENG Yan-fen, CHEN Xian-hua, et al. Prediction for asphalt pavement water film thickness based on artificial neural network[J]. Journal of Southeast University (English Edition), 2017, 33(4): 490-495.
[19] LI H, KAYHANIAN M, HARVEY J T. Comparative field permeability measurement of permeable pavements using ASTM C1701 and NCAT permeameter methods[J]. Journal of Environmental Management, 2013, 118: 144-152.
[20] AURELI F, MARANZONI A, MIGNOSA P, et al. A weighted surface-depth gradient method for the numerical integration of the 2D shallow water equations with topography[J]. Advances in Water Resources, 2008, 31(7): 962-974.
[21] COSTABILE P, COSTANZO C, MACCHIONE F. Performances and limitations of the diffusive approximation of the 2-D shallow water equations for flood simulation in urban and rural areas[J]. Applied Numerical Mathematics, 2017, 116: 141-156.
[22] 罗京,刘建蓓,王元庆.路面水膜深度预测模型验证试验[J].中国公路学报,2015,28(12):57-63.LUO Jing, LIU Jian-bei, WANG Yuan-qing. Validation test on pavement water film depth prediction model[J]. China Journal of Highway and Transport, 2015, 28(12): 57-63. (in Chinese)
[23] 张理,张卓.路面坡度对水膜厚度的影响分析[J].重庆交通大学学报(自然科学版),2013,32(3):404-406.ZHANG Li, ZHANG Zhuo. Impact of road slope on water film thickness[J]. Journal of Chongqing Jiaotong University(Natural Science), 2013, 32(3): 404-406. (in Chinese)
[24] AKAN A O. Drainage of pavements under nonuniform rainfall[J]. Journal of Transportation Engineering, 1986, 112(2): 172-183.
[25] JEONG J, CHARBENEAU R J. Diffusion wave model for simulating stormwater runoff on highway pavement surfaces at superelevation transition[J]. Journal of Hydraulic Engineering, 2010, 136(10): 770-778.
[26] LIU Xiao-feng, CHEN Yun-xiang, SHEN Chao-peng. Coupled two-dimensional surface flow and three-dimensional subsurface flow modeling for drainage of permeable road pavement[J]. Journal of Hydrology Engineering, 2016, 21(12): 04016051-1-13.
[27] KHAN M U, MESBAH M, FERREIRA L, et al. Estimating pavement's flood resilience[J]. Journal of Transportation Engineering, Part B: Pavements, 2017, 143(3): 04017009-1-8.
[28] WANG Zhi-li, GENG Yan-fen. Two-dimensional shallow water equations with porosity and their numerical scheme on unstructured grids[J]. Water Science and Engineering, 2013, 6(1): 91-105.
[29] LI Zhe, ZHANG Jun-tao. Calculation of field Manning's roughness coefficient[J]. Agricultural Water Management, 2001, 49(2): 153-161.
[30] CHEN Xian-hua, GENG Yan-fen, JIANG Qing-lin, et al. Innovative approach for pavement runoff characterization[J]. Journal of Performance of Constructed Facilities, 2017, 31(5): 04017047-1-7.
[2] DAN Han-cheng, TAN Jia-wei, ZHANG Zhi, et al. Modelling and estimation of water infiltration into cracked asphalt pavement[J]. Road Materials and Pavement Design, 2017, 18(3): 1-22.
[3] MORITA M. Flood risk impact factor for comparatively evaluating the main causes that contribute to flood risk in urban drainage areas[J]. Water, 2014, 6: 253-270.
[4] 张驰,郭鑫鑫,崔卜心.不均匀积水条件对路面行车安全的影响[J].公路交通科技,2014,31(10):104-111.ZHANG Chi, GUO Xin-xin, CUI Bu-xin. Influence of uneven wet pavement surface condition on driving safety[J]. Journal of Highway and Transportation Research and Development, 2014, 31(10): 104-111. (in Chinese)
[5] 赵鸿铎,伍梦竹,吴世涛.沥青道面摩擦系数随水膜厚度的变化规律[J].中国民航大学学报,2015,33(2):47-52.ZHAO Hong-duo, WU Meng-zhu, WU Shi-tao. Variation of asphalt pavement friction coefficient with change of water film thickness[J]. Journal of Civil Aviation University of China, 2015, 33(2): 47-52. (in Chinese)
[6] 滕旭秋,王海峰,文华.基于动量原理的大坡度沥青路面动水压力计算及影响因素分析[J].计算力学学报,2016,33(2):257-261.TENG Xu-qiu, WANG Hai-feng, WEN Hua. Calculation and influence factors analysis for hydrodynamic pressure of asphalt pavement with large slope based on momentum theorem[J]. Chinese Journal of Computational Mechanics, 2016, 33(2): 257-261. (in Chinese)
[7] COMPORT B C, THORNTON C I. Hydraulic efficiency of grate and curb inlets for urban storm drainage[J]. Journal of Hydraulic Engineering, 2012, 138(10): 878-884.
[8] 李家春,田伟平,吕亚莉.高等级公路路面集中排水水力计算[J].重庆交通学院学报,2002,21(4):54-56.LI Jia-chun,TIAN Wei-ping,LYU Ya-li. Hydraulic calculation for expressway pavement surface drainage[J]. Journal of Chongqing Jiaotong University, 2002, 21(4): 54-56. (in Chinese)
[9] 梁小光,程松青.道路坡度对路面排水的影响研究[J].给水排水,2018,44(3):9-15.LIANG Xiao-guang, CHENG Song-qing. Study on the influence of roadway slope on pavement drainage[J]. Water and Wastewater Engineering, 2018, 44(3): 9-15. (in Chinese)
[10] 刘毓氚,缪宏杰.降雨入渗条件下新型路面排水系统性能研究[J].中国公路学报,2017,30(5):1-9.LIU Yu-chuan, MIAO Hong-jie. Research on performance of new pavement drainage system under rainfall infiltration[J]. China Journal of Highway and Transport, 2017, 30(5): 1-9. (in Chinese)
[11] 季天剑,黄晓明,刘清泉,等.沥青路面表面水膜厚度试验[J].公路交通科技,2004,21(12):14-17.JI Tian-jian, HUANG Xiao-ming, LIU Qing-quan, et al. Test depth of water film on asphalt pavement surface[J]. Journal of Highway and Transportation Research and Development, 2004, 21(12): 14-17. (in Chinese)
[12] CRISTINA C M, SANSALONE J J. Kinematic wave model of urban pavement rainfall-runoff subject to traffic loadings[J]. Journal of Environmental Engineering, 2003, 129(7): 629-636.
[13] BRUFAU P, GARCíA-NAVARRO P, VáZQUEZ-CENDóN M E. Zero mass error using unsteady wetting-drying conditions in shallow flows over dry irregular topography[J]. International Journal for Numerical Methods in Fluids, 2004, 45(10): 1047-1082.
[14] 张大伟,权锦,何晓燕,等.基于一维运动波理论的坡面汇流和沟道汇流数学模型研究[J].中国防汛抗旱,2014,24(5):33-35,47.ZHANG Da-wei, QUAN Jin, HE Xiao-yan, et al. Numerical modeling of overland flow and channel flow based on 1D kinematic wave theory[J]. China Flood and Drought Management, 2014, 24(5): 33-35, 47. (in Chinese)
[15] CEA L, GARRIDO M, PUERTAS J. Experimental validation of two-dimensional depth-averaged models for forecasting rainfall-runoff from precipitation data in urban areas[J]. Journal of Hydrology, 2010, 382(1-4): 88-102.
[16] STAUFER P, SIEKMANN M, LOOS S, et al. Numerical modeling of water levels on pavements under extreme rainfall[J]. Journal of Transportation Engineering, 2012, 138(6): 732-740.
[17] ESCARAMEIA M, GASOWSKI Y, MAY R W P, et al. Estimation of runoff depths on paved areas[J]. Urban Water Journal, 2006, 3(4): 185-197.
[18] MA Yao-lu, GENG Yan-fen, CHEN Xian-hua, et al. Prediction for asphalt pavement water film thickness based on artificial neural network[J]. Journal of Southeast University (English Edition), 2017, 33(4): 490-495.
[19] LI H, KAYHANIAN M, HARVEY J T. Comparative field permeability measurement of permeable pavements using ASTM C1701 and NCAT permeameter methods[J]. Journal of Environmental Management, 2013, 118: 144-152.
[20] AURELI F, MARANZONI A, MIGNOSA P, et al. A weighted surface-depth gradient method for the numerical integration of the 2D shallow water equations with topography[J]. Advances in Water Resources, 2008, 31(7): 962-974.
[21] COSTABILE P, COSTANZO C, MACCHIONE F. Performances and limitations of the diffusive approximation of the 2-D shallow water equations for flood simulation in urban and rural areas[J]. Applied Numerical Mathematics, 2017, 116: 141-156.
[22] 罗京,刘建蓓,王元庆.路面水膜深度预测模型验证试验[J].中国公路学报,2015,28(12):57-63.LUO Jing, LIU Jian-bei, WANG Yuan-qing. Validation test on pavement water film depth prediction model[J]. China Journal of Highway and Transport, 2015, 28(12): 57-63. (in Chinese)
[23] 张理,张卓.路面坡度对水膜厚度的影响分析[J].重庆交通大学学报(自然科学版),2013,32(3):404-406.ZHANG Li, ZHANG Zhuo. Impact of road slope on water film thickness[J]. Journal of Chongqing Jiaotong University(Natural Science), 2013, 32(3): 404-406. (in Chinese)
[24] AKAN A O. Drainage of pavements under nonuniform rainfall[J]. Journal of Transportation Engineering, 1986, 112(2): 172-183.
[25] JEONG J, CHARBENEAU R J. Diffusion wave model for simulating stormwater runoff on highway pavement surfaces at superelevation transition[J]. Journal of Hydraulic Engineering, 2010, 136(10): 770-778.
[26] LIU Xiao-feng, CHEN Yun-xiang, SHEN Chao-peng. Coupled two-dimensional surface flow and three-dimensional subsurface flow modeling for drainage of permeable road pavement[J]. Journal of Hydrology Engineering, 2016, 21(12): 04016051-1-13.
[27] KHAN M U, MESBAH M, FERREIRA L, et al. Estimating pavement's flood resilience[J]. Journal of Transportation Engineering, Part B: Pavements, 2017, 143(3): 04017009-1-8.
[28] WANG Zhi-li, GENG Yan-fen. Two-dimensional shallow water equations with porosity and their numerical scheme on unstructured grids[J]. Water Science and Engineering, 2013, 6(1): 91-105.
[29] LI Zhe, ZHANG Jun-tao. Calculation of field Manning's roughness coefficient[J]. Agricultural Water Management, 2001, 49(2): 153-161.
[30] CHEN Xian-hua, GENG Yan-fen, JIANG Qing-lin, et al. Innovative approach for pavement runoff characterization[J]. Journal of Performance of Constructed Facilities, 2017, 31(5): 04017047-1-7.