دانشگاه شهرکرد پژوهش آب ایران 2008-1235 20 2 2026 06 22 Investigation of the simultaneous effect of pier aspect ratio and pier alignment angle on the local scour depth around round-nosed rectangular bridge piers. بررسی اثر همزمان نسبت طول‌به‌عرض و زاویه انحراف پایه بر عمق آبشستگی موضعی پایه‌های مستطیلی دماغه‌گرد. 1 18 116613 10.22034/iwrj.2026.14840.2618 FA اعظم شیبانی تذرجی سازه های آبی ، گروه علوم و مهندسی آب ، دانشکده کشاورزی ، دانشگاه صنعتی اصفهان ، اصفهان ، ایران منوچهر حیدرپور دانشکده کشاورزی ، دانشگاه صنعتی اصفهان ، اصفهان ، ایران Journal Article 2025 12 30 Introduction: Bridge local scour which is responsible for structural failures in river-crossing bridges, occurs as a result of the interaction between the flow field and the bridge pier, leading to the removal of bed material and the formation of a scour hole around the foundation. Most existing research on the geometry of bridge piers focus on circular or rectangular piers aligned with the flow. However, real-world bridge piers often deviate from the flow direction due to hydraulic constraints or structural alignment. The alignment angle (α), defined as the deviation of the pier’s longitudinal axis from the flow direction, alters the symmetry of the horseshoe vortex and significantly affects the magnitude and position of the maximum scour depth. Moreover, the ratio of pier length (in the direction of flow) to its width (L/B) modifies the distribution of flow velocities and shear stresses around the pier. Despite numerous experimental studies, the simultaneous effect of these two parameters on local scour depth around non-circular piers, particularly rounded-nosed rectangular piers, has received limited attention. The present study aims to investigate the combined influence of L/B and α on the local scour depth under clear-water conditions. Materials and Methods: The experiments were conducted in the hydraulic laboratory of Isfahan University of Technology (IUT), Iran. The flume used for this study is a 12-meter-long, 0.6-meter-wide, and 0.5-meter-deep rectangular open channel with a water circulation system. The bed material consisted of uniform sand with a median particle size of d_50=0.78" " mmand a geometric standard deviation σ_g=1.29. Flow depth and discharge were controlled using a tailgate and calibrated pump system. Two pier models were fabricated from transparent Plexiglas to allow clear observation of flow structures. The reference circular pier had a diameter =3" " cm, while the rounded-nosed rectangular pier had a constant width B=3" " cm(equal to the circular pier’s diameter) and variable lengths L=6,9 and 12" " cm, corresponding to aspect ratios L/B=2,3 and 4. The piers were tested at three different alignment angles relative to the flow direction: α=5°,10° and 20°. Thus, a total of 13 experiments were conducted, including the reference circular pier case. The flow velocity was adjusted to achieve clear-water conditions at U/U_c=0.86, where U_c is the critical velocity for the initiation of sediment motion, determined using the Shields criterion. The steady discharge was set at 50 liters per second, corresponding to a flow depth of 18.8 cm. Before each run, the sand bed was leveled and compacted to ensure uniform initial conditions. Each test continued until the scour hole reached equilibrium. After completion, the final bed profile was measured using a digital point gauge with 0.1 mm precision. Longitudinal and transverse profiles were recorded at multiple sections to obtain the maximum local scour depth d_s. All experiments were repeated twice to ensure reproducibility, and the mean values were reported. Flow fluctuations were maintained within ±2% of the set discharge. The experimental data were analyzed using dimensional analysis and regression techniques. Results and Discussion: The scour process followed the formation of a strong downflow on the upstream face, followed by the development of a horseshoe vortex that transported sediment away from the pier base. The equilibrium scour depth was achieved within 5–6 hours. Effect of Aspect Ratio: At α ≤ 5°, increasing the aspect ratio from 2 to 4 led to a reduction in maximum scour depth which can be attributed to the redistribution of flow momentum along the elongated pier. At α ≥ 10°, the opposite trend was observed. Quantitatively, increasing L/Bfrom 2 to 4 resulted in a 20% decrease in scour depth at α=5°, but a 35% increase at α=20°. Effect of Alignment Angle: Increasing α from 5° to 20° caused the scour hole to deepen and shift laterally toward the upstream corner of the pier. This behavior results from the asymmetric horseshoe vortex system generated under oblique flow conditions. The rounded-nosed rectangular pier produced 15–20% less scour depth at α ≤ 5°, confirming its hydraulic efficiency in near-aligned conditions. However, for α ≥ 10°, the scour depth for rectangular piers exceeded that of the circular pier, indicating the negative impact of larger misalignment angles. Combined Effect of L/B and α: The combined influence of aspect ratio and alignment angle was found to be nonlinear and interactive. For moderate aspect ratios (L/B = 3), the influence of α dominated the scour behavior, while at extreme aspect ratios, both parameters interacted to amplify scour depth. Bed Morphology: Topographic surveys revealed that for α ≤ 5°, the scour hole was nearly symmetrical and shallow, while at α ≥ 10°, the hole became elongated and skewed toward the upstream corner. The deposition zone downstream expanded with increasing α, reflecting stronger wake vortices. Conclusion: The present experimental investigation demonstrated that both pier aspect ratio and alignment angle play crucial and interdependent roles in determining local scour depth around bridge piers. The major conclusions are summarized as follows: For alignment angles below 5°, increasing the pier aspect ratio (L/B) decreases local scour depth by distributing flow energy along the pier face. For α ≥ 10°, larger aspect ratios intensify scour by promoting asymmetric vortex formation and higher local shear stresses. Rounded-nosed rectangular piers perform better than circular piers under small alignment angles (α ≤ 5°), but their performance deteriorates at higher angles. A modified empirical relationship was proposed to estimate the alignment coefficient K_α, which accurately predicts scour depth with R^2=0.94. From a practical perspective, pier alignment angles greater than 10° should be avoided in bridge design to minimize local scour risks. Future work is recommended to examine the effects of surface roughness, pier spacing (group effects), and unsteady flow conditions such as floods using both experimental and computational fluid dynamics (CFD) modeling approaches. چکیده آبشستگی موضعی یکی از شایع‌ترین علل خرابی پل‌ها می‎باشد و معمولا در اطراف پایه و تکیه‌گاه پل‌ها رخ می‌دهد. این مطالعه به بررسی تغییرات آبشستگی موضعی در اطراف پایه مستطیلی دماغه‌گرد می‎پردازد. بدین منظور از یک پایه دایره‌ای به قطر 3 سانتی‌متر و یک پایه مستطیلی دماغه‌گرد به عرض 3 سانتی‌متر استفاده شد. تمرکز اصلی این مطالعه بر روی پایه مستطیلی دماغه‌گرد بوده و تاثیر دو متغیر بر عمق آبشستگی مد نظر قرار گرفت: 1) نسبت طول به عرض پایه (L/D) و 2) زاویه انحراف پایه از مسیر جریان (α). آزمایش‌های آبشستگی (13 آزمایش) در شرایط آب زلال با شدت جریان ثابت U/Uc=0.86 با در نظر گرفتن 3 نسبت L/D=2، L/D=3 و L/D=4 و 3 زوایه انحراف پایه 5، 10 و 20 درجه انجام شده و دبی جریان lit/s50 و عمق جریان cm 8/18 تنظیم شدند. نتایج نشان می‎دهد که در زوایای کوچکتر از 5 درجه، با افزایش نسبت L/D عمق آبشستگی کاهش می‌یابد و در زاویه بزرگتر از 10 درجه، افزایش طول پایه آب شستگی را افزایش می دهد. مشخص شد که پایه مستطیلی دماغه‌گرد در زوایای انحراف پایه از مسیر جریان کوچکتر از 5، عمق آبشستگی کمتری را نسبت به پایه دایره‌ای متحمل می‌شود. واژه‌های کلیدی: آبشستگی موضعی، پایه پل، پایه مستطیلی دماغه گرد، زاویه انحراف پایه از مسیر جریان

https://iwrj.sku.ac.ir/article_116613_42a31dd5f887e84dd47cae2868e31fa5.pdf

دانشگاه شهرکرد پژوهش آب ایران 2008-1235 20 2 2026 06 22 Experimental and Data-Driven Investigation of Hydraulic Performance in Type-A Piano Key Weirs بررسی تجربی و داده محور عملکرد هیدرولیکی سرریز کلید پیانویی تیپ A 19 34 116622 10.22034/iwrj.2026.14922.2632 FA مرتضی شکری استادیار گروه عمران، دانشکده فنی مهندسی، دانشگاه بوعلی سینا، همدان، ایران. Journal Article 2026 02 12 Introduction Piano key weirs (PKWs) are increasingly used as efficient spillway structures due to their ability to significantly increase discharge capacity without requiring an increase in dam crest width. This advantage makes them particularly suitable for dam rehabilitation and for sites where spillway expansion is constrained by topographic or structural limitations. Among different PKW configurations, Type‑A piano key weirs have received considerable attention because of their favorable hydraulic performance and structural simplicity. Despite extensive research on PKWs, the influence of geometric modifications—especially the inclination of side walls and their orientation relative to the flow direction—has not been sufficiently investigated. Side‑wall geometry can affect the flow pattern entering the inlet keys, the formation of separation zones, and the overall hydraulic efficiency of the spillway. Understanding these effects is essential for optimizing PKW performance. Therefore, the present study experimentally investigates the hydraulic behavior of Type‑A piano key weirs with different side‑wall inclinations and orientations. In addition, data‑driven models are employed to predict the discharge coefficient and evaluate the capability of machine‑learning techniques in modeling complex nonlinear hydraulic relationships. Materials and Methods The present study was conducted using a laboratory experimental setup designed to investigate the hydraulic performance of Type A piano key weirs under controlled flow conditions. The experiments were carried out in a rectangular flume with a constant width and adjustable discharge system that allowed accurate control of flow rates. Two geometric configurations of piano key weirs were tested: rectangular and trapezoidal inlet–outlet key shapes. The main objective was to evaluate how the inclination and orientation of the side walls influence the hydraulic efficiency and discharge coefficient of the structure. Side wall inclination angles of 5°, 7.5°, and 10° were selected based on common ranges used in hydraulic structures and previous studies on PKW optimization. For each inclination angle, two orientations were considered: inclination with the flow direction and inclination against the flow direction. These configurations allowed the evaluation of how flow alignment and entrance conditions affect discharge characteristics. During the experiments, the upstream water head was carefully measured using precise point gauges, while the flow discharge was controlled and monitored using calibrated flow measurement devices. The discharge coefficient (C_d) was calculated for each experimental condition to quantify the hydraulic performance of the tested configurations. The collected dataset was then used for developing predictive data driven models. Several machine learning algorithms were employed, including Artificial Neural Networks (ANN), Extreme Gradient Boosting (XGBoost), Random Forest, and Support Vector Regression (SVR). The input parameters consisted of hydraulic and geometric variables such as upstream head and side wall inclination characteristics, while the output variable was the discharge coefficient. Model performance was evaluated using common statistical indicators including the coefficient of determination (R^2), root mean square error (RMSE), and mean absolute error (MAE). These indicators were used to assess the accuracy and reliability of each model and to determine the most suitable approach for predicting PKW discharge performance Results and Discussion The experimental results clearly demonstrate that the inclination and orientation of side walls significantly influence the hydraulic performance of Type A piano key weirs. Flow observations indicated that the side wall geometry directly affects the way water enters the inlet keys and how the flow is distributed along the crest. When the side walls were inclined against the flow direction, the incoming water was guided more effectively toward the inlet openings. This configuration improved the alignment of streamlines and reduced the formation of recirculation zones near the inlet edges. As a result, flow contraction and energy losses were reduced, leading to an increase in the discharge coefficient. In contrast, when the side walls were inclined with the flow direction, the inflow pattern tended to produce local separation zones near the entrance of the inlet keys. These separation regions reduced the effective flow area and caused additional energy dissipation. Consequently, the discharge coefficient obtained in these cases was generally lower than that of the opposite orientation. The influence of the inclination angle was also evident in the experimental data. Increasing the side wall inclination from 5° to 7.5° and 10° generally improved hydraulic performance, particularly when the inclination was directed against the flow. Among the tested configurations, the best hydraulic behavior was observed for trapezoidal models with side wall inclinations between 7.5° and 10° oriented against the flow direction. These configurations provided the most favorable flow guidance and minimized hydraulic disturbances near the inlet region. A comparison between the two tested geometries showed that trapezoidal PKWs consistently produced higher discharge coefficients than rectangular ones under similar hydraulic conditions. The trapezoidal configuration appears to facilitate smoother flow transitions and better distribution of water across the inlet keys, which enhances the overall discharge efficiency. In some cases, the improvement in discharge coefficient reached approximately 15% compared with the corresponding rectangular configurations. The data driven modeling results further confirmed the experimental findings. Among the applied machine learning techniques, Artificial Neural Networks (ANN) and Extreme Gradient Boosting (XGBoost) showed the best predictive capability. These models successfully captured the nonlinear relationships between geometric parameters and hydraulic performance. The predictive accuracy of these models exceeded 98%, while the associated prediction errors remained below 2%, indicating excellent agreement with the experimental measurements. The results highlight the effectiveness of combining experimental investigations with modern machine learning techniques to better understand and predict the hydraulic performance of complex spillway structures such as piano key weirs. Conclusions This study investigated the effects of side wall inclination and orientation on the hydraulic performance of Type A piano key weirs using laboratory experiments and data driven modeling. The results showed that inclining the side walls against the flow direction significantly improves flow alignment and reduces energy losses, resulting in higher discharge coefficients. Trapezoidal configurations demonstrated superior performance compared with rectangular geometries, with improvements reaching approximately 15%. Machine learning models, particularly ANN and XGBoost, provided highly accurate predictions of the discharge coefficient. The findings provide useful guidance for optimizing PKW design and demonstrate the value of integrating experimental data with advanced predictive modeling techniques. The study contributes a validated experimental dataset and robust machine learning formulations that can assist designers in optimizing PKW configurations for enhanced hydraulic efficiency and safer spillway design. سرریزهای کلیدپیانویی (PKW) به‌عنوان سازه‌هایی مؤثر برای افزایش ظرفیت تخلیه جریان بدون نیاز به افزایش ارتفاع تاج سد شناخته می‌شوند. بااین‌حال، تأثیر زاویه و جهت شیب دیواره‌های جانبی بر عملکرد هیدرولیکی آن‌ها کمتر مورد بررسی قرار گرفته است. در این پژوهش، عملکرد هیدرولیکی سرریزهای کلیدپیانویی نوع A با استفاده از آزمایش‌های فیزیکی و مدل‌سازی داده‌محور مورد بررسی قرار گرفت. اثر زاویه و جهت شیب دیواره‌های جانبی برای دو هندسه مستطیلی و ذوزنقه‌ای در یک فلوم آزمایشگاهی به طول ۱۵ متر و ارتفاع ۰٫۶ متر تحت شرایط جریان آزاد و زیربحرانی مطالعه شد. مدل‌ها با زوایای شیب ۵، ۷٫۵ و ۱۰ درجه در دو جهت موافق و مخالف جریان آزمایش شدند. ضریب تخلیه با استفاده از داده‌های دبی–اشل محاسبه و به کمک روش‌های رگرسیون چندمتغیره، شبکه عصبی مصنوعی (ANN)، جنگل تصادفی و XGBoost پیش‌بینی گردید. نتایج نشان داد شیب دیواره در خلاف جهت جریان با بهبود الگوی ورود جریان، کاهش جدایش و افت انرژی، موجب افزایش ضریب تخلیه می‌شود. مدل‌های ذوزنقه‌ای نسبت به مدل‌های مستطیلی عملکرد بهتری داشتند و افزایش ضریب تخلیه تا حدود ۱۵ درصد مشاهده شد. در میان مدل‌های داده‌محور، ANN و XGBoost بالاترین دقت پیش‌بینی (بیش از ۹۸ درصد) و کمترین خطا (کمتر از ۲ درصد) را نشان دادند.

https://iwrj.sku.ac.ir/article_116622_8c237a6bdbaae0881afb1c416e6f25b5.pdf