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Superficie óptima para zapatas rectangulares huecas o cimentacionescorridas cerradas: el área en contacto con el suelo está parcialmente comprimida
Optimal surface for hollow rectangular footings or closed stripfoundations: the contact area with the soil is partially compressed
DOI:
https://doi.org/10.15446/rbct.n60.128324Palabras clave:
superficie mínima, zapata rectangular hueca, cimentación corrida cerrada, distribución de la presión lineal del suelo, la superficie de contacto trabaja parcialmente a compresión (es)minimum surface, hollow rectangular footings, closed strip foundation, linear soil pressure distribution, contact surface works partially under compression (en)
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Este artículo muestra un modelo para determinar la superficie mínima de una zapata rectangular hueca o una cimentación corrida cerrada (el ancho y la posición donde la presión es cero, ya que los lados de la construcción están sujetos a las condiciones de la superestructura), asumiendo que el suelo es elástico, la distribución de presiones en el suelo es lineal y la superficie en contacto con el suelo trabaja parcialmente a compresión. La metodología se desarrolla mediante integración para determinar la carga axial “P”, los momentos “Mx” y “My” con respecto a los ejes X e Y. Se presentan varios estudios numéricos para determinar la superficie mínima de contacto con el suelo para zapatas rectangulares huecas o cimentaciones corridas cerradas bajo flexión biaxial y flexión uniaxial. Los principales hallazgos son: para la flexión biaxial, el área del nuevo modelo (la superficie trabaja parcialmente bajo compresión) presenta una reducción de hasta 98.49% con respecto al área del modelo actual (la superficie trabaja totalmente bajo compresión); para la flexión uniaxial, el área del nuevo modelo (la superficie trabaja parcialmente bajo compresión) presenta una reducción de hasta 96.13 % con respecto al área del modelo actual (la superficie trabaja totalmente bajo compresión). Por lo tanto, se recomienda el nuevo modelo, ya que será de gran utilidad para los especialistas en cimentaciones estructurales.
This work shows a model to estimate the minimum surface of a hollow rectangular footing or closed strip foundation (the width and the position where pressure is zero, since the sides of the construction are subject to the conditions of the superstructure), assuming that the soil is elastic, the distribution of pressures in the soil is linear and the surface in contact with the soil works partially in compression. The methodology is developed by integration to determine the axial load “P”, the moments “Mx” and “My” with respect to X and Y axes. Several numerical studies are presented to determine the minimum soil contact surface for hollow rectangular footings or closed strip foundations under biaxial bending and uniaxial bending. Main findings are: for biaxial bending, the area of the new model (the surface works partially under compression) shows a reduction up to 98.49 % with respect to the area of the current model (the surface works totally under compression); for uniaxial bending, the area of the new model (the surface works partially under compression) shows a reduction up to 96.13 % with respect to the area of the current model (the surface works totally under compression). Therefore, the new model is recommended as it will be of great help to structural foundation specialists.
Referencias
[1] Khazaie, J., and Amirshahkarami, S.A., Numerical analysis of interaction between earth and large foundations regarding size effect. Journal of Applied Sciences, 9(6), pp.1036-1045, 2009. DOI: https://doi.org/10.3923/jas.2009.1036.1045
[2] Jahanandish, M., Veiskarami M., and Ghahramani, Effect of Foundation Size and Roughness on the Bearing Capacity Factor, Nγ, by Stress Level-Based ZEL Method. Arabian Journal for Science and Engineering, 37(7), pp.1817-1831, 2012. DOI: https://doi.org/10.1007/s13369-012-0293-3
[3] Vyacheslavovich, G.A., and Adolfovich, B.L., Influence of the form and size of the isolated foundations on the stress-strain state of the soil base. Journal of Applied Engineering Science, 14(1), pp.28-35, 2016. DOI: https://doi.org/10.5937/jaes14-9136
[4] Filho, W.L., Carvalho, R.C.H., Christoforo, A.L., and Lahr, F.A.R., Dimensioning of isolated footing submitted to the under biaxial bending considering the low concrete consumption. International Journal of Materials Engineering, 7(1), pp.1-11, 2017.
[5] Luévanos-Rojas, A., Minimum cost design for rectangular isolated footings taking into account that the column is located in any part of the footing. Buildings, 13(9), pp.1-16, 2023. DOI: https://doi.org/10.3390/buildings13092269
[6] Luévanos-Rojas, A., Moreno-Landeros, V.M., Santiago-Hurtado, G., Olguin-Coca, F.J., López-León, L.D., and Diaz-Gurrola, E.R., Mathematical modeling for the optimal cost design of circular isolated footings with eccentric column. Mathematics, 12(5), pp.1-19, 2024. DOI: https://doi.org/10.3390/math12050733
[7] Luévanos-Rojas, A., Design of boundary combined footings of rectangular shape using a new model. DYNA, 81(188), pp.199-208, 2014. DOI: https://doi.org/10.15446/dyna.v81n188.41800
[8] Luévanos-Rojas, A., López-Chavarría, S., Medina-Elizondo, M., Sandoval-Rivas, R., and Farías-Montemayor, O.M., An analytical model for the design of corner combined footings. Revista ALCONPAT, 10(3), pp.317-335, 2020. DOI: https://doi.org/10.21041/ra.v10i3.432
[9] Luévanos-Rojas, A., Optimization for trapezoidal combined footings: Optimal design. Advances in Concrete Construction, 16(1), pp.21-34, 2023. DOI: https://doi.org/10.12989/acc.2023.16.1.021
[10] Luévanos-Rojas, A., Santiago-Hurtado, G., Moreno-Landeros, V.M., Olguin-Coca, F.J., López-León, L.D., and Diaz-Gurrola, E.R., Mathematical modeling of the optimal cost for the design of strap combined footings. Mathematics, 12(2), pp.1-20, 2024. DOI: https://doi.org/10.3390/math12020294
[11] Irles-Más, R., and Irles-Más, F., Alternativa analítica a la determinación de tensiones bajo zapatas rectangulares con flexión biaxial y despegue parcial. Informes de la Construcción, 44(419), pp.77-90, 1992. DOI: https://doi.org/10.3989/ic.1992.v44.i419.1338
[12] Algin, H.M., Stresses from linearly distributed pressures over rectangular areas. International Journal Numerical Analytical Methods in Geomechanics, 24 (8), pp.681-692, 2000. DOI: https://doi.org/10.1002/1096-9853(200007)24:8%3C681::AID-NAG89%3E3.0.CO;2-X
[13] Algin, H.M., Practical formula for dimensioning a rectangular footing, Engineering Structures, 29(6), pp.1128-1134, 2007. DOI: https://doi.org/10.1016/j.engstruct.2006.08.009
[14] Özmen, G., Determination of base stresses in rectangular footings under biaxial bending. Teknik dergi, [32] 22(110), pp.1519-1535, 2011. Available at: https://izlik.org/JA74GX74LY
[15] Girgin, K., Simplified formulations for the determination of rotational spring constants in rigid spread footings resting on tensionless soil. Journal of Civil Engineering and Management, 23(4), pp.464-474, 2017. DOI: https://doi.org/10.3846/13923730.2016.1210218
[16] Vela-Moreno, V.B., Luévanos-Rojas, A., López-Chavarría, S., Medina-Elizondo, M., Sandoval-Rivas, R., and Martínez-Aguilar, C., Optimal area for rectangular isolated footings considering that contact surface works partially to compression. Structural Engineering and Mechanics, 84(4), pp.561-573, 2022. DOI: https://doi.org/10.12989/sem.2022.84.4.561
[17] Moreno-Landeros, V.M., Luévanos-Rojas, A., Santiago-Hurtado, G., López-León, L.D., and Díaz-Gurrola, E.R., Optimal area for a rectangular isolated footing with an eccentric column and partial ground compression. Applied Sciences, 14(15), pp.1-16, 2024. DOI: https://doi.org/10.3390/app14156453
[18] Luévanos-Soto, I., Luévanos-Rojas, A., Moreno-Landeros, V.M., and Santiago-Hurtado, G., Minimum area for circular isolated footings with eccentric column taking into account that the surface in contact with the ground works partially in compression. Coupled Systems Mechanics, 13(3), pp. 201-217, 2024. DOI: https://doi.org/10.12989/csm.2024.13.3.201
[19] Luévanos-Rojas, A., Estrada-Mendoza, B.L., and Juárez-Ramirez, M., Comparative study for minimum areas in contact with the ground of rectangular and circular isolated footings working partially under compression. Boletín Ciencias de la Tierra, 55(1), pp.85-98, 2024. DOI: https://doi.org/10.15446/rbct.n55.111624
[20] Montes-Paramo, P., Luévanos-Rojas, A., López-Chavarría, S., Medina-Elizondo, M. and Sandoval-Rivas, R. Área óptima para zapatas combinadas rectangulares asumiendo que la superficie de contacto con el suelo trabaja parcialmente a compresión. Ingeniería, investigación y tecnología, 24(2), pp. 1-15, 2023. DOI: https://doi.org/10.22201/fi.25940732e.2023.24.2.012
[21] Luévanos-Soto, R.M., Luévanos-Rojas, A., and Luévanos-Soto, I., Minimum surface for trapezoidal combined footings: the soil contact area is partially compressed. International Journal of Innovative Computing, Information and Control, 22(3), pp.701-721, 2026. DOI: https://doi.org/10.24507/ijicic.22.03.701
[22] Luévanos-Rojas, A., Estrada-Mendoza, B.L., and Juárez-Ramírez, M., Optimal area for T-shaped combined footing assuming that the contact area with the soil works partially in compression. Boletín de Ciencias de la Tierra, 58(2), pp.51-71, 2025. DOI: https://doi.org/10.15446/rbct.n58.120221
[23] Luévanos-Rojas, A., Optimal surface for corner combined footings assuming that the ground contact area works partially in compression considering that the maximum pressure is located at the corner of the footing: Part 1. Advances in Concrete Construction, 19(6), pp.349-362, 2025 DOI: https://doi.org/10.12989/acc.2025.19.6.349
[24] Luévanos-Rojas, A., Optimal surface for corner combined footings assuming that the ground contact area works partially in compression considering that the maximum pressure is located at one end and on the outer and inner side of the footing: part 2. Advances in Concrete Construction, 19(6), pp.363-380, 2025. DOI: https://doi.org/10.12989/acc.2025.19.6.349
[25] Luévanos-Soto, I., Luévanos-Rojas, A., and Luévanos-Soto, R.M., Optimal surface in plan for strip footings assuming that the contact surface with soil works partially under compression. International Journal of Innovative Computing Information and Control, 21(4), pp.937-953, 2025. DOI: https://doi.org/10.24507/ijicic.21.04.937
[26] Sankaran, K.S., and Subrahmanyam, M.S., Analytical solution for annular ring-uniform loading contact pressure distribution to predict machine foundation response. Soils and Foundations, 13(3), pp.17-27, 1973. DOI: https://doi.org/10.3208/sandf1972.13.3_17
[27] Cicek, E., Guler, E., and Yetimoglu, T., Stress distribution below a continuous footing on geotextile-reinforced soil. International Journal of Geomechanics, 18(3), pp.149-157, 2014. DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0001095
[28] Imanzadeh, S., Denis, A., and Marache, A., Foundation and overall structure designs of continuous spread footings along with soil spatial variability and geological anomaly. Engineering Structures, 72(15), pp. 212-221, 2014. DOI: http://doi.org/10.1016/j.engstruct.2014.04.019
[29] Imanzadeh, S., Denis, A., and Marache, A., settlement uncertainty analysis for continuous spread footing on elastic soil. Geotechnical and Geological Engineering, 33, pp.105-122, 2015. DOI: https://doi.org/10.1007/s10706-014-9828-6
[30] Chakraborty, D., Bearing capacity of strip footings by incorporating a non-associated flow rule in lower bound limit analysis. International Journal of Geotechnical Engineering, 10(3), pp.311-315, 2016. DOI: https://doi.org/10.1080/19386362.2016.1142272
[31] Tang, C., and Phoon, K.K., Prediction of bearing capacity of ring foundation on dense sand with regard to stress level effect. International Journal of Geomechanics, ASCE, 18(11), art. 1312, 2018. DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0001312
[32] Galvis, F.A., and Smith-Pardo, J.P., Axial load biaxial moment interaction (PMM) diagrams for shallow foundations: design aids, experimental verification, and examples. Engineering Structures, 213, art. 110582, 2020. DOI: https://doi.org/10.1016/j.engstruct.2020.110582
[33] Chavda, J.T., and Dodagoudar, G.R., On vertical bearing capacity of ring footings: finite element analysis, observations and recommendations. International Journal of Geotechnical Engineering, 15(10), pp. 1207-1219, 2021. DOI: https://doi.org/10.1080/19386362.2019.1648737
[34] Kim, B.S., Kwon, O., Choi, Y.H., and Lee, J.K., Bearing capacity of annular foundations on rock mass with heterogeneous disturbance by finite element limit analysis. Buildings, 12(5), pp.1-11, 2022. DOI: https://doi.org/10.3390/buildings12050646
[35] Rathor, A.P.S., and Sharma, J.K., Engineering significance of annular raft foundations over solid raft foundations. International Journal for Research in Applied Science & Engineering Technology, 11(9), pp.930-934, 2023. DOI: https://doi.org/10.22214/ijraset.2023.55783
[36] Singh-Rathor, A.P., Sharma, J.K., and Madhira, M., an analytical study of annular raft on granular piles. Studia Geotechnica et Mechanica, 46(1), pp.21-44, 2024. DOI: https://doi.org/10.2478/sgem-2024-0002
[37] Chouhan, K., Lai, V.Q., Chavda, J.T., Yoonirundorn, K., and Keawsawasvong, S., Evaluation of bearing capacity of ring footing with varying base roughness using finite element limit analysis. Transportation Infrastructure Geotechnology, 11, pp.381-405, 2024. DOI: https://doi.org/10.1007/s40515-023-00286-2
[38] Díaz-Gurrola, E.R., Luévanos-Rojas, A., Montiel-Sánchez, G.J., and Martínez-Aguilar, C., Optimal surface in plan for hollow circular footings assuming that the contact surface with soil works partially under compression. International Journal of Innovative Computing, Information and Control, 21(2), pp.407-422, 2025. DOI: https://doi.org/10.24507/ijicic.21.02.407
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