DIAGNOSTICS OF THE SEISMIC STATE OF BRIDGES, WHERE PILE FOUNDATIONS ARE LOCATED IN PAIRS

ABSTRACT

In this study, nonlinear static lateral force analyses are conducted to bridges with different extent of scouring of group pile foundations using properly assigned plastic hinges properties. Capacity spectrum method is used then to assess the seismic capacity for bridges with and without scouring. After the analysis for several commonly used bridges with different degree of scouring, this study find that when scouring depth is deep enough, the plastic hinges will formed at the top of the piles instead of at the bottom of the columns as we expected in the design. Since the total base shear and ductility for bridges with scoured foundations are much smaller than that of the bridges without scouring, so the seismic capacity of bridges with scoured group pile foundations are becomes lower and lower as the depth of scouring are getting deeper and deeper.

АННОТАЦИЯ

В этом исследовании нелинейный статический анализ поперечных сил проводится для мостов с различной степенью размыва групповых свайных фундаментов с использованием надлежащим образом заданных свойств пластиковых шарниров. Затем для оценки сейсмостойкости мостов с размывом и без него используется метод спектра мощности. После анализа нескольких часто используемых мостов с различной степенью очистки в этом исследовании было обнаружено, что при достаточной глубине очистки пластиковые петли будут формироваться в верхней части свай, а не в нижней части колонн, как мы ожидали при проектировании. Поскольку общий сдвиг основания и пластичность для мостов с промытыми фундаментами намного меньше, чем у мостов без промывки, сейсмостойкость мостов с промытыми групповыми свайными фундаментами становится все ниже и ниже по мере того, как глубина промывки становится все глубже и глубже.

Keywords: seismic capacity evaluation, bridges, scoured pile foundations, plastic hinges.

Ключевые слова: оценка сейсмостойкости, мосты, забивные свайные фундаменты, пластиковые шарниры.

Introduction

Foundation scoured bridges may be unsafe under the attack of flood because of local souring will add to the depth of scouring dramatically. On the other hand, these bridges may also be unsafe under the attack of strong grounding motions because of premature failures of scoured foundation like piles.

In this paper, seismic capacity evaluation of bridges with scoured group pile foundations will be examined to prove that premature failures of scoured piles will be harmful to its seismic capacity, especially when depth of scour becomes deep enough [1, p. 2].

The modified capacity spectrum method which cooperating the nonlinear static lateral force analysis will be used to assess the seismic capacity of the bridges both with and without scouring. In this analysis, the key points to reliable results is the suitable assignment of hinges properties where nonlinear deformation are supposed to happen. In the following sections, hinges properties assignments will be carefully studied followed by the description of the modified capacity spectrum method in the next section. Some commonly used bridges with different degree of scouring will be illustrated to highlight the fact that when scouring becoming deeper and deeper, the seismic capacity of the bridge will be lower and lower [2, p. 3].

Modified capacity spectrum method

Capacity spectrum method is now becoming a popular method to carry out seismic capacity evaluation of bridges in recent years. This method consists of several st andard steps as will be briefly reviewed in the following.

Capacity Curve of the Bridges lateral force in certain distribution is applied to the bridge gradually to trace the static nonlinear response of the bridges studied. Capacity curve of the bridge represents the relation of lateral displacement of the top of the bridge with the total base shear forces applied. Since plastic hinges are assigned in proper locations prior to the analysis, so the curve traces the whole response of the bridge beyond yielding of the bridges [3, p. 3].

Figure 1. Capacity curve and capacity spectrum

Figure 1 shows the typical capacity curve obtained. As you can see, the response is linear in the beginning, and becomes nonlinear as deformation increases. Several computer programs like ETABS or SAP 2000 pose the function to carry out so called push-over analysis.

Capacity Spectrum of the bridge capacity spectrum of the bridge is transformed from capacity curve via following relations:

in which, V_i and ∆_{top, i} are the vertical and horizontal coordinates of capacity curve for performance point i, W is the total dead weight of the bridge,α₁ is the effective modal mass ratio of the first mode, PF₁ is the participating factor of the first mode, ϕ_{1, top} is the first mode shape at the top. S_ai and S_di are acceleration and displacement spectral values for performance point i as you can see on the left side of Figure 1.

Equivalent period and damping ratio for certain performance point referred to Figure 2, equivalent period T_i and damping ratio β_pi for performance point i can be determined by the following relations: 

Figure 2. Equivalent period and damping ratio for certain performance point

Corresponding ground acceleration for certain performance point for certain performance point, the ground acceleration Z(g) to which this performance point will be reached can be calculated as following:

Here, S_a(T_i) is the normalized acceleration response spectrum with 5% dampin g ratio, CD is a coefficient for damping ratio correction as you can find its value from seismic design code. In this case, inherent damping ratio 5% is added [4, p. 4].

Assignment of plastic hinge properties

Assignment of plastic hinge properties for flexural M3 plastic hinges The assignment of flexural M3 plastic hinges includes yielding moment and ultimate plastic hinge rotation. For bridge column and pile sections, because of the existence of axial forces, so the yielding moment are determined according to Figure 3, in which P-M curve of the section considered are constructed first. Axial force and moment due to dead load are filled into the diagram as shown and axial force and moment due to 0.1g ground motion are added to as shown also. Extend the second line until it intersects the P-M curve, then both yielding moment and axial force are determined [5, p. 32].

For M3 plastic hinges in this study, the ultimate plastic hinge rotation of columns and piles are assigned to be 0.015rad if transverse reinforcement are provided as required by the code. For existing bridges, confinement reinforcement are usual less than code required. In this case, ultimate plastic hinge rotation should be reduced by a factor r which is related to aratioαequaltotheratioof volumetric ratio of transverse reinforcement provided to the value according to the code as follows: 

The relation between moment and plastic hinge rotation is shown as in Fig. 4 where strain hardening and decrement of moment with plastic hinge rotation after maximum moment i s also considered [6, p. 54].

Reduction of shear strength of concrete with plastic hinge rotation at plastic hinge to reverse deformation into plastic range in plastic hinge location, the shear strength of concrete is decreasing dramatically as shown in Figure 5. In this figure, shear strength before yielding and at the last stage where ultimate plastic hinge rotation is developed are equal to the following , respectively:

in which VS represents the shear strength of shear reinforcement, Ae is the effective area of concrete to resist shear and is equal to 0.8 times the gross area of the section. F accounts for the effect of axial force to the shear strength of concrete.γin Figure 6 is a factor transforming shear forces into moments for sections considered [7, p. 2].

Because of the shear strength at plastic hinge regions are decreasing as plastic hinges rotation are getting larger, so the failure mode of a plastic hinge consists of three different kinds of behavior as depicted in Figure 6. The first kind is the best one, where the shear strength demand at ultimate plastic hingerotationθu is smaller than the shear strength at that time (see Fig.4). The second kind indicates that plastic hinge is developed only by a fraction where shear failure dominate the rest portion due to decreasing shear strength. In this case, the assignment of plastic hinge properties shall follow the route from A, B, C to D and E instead. The third kind is the worst case where plastic hinge has no chance to occur because of shear strength is lower than the shear force induced when yielding moment is happened at the section like bottom of the column or top of the pile. In this case, the assignment of plastic hinge properties shall follow the path from A, B, C to D as you can see in the figure [8, p. 1].

Illustrative examples

Design of bridges without scouring for illustration Simply supported bridges with group pile foundations as shown in Figure 7 without scouring is designed for illustrative purpose according to bridge design code. The span of the bridges is 30m and is assumed to be located in Taipei area [9, p. 2]. In Figure 9, you can see the height of single round RC column is 10 m, the diameter of the column is 2.2m. Longitudinal reinforcement of the column consists of 53 bars of #11 throughout the whole length. When it comes to shear and confinement reinforcement, double hoop steels of #5 with spa cing 10 cm was provided at the bottom of the column whereas along the rest part of the column, single hoop steels of #5 with spacing 25cm was provided as shown in Figure 8. As for the design of group piles, depicted in Figure 9, one find that we have totally nine round RC piles with diameter 70cm with total length equal to 30m. Main reinforcing bars consists of 14 #6 bars, in the range of top 6m, and reduced to 7 #6 bars along the rest part of the piles. Shear and confined reinforcement at the upper 1.2m were provided with #4 bars with 10cm in spacing, and were equal to #4 bars with 30 cm in spacing, for the rest part [10, p. 3].

Figure 7. Simply supported bridges with group pile foundations

Seismic capacity evaluation of bridges with different extent of scouring Structural models used to access seismic capacity of the bridges are shown in Figure 10. Soil springs are provided at the lateral direction of the piles with another vertical spring at the bottom. When bridges are scoured to certain depth, lateral soil springs above the riverbed will be removed then [11, p. 5].

Seismic capacity evaluation for bridges without scouring Seismic capacity evaluation for bridges without scouring was analyzed first as a benchmark to assess the effect of scouring to seismic capacity. Hinge properties used at the bottom of the columns are determined as depicted in Fig.11, and the capacity spectrum curve is shown in Figure 12. Further calculation reveals that the equivalent period at yield is equal to T y=0.836 sec, and the corresponding peak ground acceleration is equal to 0.148g. For ultimate performance point where Sa is maximum, the equivalent period is equal to T_c=1.425 sec, and the effective damping ratio and peak ground acceleration are equal to 0.338 and 0.332 g, respectively. One thing worthy to mention is that the shear force of the column is equal to 250.28 T_f when plastic hinge is fully developed at the bottom of the column [12, p. 2].

Figure 8. Dimensions and reinforcements of columns

Figure 9. Dimensions and reinforcements of piles

Figure 10. Structural model of scoured bridges

Figure 13. The capacity curve of bridges with 3m of scouring depth

Seismic capacity evaluation for bridges with scouring depth equal to 3m In this case, in addition to plastic hinge at the bottom of column are assigned, plastic hinges at the top of piles , 1.2 m below the top as well as 3m below the top of the piles are also assigned. For plastic hinges below 3m below the top, shear failure will happen, whereas for other three kinds of plastic hinges full plastic rotation are preserved. Capacity curve is shown in Figure13 where you can find plastic hinges at the top of piles occurs first, followed with the reach of ultimate plastic hinge rotation of those hinges [13, p. 4]. The equivalent period at yield is equal to T_y=1.049 sec and the corresponding peak ground acceleration is equal to 0.097 g. At ultimate performance point, the equivalent period is equal to T_c=1.361 sec and the peak ground acceleration is equal to 0.205g, which is much lower than the case without scouring. The shear force is equal to 164.59 T_f when plastic hinges are fully developed at the top of the piles. We want to mention here that yielding are shifted from column end to pile top and at ultimate point the lateral force resistance and ductility developed are both less than cases without scouring [14, p. 4].

Seismic capacity evaluation for bridges with scouring depth equal to 6 m and 9 m. For bridges with scouring depth equal to 6 m and 9 m, results of analysis reveals the same situation as for scouring depth equal to 3 m. Plastic hinges always formed first at the top of piles and ended up with the exhaustion of its ductility. At the ultimate point, lateral force resisted by the bridges is getting smaller and smaller as scouring depth is becoming deeper and deeper. The capacity spectrum curves and peak ground acceleration for these cases can be found in Figure 14 and 16where we put four different scouring cases together.

Conclusion

From this study some important conclusions can be drawn as follows:

1. Scouring of group pile foundations will indeed lower the seismic capacity of bridges. The severe the scouring occurs, the less the seismic capacity will result.

2. As a result of shift of plastic hinges from the end of columns to top of piles, the lateral force resistance and ductility developed are both less than cases without scouring. That is the reason why scoured bridges posses lower seismic capacity.

3. When design a bridge in a river with high potential of scouring in the future, put good confinement steel at the top of piles will have some benefits to enhance its seismic capacity after scouring.

4. For continuous bridges with different depth of scouring, owing to different stiffness for different scouring depth, the sequence of the formation of plastic hinges are more complicated than cases presented in this paper.

References:

1. K Muhammadjonov, A Muhammadjonov, A Xurramov. Digitalization of Higher Education: Trends and Their Influence on the Institute of Higher Education. International Journal of Engineering and Information Systems, volume 5, issue 2, p. 123 – 124. Posted: 2021.
2. Mars Berdibaev, Batir Mardonov and Asror Khurramov. Vibrations of a Girder on Rigid Supports of Finite Mass Interacting With Soil under Seismic Loads. E3S Web of Conferences 264, 02038 (2021). CONMECHYDRO – 2021. https://doi.org/10.1051/e3sconf/202126402038.
3. Nematilla Nishonov, Diyorbek Bekmirzaev, Akbar Ergashov, Ziyoviddin Rakhimjonov and Asror Khurramov. Underground polymeric l-shaped pipeline vibrations under seismic effect. E3S Web of Conferences 264, 02037 (2021). CONMECHYDRO – 2021. https://doi.org/10.1051/e3sconf/202126402037.
4. Rayimov, F., & Khurramov, A. (2021). Landscaping of roads in mountainous areas. Science and Education, 2(6), 247–251. Retrieved from https://openscience.uz/index.php/sciedu/article/view/1554.
5. Tsai, I-Chau. “Seismic Capacity and Performance Evaluation of Bridges”, Research Report of Taiwan Area National Freeway Bureau, Ministry of Transportation and Communications ,2004.
6. Yenhao Chen. “Seismic Capacity Assessment of Foundation Scoured Bridges ”, Master Thesis, Advised by Professor I-Chau Tsai, Department of Civil Engineering, National Taiwan University, June, 2006.
7. Абдурашидович, Т. Т. ., Чориевич, Х. А. ., & Урозбоева, М. Т. . (2023). ПОВЫШЕНИЕ ЭФФЕКТИВНОСТИ ОБУЧЕНИЯ МАТЕМАТИКЕ БАКАЛАВРОВ ТЕХНОЛОГИЧЕСКИХ НАПРАВЛЕНИЙ ПОСРЕДСТВОМ РЕШЕНИЯ ПРИКЛАДНЫХ ЗАДАЧ МЕТОДАМИ МАТЕМАТИЧЕСКОГО МОДЕЛИРОВАНИЯ. Новости образования: исследование в XXI веке, 1(7), 154–158. извлечено от https://nauchniyimpuls.ru/index.php/noiv/article/view/5159.
8. Асрор Чориевич Хуррамов, Илхомжон Юсуфжонович Мирзаолимов, Шахзод Шухратович Сафаров. Способы защиты мостовых конструкций от внешних воздействий и их сравнительный анализ. ACADEMIC RESEARCH IN EDUCATIONAL SCIENCES  VOLUME 2 | ISSUE 8 | 2021. ISSN: 2181-1385. Scientific Journal Impact Factor (SJIF) 2021: 5.723. Directory Indexing of International Research Journals-CiteFactor 2020-21: 0.89. https://doi.org/10.24412/2181-1385-2021-8-204-212.
9. Бердибаев М. Ж., Намозов Ш. З., Хуррамов А. Ч., Эгамбердиев И. Б. Причины возникновения солевой коррозии железобетонных элементов конструкции. Текст: непосредственный // Молодой ученый. 2020. № 42 (332). С.: 23–25. URL: https://moluch.ru/archive/332/74187/ (дата обращения: 25.08.2021).
10. Н.А. Нишонов, Ш.З. Намозов, А.Ч. Хуррамов. Автомобиль йўлларидаги кўприкларнингмустаҳкамлигини ошириш ва узоқ муддат хизмат қилишини таъминлаш чора-тадбирларини ишлаб чиқиш. ACADEMIC RESEARCH IN EDUCATIONAL SCIENCES VOLUME 2 | ISSUE 6 | 2021. ISSN: 2181-1385, Scientific Journal Impact Factor (SJIF) 2021: 5.723. https://doi.org/10.24412/2181-1385-2021-6-162-169.
11. Нишонов, Н. А., Хуррамов, А. Ч., & Рахматов, Ш. Н. (2022). НАПРЯЖЕННО-ДЕФОРМИРУЕМОЕ СОСТОЯНИЕ ПОДЗЕМНЫХ ПОЛИМЕРНЫХ ТРУБОПРОВОДОВ ПРИ СЕЙСМИЧЕСКОМ ВОЗДЕЙСТВИИ В ВИДЕ РЕАЛЬНЫХ ЗАПИСЕЙ ЗЕМЛЕТРЯСЕНИЙ. Central Asian Research Journal For Interdisciplinary Studies, 2(4), 450-459. https://doi.org/10.24412/2181-2454-2022-4-450-459
12. Х Алменов, АЧ Хуррамов, ШШ Сафаров, ИЮ Мирзаолимов. Сравнительный анализ методики расчета на раскрытие трещин в железобетонных элементах со традиционным армированием и армированием фиброй. Central Asian Research Journal For Interdisciplinary Studie, Vol 2 Issue 3 2022, 449-456. https://doi.org/10.24412/2181-2454-2022-3-449-456.
13. Хуррамов А. Ч. и др. УСИЛЕНИЕ ЖЕЛЕЗОБЕТОННЫХ ПРОЛЕТНЫХ СТРОЕНИЙ ДОПОЛНИТЕЛЬНОЙ АРМАТУРОЙ //Интернаука. – 2021. – Т. 20. – №. 196 часть 1. – С. 13.
14. Чориевич, Х. А., Урозбоева, . М. Т., Мухаммади углы , Ж. З. ., & Сайдуллаевич, Н. Х. (2023). ПРИМЕНЕНИЕ ОПТИМАЛЬНЫХ МЕТОДОВ ПОВЫШЕНИЯ СЕЙСМОСТОЙКОСТИ МОСТОВЫХ КОНСТРУКЦИЙ. Scientific Impulse, 1(6), 1055–1062. Retrieved from https://nauchniyimpuls.ru/index.php/ni/article/view/4654.