Technical Papers
Jul 15, 2019

Simulation of Reinforced Concrete Member Response Using Lattice Model

Publication: Journal of Structural Engineering
Volume 145, Issue 9

Abstract

Lattice models are well suited for crack simulations; however, their use has been mostly limited to the fracture of plain concrete. In this study, a practical two-dimensional mesoscale lattice composed of overlapping elements was employed to simulate the monotonic response of reinforced concrete elements. The force-deformation response of each element is calibrated from direct tension tests. An explicit time integration technique with novel proportional-integral-derivative control is used to efficiently simulate the response under monotonic loading. Six different reinforced concrete member simulations were conducted to validate the proposed approach. It was found that the proposed approach was capable of reproducing the load-deformation characteristics of elements failing in shear or flexure with a reasonable accuracy. A deterministic sensitivity analysis was conducted to uncover the response parameters with the most influence on the response estimations. Concrete tensile strength and steel yield strength were found to be the most influential parameters affecting strength and energy absorption capacities. Interestingly, the variation in fracture energy and tensile-softening parameters appeared to exhibit insignificant differences for strength and energy absorption estimations in the reinforced concrete simulations.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

This research was supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under Grant No. 215 M870.

References

ACI (American Concrete Institute). 2011. Building code requirements for structural concrete and commentary. ACI 318. Farmington Hills, MI: ACI.
Acun, B. 2010. “Energy based seismic performance assessment of reinforced concrete columns.” Ph.D. thesis, Dept. of Civil Engineering, Middle East Technical Univ.
Acun, B., and H. Sucuoglu. 2010. “Performance of reinforced concrete columns designed for flexure under severe displacement cycles.” ACI Struct. J. 107 (3): 364–371. https://doi.org/10.14359/51663702.
Aldemir, A., B. Binici, and E. Canbay. 2017. “Cyclic testing of reinforced concrete double walls.” ACI Struct. J. 114 (2): 395–406. https://doi.org/10.14359/51689432.
Askari, E., F. Bobaru, R. B. Lehoucq, M. L. Parks, S. A. Silling, and O. Weckner. 2008. “Peridynamics for multiscale materials modeling.” J. Phys.: Conf. Ser. 125 (1): 012078. https://doi.org/10.1088/1742-6596/125/1/012078.
Aydin, B. B. 2017. “Overlapping lattice modeling for concrete fracture simulations using sequentially linear analysis.” Master’s thesis, Dept. of Civil Engineering, Middle East Technical Univ.
Aydin, B. B., K. Tuncay, and B. Binici. 2018. “Overlapping lattice modeling for concrete fracture simulations using sequentially linear analysis.” Struct. Concr. 19 (2): 568–581. https://doi.org/10.1002/suco.201600196.
Aziz, A. 2014. “Simulation of fracture of concrete using micropolar peridynamics.” Master’s thesis, Dept. of Civil Engineering, Univ. of New Mexico.
Baudet, V., M. Beuve, F. Jaillet, B. Shariat, and F. Zara. 2007. New mass-spring system integrating elasticity parameters in 2D. Lyon, France: Univ. of Lyon.
Bažant, Z. P., F. B. Lin, and H. Lippmann. 1993. “Fracture energy release and size effect in borehole breakout.” Int. J. Numer. Anal. Methods Geomech. 17 (1): 1–14. https://doi.org/10.1007/BF02486267.
Bažant, Z. P., and B. H. Oh. 1983. “Crack band theory for fracture of concrete.” Matér. Constr. 16 (3): 155–177. https://doi.org/10.1007/BF02486267.
Bažant, Z. P., M. R. Tabbara, M. T. Kazemi, and G. Pijaudier-Cabot. 1990. “Random particle model for fracture of aggregate or fiber composites.” J. Eng. Mech. 116 (8): 1686–1705. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:8(1686).
Bažant, Z. P., and Y. Xiang. 1997. “Size effect in compression fracture: Splitting crack band propagation.” J. Eng. Mech. 123 (2): 162–172. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:2(162).
Beale, P. D., and D. J. Srolovitz. 1988. “Elastic fracture in random materials.” Phys. Rev. B 37 (10): 5500–5507. https://doi.org/10.1103/PhysRevB.37.5500.
Belletti, B., M. Scolari, and F. Vecchio. 2017. “PARC_CL 2.0 crack model for NLFEA of reinforced concrete structures under cyclic loadings.” Comput. Struct. 191 (C): 165–179. https://doi.org/10.1016/j.compstruc.2017.06.008.
Binici, B. 2005. “An analytical model for stress-strain behavior of confined concrete.” Eng. Struct. 27 (7): 1040–1051. https://doi.org/10.1016/j.engstruct.2005.03.002.
Blacklock, J. R., and R. M. Richard. 1969. “Finite element analysis of inelastic structures.” AIAA J. 7 (3): 432–438. https://doi.org/10.2514/3.512510.2514/3.5125.
Bobaru, F., Y. D. Ha, and W. Hu. 2012. “Damage progression from impact in layered glass modeled with peridynamics.” Cent. Eur. J. Eng. 2 (4): 551–561. https://doi.org/10.2478/s13531-012-0020-6.
Caldarelli, G., C. Castellano, and A. Petri. 1999. “Criticality in models for fracture in disordered media.” Phys.: Stat. Mech. Appl. 270 (1): 15–20. https://doi.org/10.1016/S0378-4371(99)00145-4.
Carol, I., P. C. Prat, and C. M. López. 1997. “Normal/shear cracking model: Application to discrete crack analysis.” J. Eng. Mech. 123 (8): 765–773. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:8(765).
CEB-FIP. 1993. CEB-FIP model code 1990. Bull. d’Information No. 213/214. Lausanne, Switzerland: Comite Euro-International du Beton.
Chung, J., and J. M. Lee. 1994. “A new family of explicit time integration methods for linear and non-linear structural dynamics.” Int. J. Numer. Methods Eng. 37 (23): 3961–3976. https://doi.org/10.1002/nme.1620372303.
Clemen, R. T. 1996. Making hard decisions: An introduction to decision analysis. 2nd ed. Belmont, CA: Duxbury.
Cornelissen, H. A. W., D. A. Hordijk, and H. W. Reinhardt. 1986. “Experimental determination of crack softening characteristics of normal weight and lightweight concrete.” Heron 31 (2): 45–56.
Cusatis, G., Z. P. Bažant, and L. Cedolin. 2003. “Confinement-shear lattice model for concrete damage in tension and compression: I. Theory.” J. Eng. Mech. 129 (12): 1439–1448. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:12(1439).
Cusatis, G., Z. P. Bažant, and L. Cedolin. 2006. “Confinement-shear lattice CSL model for fracture propagation in concrete.” Comput. Methods Appl. Mech. Eng. 195 (52): 7154–7171. https://doi.org/10.1016/j.cma.2005.04.019.
Cusatis, G., A. Mencarelli, D. Pelessone, and J. Baylot. 2011a. “Lattice discrete particle model (LDPM) for failure behavior of concrete. II: Calibration and validation.” Cem. Concr. Compos. 33 (9): 891–905. https://doi.org/10.1016/j.cemconcomp.2011.02.010.
Cusatis, G., D. Pelessone, and A. Mencarelli. 2011b. “Lattice discrete particle model (LDPM) for failure behavior of concrete. I: Theory.” Cem. Concr. Compos. 33 (9): 881–890. https://doi.org/10.1016/j.cemconcomp.2011.02.011.
Donze, F., and S. A. Magnier. 1995. “Formulation of a 3-D numerical model of brittle behaviour.” Geophys. J. Int. 122 (3): 790–802. https://doi.org/10.1111/j.1365-246X.1995.tb06838.
Fascetti, A., L. Feo, N. Nisticò, and R. Penna. 2016. “Web-flange behavior of pultruded GFRP I-beams: A lattice model for the interpretation of experimental results.” Compos. Part B: Eng. 100 (Sep): 257–269. https://doi.org/10.1016/j.compositesb.2016.06.058.
Foster, S. J., and R. I. Gilbert. 1998. “Experimental studies on high-strength concrete deep beams.” ACI Struct. J. 95 (4): 382–390. https://doi.org/10.14359/554.
Ganzenmüller, G. C., S. Hiermaier, and M. May. 2015. “On the similarity of meshless discretizations of peridynamics and smooth-particle hydrodynamics.” Comput. Struct. 150 (Apr): 71–78. https://doi.org/10.1016/j.compstruc.2014.12.011.
Gerstle, W. 2015. Introduction to practical peridynamics. Hong Kong: World Scientific.
Gerstle, W., H. H. Geitanbaf, and A. Asadollahi. 2013. “Computational simulation of reinforced concrete using the micropolar state-based peridynamic hexagonal lattice model.” In Proc., 8th Int. Conf. on Fracture Mechanics of Concrete and Concrete Structures, 261–270. Toledo, Spain: IA-FRAMCOS.
Gerstle, W., and N. Sau. 2004. “Peridynamic modeling of concrete structures.” In Proc., 5th Int. Conf. on Fracture Mechanics of Concrete Structures, edited by L. Li, K. Willam, and S. Billington, 949–956. Vail, CO: IA-FRAMCOS.
Ghajari, M., L. Iannucci, and P. Curtis. 2014. “A peridynamic material model for the analysis of dynamic crack propagation in orthotropic media.” Comput. Methods Appl. Mech. Eng. 276 (Jul): 431–452. https://doi.org/10.1016/j.cma.2014.04.002.
Griffiths, D. V., and G. G. W. Mustoe. 2001. “Modelling of elastic continua using a grillage of structural elements based on discrete element concepts.” Int. J. Numer. Methods Eng. 50 (7): 1759–1775. https://doi.org/10.1002/nme.99.
Ha, Y. D., and F. Bobaru. 2010. “Studies of dynamic crack propagation and crack branching with peridynamics.” Int. J. Fract. 162 (1–2): 229–244. https://doi.org/10.1007/s10704-010-9442-4.
Ha, Y. D., and F. Bobaru. 2011. “Characteristics of dynamic brittle fracture captured with peridynamics.” Eng. Fract. Mech. 78 (6): 1156–1168. https://doi.org/10.1016/j.engfracmech.2010.11.020.
Hrennikoff, A. 1941. “Solution of problems of elasticity by the framework method.” J. Appl. Mech. Tech. Phys. 8 (4): 169–175.
Hu, W., Y. D. Ha, and F. Bobaru. 2012. “Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites.” Comput. Methods Appl. Mech. Eng. 217–220 (Apr): 247–261. https://doi.org/10.1016/j.cma.2012.01.016.
Jirásek, M., and Z. P. Bažant. 1995. “Particle model for quasibrittle fracture and application to sea ice.” J. Eng. Mech. 121 (9): 1016–1025. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:9(1016).
Karihaloo, B. L., P. F. Shao, and Q. Z. Xiao. 2003. “Lattice modelling of the failure of particle composites.” Eng. Fract. Mech. 70 (17): 2385–2406. https://doi.org/10.1016/S0013-7944(03)00004-3.
Kawai, T. 1978. “New discrete models and their application to seismic response analysis of structures.” Nucl. Eng. Des. 48 (1): 207–229. https://doi.org/10.1016/0029-5493(78)90217-0.
Kendall, K. 1978. “Complexities of compression failure.” Proc. R. Soc. London, A Math. Phys. Sci. 361 (1705): 245–263. https://doi.org/10.1098/rspa.1978.0101.
Kilic, B., A. Agwai, and E. Madenci. 2009. “Peridynamic theory for progressive damage prediction in center-cracked composite laminates.” Compos. Struct. 90 (2): 141–151. https://doi.org/10.1016/j.compstruct.2009.02.015.
Koutromanos, I., and P. B. Shing. 2012. “Cohesive crack model to simulate cyclic response of concrete and masonry structures.” ACI Struct. J. 109 (3): 349–358. https://doi.org/10.14359/51683748.
Kupfer, H., H. K. Hilsdorf, and H. Rusch. 1969. “Behavior of concrete under biaxial stresses.” ACI J. 66 (8): 656–666. https://doi.org/10.14359/7388.
Lai, X., B. Ren, H. Fan, S. Li, C. T. Wu, R. A. Regueiro, and L. Liu. 2015. “Peridynamics simulations of geomaterial fragmentation by impulse loads.” Int. J. Numer. Anal. Methods Geomech. 39 (12): 1304–1330. https://doi.org/10.1002/nag.2356.
Liang, Q. Q., Y. M. Xie, and G. P. Steven. 2000. “Topology optimization of strut-and-tie models in reinforced concrete structures using an evolutionary procedure.” ACI Struct. J. 97 (2): 322–330. https://doi.org/10.14359/863.
Lilliu, G., and J. G. M. van Mier. 2003. “3D lattice type fracture model for concrete.” Eng. Fract. Mech. 70 (7–8): 927–941. https://doi.org/10.1016/S0013-7944(02)00158-3.
Lim, J. C., and T. Ozbakkaloglu. 2014. “Lateral strain-to-axial strain relationship of confined concrete.” J. Struct. Eng. 141 (5): 04014141. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001094.
Littlewood, D. J. 2010. “Simulation of dynamic fracture using peridynamics, finite element modeling, and contact.” In Vol. 9 of Proc., ASME 2010 Int. Mechanical Engineering Congress and Exposition. New York: ASME.
Littlewood, D. J. 2011. “A nonlocal approach to modeling crack nucleation.” In Vol. 8 of Proc., ASME 2011 Int. Mechanical Engineering Congress and Exposition. New York: ASME.
Liu, J. X., S. C. Deng, J. Zhang, and N. G. Liang. 2007. “Lattice type of fracture model for concrete.” Theor. Appl. Fract. Mech. 48 (3): 269–284. https://doi.org/10.1016/j.tafmec.2007.08.008.
Lu, Y., and M. Panagiotou. 2014. “Three-dimensional cyclic beam-truss model for nonplanar reinforced concrete walls.” J. Struct. Eng. 140 (3): 04013071. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000852.
Lucy, L. B. 1977. “A numerical approach to the testing of the fission hypothesis.” Astron. J. 82 (12): 1013–1024. https://doi.org/10.1086/112164.
Mirmiran, A., and M. Shahawy. 1997. “Dilation characteristics of confined concrete.” Mech. Cohesive-Frictional Mater.: Int. J. Exp. Modell. Comput. Mater. Struct. 2 (3): 237–249. https://doi.org/10.1002/(SICI)1099-1484(199707)2:3%3C237::AID-CFM32%3E3.0.CO;2-2.
Mirza, S. A., and J. G. MacGregor. 1979. “Variability of mechanical properties of reinforcing bars.” J. Struct. Div. 105 (5): 921–937.
Mirza, S. A., J. G. MacGregor, and M. Hatzinikolas. 1979. “Statistical descriptions of strength of concrete.” J. Struct. Div. 105 (6): 1021–1037.
Moharrami, M., I. Koutromanos, M. Panagiotou, and S. C. Girgin. 2015. “Analysis of shear-dominated RC columns using the nonlinear truss analogy.” Earthquake Eng. Struct. Dyn. 44 (5): 677–694. https://doi.org/10.1002/eqe.2480.
Monette, L., and M. P. Anderson. 1994. “Elastic and fracture properties of the two-dimensional triangular and square lattices.” Modell. Simul. Mater. Sci. Eng. 2 (1): 53–66. https://doi.org/10.1088/0965-0393/2/1/004.
Nagai, K., D. Hayashi, and L. Eddy. 2014. “Numerical simulation of failure of anchorage with shifted mechanical anchorage bars by 3D discrete model.” Adv. Struct. Eng. 17 (6): 861–869. https://doi.org/10.1260/1369-4332.17.6.861.
Nayfeh, A. H., and M. S. Hefzy. 1978. “Continuum modeling of three-dimensional truss-like space structures.” AIAA J. 16 (8): 779–787. https://doi.org/10.2514/3.7581.
Ngo, D., and A. C. Scordelis. 1967. “Finite element analysis of reinforced concrete beams.” J. Proc. 64 (3): 152–163. https://doi.org/10.14359/7551.
Nikravesh, S., and W. Gerstle. 2018. “Improved state-based peridynamic lattice model including elasticity, plasticity and damage.” CMES-Comput. Model. Eng. Sci. 116 (3): 323–347. https://doi.org/10.31614/cmes.2018.04099.
Ostoja-Starzewski, M., P. Y. Sheng, and K. Alzebdeh. 1996. “Spring network models in elasticity and fracture of composites and polycrystals.” Comput. Mater. Sci. 7 (1–2): 82–93. https://doi.org/10.1016/S0927-0256(96)00064-X.
Oterkus, E., E. Madenci, O. Weckner, S. Silling, P. Bogert, and A. Tessler. 2012. “Combined finite element and peridynamic analyses for predicting failure in a stiffened composite curved panel with a central slot.” Compos. Struct. 94 (3): 839–850. https://doi.org/10.1016/j.compstruct.2011.07.019.
Ozcebe, G., and M. Saatcioglu. 1987. “Confinement of concrete columns for seismic loading.” ACI Struct. J. 84 (4): 308–315. https://doi.org/10.14359/1660.
Parisi, A., and G. Caldarelli. 2000. “Self-affine properties of fractures in brittle materials.” Phys. A: Stat. Mech. Appl. 280 (1): 161–165. https://doi.org/10.1016/S0378-4371(99)00633-0.
Rahman, A. S. M. 2012. “Lattice-based peridynamic modeling of linear elastic solids.” Master’s thesis, Dept. of Civil Engineering, Univ. of New Mexico.
Rashid, Y. R. 1968. “Analysis of prestressed concrete pressure vessels.” Nucl. Eng. Des. 7 (4): 334–344. https://doi.org/10.1016/0029-5493(68)90066-6.
Rots, J. G. 1988. “Computational modeling of concrete fracture.” Ph.D. thesis, Civil Engineering and Geosciences, Delft Univ. of Technology.
Rots, J. G. 2001. “Sequentially linear continuum model for concrete fracture.” In Fracture mechanics of concrete structures, edited by R. de Borst, J. Mazars, G. Pijaudier-Cabot, and J. van Mier, 831–839. Lisse, Netherlands: A.A. Balkema.
Rots, J. G., B. Belletti, and S. Invernizzi. 2008. “Robust modeling of RC structures with an ‘event-by-event’ strategy.” Eng. Fract. Mech. 75 (3–4): 590–614. https://doi.org/10.1016/j.engfracmech.2007.03.027.
Rots, J. G., S. Invernizzi, and B. Belletti. 2006. “Saw-tooth softening/stiffening—A stable computational procedure for RC structures.” Comput. Concr. 3 (4): 213–233. https://doi.org/10.12989/cac.2006.3.4.213.
Schlaich, J., K. Schäfer, and M. Jennewein. 1987. “Toward a consistent design of structural concrete.” PCI J. 32 (3): 74–150. https://doi.org/10.15554/pcij.05011987.74.150.
Schlangen, E., and J. G. M. van Mier. 1992. “Experimental and numerical analysis of micromechanisms of fracture of cement-based composites.” Cem. Concr. Compos. 14 (2): 105–118. https://doi.org/10.1016/0958-9465(92)90004-F.
Scott, R. M., J. B. Mander, and J. M. Bracci. 2012. “Compatibility strut-and-tie modeling. I: Formulation.” ACI Struct. J. 109 (5): 635. https://doi.org/10.14359/51684041.
Seleson, P., and M. L. Parks. 2011. “On the role of the influence function in the peridynamic theory.” Int. J. Multiscale Comput. Eng. 9 (6): 689–706. https://doi.org/10.1615/IntJMultCompEng.2011002527.
Silling, S. A. 2000. “Reformulation of elasticity theory for discontinuities and long-range forces.” J. Mech. Phys. Solids 48 (1): 175–209. https://doi.org/10.1016/S0022-5096(99)00029-0.
Silling, S. A., and E. Askari. 2005. “A meshfree method based on the peridynamic model of solid mechanics.” Comput. Struct. 83 (17–18): 1526–1535. https://doi.org/10.1016/j.compstruc.2004.11.026.
Silling, S. A., M. Epton, O. Weckner, J. Xu, and E. Askari. 2007. “Peridynamic states and constitutive modeling.” J. Elast. 88 (2): 151–184. https://doi.org/10.1007/s10659-007-9125-1.
Silling, S. A., O. Weckner, E. Askari, and F. Bobaru. 2010. “Crack nucleation in a peridynamic solid.” Int. J. Fract. 162 (1–2): 219–227. https://doi.org/10.1007/s10704-010-9447-z.
Slobbe, A. T., M. A. N. Hendriks, and J. G. Rots. 2014. “Smoothing the propagation of smeared cracks.” Eng. Fract. Mech. 132 (Dec): 147–168. https://doi.org/10.1016/j.engfracmech.2014.10.020.
Sun, S., and V. Sundararaghavan. 2014. “A peridynamic implementation of crystal plasticity.” Int. J. Solids Struct. 51 (19–20): 3350–3360. https://doi.org/10.1016/j.ijsolstr.2014.05.027.
Thomsen, J. H., and J. W. Wallace. 1995. Displacement based design of reinforced concrete structural walls: An experimental investigation of walls with rectangular and T-shaped cross-sections. Potsdam, NY: Clarkson Univ.
Thomsen, J. H., and J. W. Wallace. 2004. “Displacement-based design of slender reinforced concrete structural walls—Experimental verification.” J. Struct. Eng. 130 (4): 618–630. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:4(618).
TSE (Turkish Standards Institute). 2000. Requirements for design and construction of reinforced concrete structures. Ankara: TSE.
Tupek, M. R., J. J. Rimoli, and R. Radovitzky. 2013. “An approach for incorporating classical continuum damage models in state-based peridynamics.” Comput. Methods Appl. Mech. Eng. 263 (Aug): 20–26. https://doi.org/10.1016/j.cma.2013.04.012.
Vecchio, F. J., and M. P. Collins. 1986. “The modified compression-field theory for reinforced concrete elements subjected to shear.” ACI J. Proc. 83 (2): 219–231. https://doi.org/10.14359/10416.
Walraven, J. C. 1978. The influence of depth on the shear strength of lightweight concrete beams without shear reinforcement. Delft, Netherlnads: Delft Univ.
Yip, M., J. Mohle, and J. E. Bolander. 2005. “Automated modeling of three-dimensional structural components using irregular lattices.” Comput.-Aided Civ. Infrastruct. Eng. 20 (6): 393–407. https://doi.org/10.1111/j.1467-8667.2005.00407.x.
Ziegler, J. G., and N. B. Nichols. 1942. “Optimum settings for automatic controllers.” Trans. ASME 64 (11): 759–768.
Zubelewicz, A., and Z. P. Bažant. 1987. “Interface element modeling of fracture in aggregate composites.” J. Eng. Mech. 113 (11): 1619–1630. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:11(1619).

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 145Issue 9September 2019

History

Received: Apr 7, 2018
Accepted: Feb 3, 2019
Published online: Jul 15, 2019
Published in print: Sep 1, 2019
Discussion open until: Dec 15, 2019

Permissions

Request permissions for this article.

Authors

Affiliations

Beyazit B. Aydin [email protected]
Ph.D. Student, Dept. of Civil Engineering, Middle East Technical Univ., Ankara K2-105, Turkey. Email: [email protected]
Kagan Tuncay [email protected]
Professor, Dept. of Civil Engineering, Middle East Technical Univ., Ankara K2-304, Turkey. Email: [email protected]
Baris Binici [email protected]
Professor, Dept. of Civil Engineering, Middle East Technical Univ., Ankara K2-308, Turkey (corresponding author). Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share