Journal of Theoretical
and Applied Mechanics

56, 4, pp. 927-938, Warsaw 2018
DOI: 10.15632/jtam-pl.56.4.927

XFEM simulation of the influence of cracking introduced by pre-loading on the strengthening of a cement treated mixture

Karol Brzeziński
The paper attempts to explain the phenomenon of a static strength increase due to the
previous cyclic loading. Finite Element Method simulation of the potential strengthening
mechanism is presented. The crack growth is controlled by the energy criterion used in the
linear fracture theory. A wedge splitting test has been performed in order to determine the
critical energy release rate of the tested mixture GIC. It was observed that the appearance
of additional cracks in the material may lead to an increase of its strength. Analysis of the
tensile stress distribution allows for a qualitative explanation of the observed phenomenon.
Keywords: fatigue life, cement-treated base layers, strengthening effect, load history, XFEM


ABAQUS Theory Manual, Ver. 6.13, 2013

Belytschko T., Black T., 1999, Elastic crack growth in finite elements with minimal remeshing,

International Journal for Numerical Methods in Engineering, 45, 601-620

Bijak-Żochowski M., Jaworski A., Zagrajek T., 1999, Basics of Solid Mechanics (in Polish),

Warsaw, Oficyna Wydawnicza Politechniki Warszawskiej

Brühwiler E., Wittmann F.H., 1990, The wedge splitting test, a new method of performing

stable fracture mechanics tests, Engineering Fracture Mechanics, 35, 1, 117-125

Brzeziński K., Adamczewski G., Tutka P., 2017, The influence of cyclic loading on the static

strength of cement-bound sand – qualitative analysis, Roads and Bridges – Drogi i Mosty, 16, 1, 37-46, DOI:

Brzeziński K., Zbiciak A., 2014, Influence of load history on fatigue life of cement treated soil

(in Polish), Drogownictwo, LXIX, 9, 288-293

Dolbow J.O.H.N., Belytschko T., 1999, A finite element method for crack growth without

remeshing, International Journal for Numerical Methods in Engineering, 46, 1, 131-150

Elfgren L., Shah S.P. (edit.), 1991, Analysis of Concrete Structure by Fracture Mechanics,

London, Chapman and Hall

Fatemi A., Yang L., 1998, Cumulative fatigue damage and life prediction theories: a survey of

the state of the art for homogeneous materials, International Journal of Fatigue, 20, 1, 9-34, ISSN 0142-1123,

Griffith A.A., 1920, The phenomena of rupture and flow in solids, Philosophical Transactions,

Royal Society of London, Series A, 221, 163-198

Hillerborg A., 1989, Stability problems in fracture mechanics testing. Fracture of concrete and

rock, [In:] Recent Developments, S.P. Shah, S.E. Swartz, B. Barr (edit), Amsterdam, Elsevier, 369-378

Koba H., 2000, Durability of Road Pavements with Cement-Bound Sub-Base (in Polish), Wrocław,

Oficyna Wydawnicza Politechniki Wrocławskiej

Kyriazopoulos A., Anastasiadis C., Triantis D., Brown C.J., 2011, Nondestructive

evaluation of cement-based materials from pressure-stimulated electrical emission

– preliminary results, Construction and Building Materials, 25, 4, 1980-1990, DOI:


Landis E.N., Shah S.P., 1995, Experimental measurements of microfracture in cement-based

materials, Fracture Mechanics of Concrete Structures, 315-328

L¨ofgren I., Stang H., Olesen J., Forbes O., 2004, Wedge splitting test-A test to determine

fracture properties of FRC, [In:] 6th International RILEM Symposium on Fibre Reinforced

Concretes, M. Di Prisco, R. Felicetti, G.A. Plizzari (edit.), RILEM Publications SARL, 1, 379-388

Marco S.M., Starkey W.L., 1954, A concept of fatigue damage, Transactions of ASME, 76, 627-632

Miner M.A., 1945, Cumulative damage in fatigue, Journal of Applied Mechanics, 67A, 159-164

Moćko W., Kowalewski Z.L., 2014, Evolution of tensile properties of the TIAL6V4 alloy due

to the prior cyclic loading history, Journal of Theoretical and Applied Mechanics, 52, 847-851

Moczko A., 1996, Acoustic emission in concrete tests (in Polish), Inżynieria i Budownictwo, 1, 42-46

Ohtsu M., 1996, The history and development of acoustic emission in concrete engineering, Magazine

of Concrete Research, 48, 321-330

PN-EN 196-1:2006 – Methods Of Testing Cement – Part 1: Determination Of Strength

Prokopski G., 2008, Mechanics of Cement Concretes Cracking (in Polish), Oficyna Rzeszów,

Wydawnicza Politechniki Rzeszowskiej

Rafalski L., 2007, Road Subbases (in Polish), Warszawa, Instytut Badawczy Dróg i Mostów

Remmers J.J.C., de Borst R., Needleman A., 2008, The simulation of dynamic crack propagation

using the cohesive segments method, Journal of the Mechanics and Physics of Solids, 56, 70-92

Ritchie R. O., 1999, Mechanisms of fatigue-crack propagation in ductile and brittle solids, International

Journal of Fracture, 100, 1, 55-83

Sitek M., Adamczewski G., Szyszko M., Migacz B., Tutka P., Natorff M., 2014, Numerical

Simulations of a Wedge Splitting Test for High-Strength Concrete, Procedia Engineering, 91, 99-104, DOI: 10.1016/j.proeng.2014.12.021

Song J.H., Areias P.M.A., Belytschko T., 2006, A method for dynamic crack and shear band

propagation with phantom nodes, International Journal for Numerical Methods in Engineering, 67, 868-893

Wawszczuk R., 2012, Self-stresses in polycrystalline materials and their variability during thermal

processing (in Polish), PhD Thesis, Cracow, Faculty of Physics and Applied Computer Science AGH

University of Science and Technology

W¨ohler A., 1870, ¨Uber die Festigkeitsversuche mit Eisen und Stahl, Zeitschrift f¨ur Bauwesen, 20, 73-106

Xi L. Songlin Z., 2009, Strengthening and damaging under low-amplitude loads below fatigue

limit, International Journal of Fatigue, 31, 2, 341-345

Zhao L., Zheng S., Feng J., 2014, Fatigue life prediction under service load considering

strengthening effect of loads below fatigue limit, Chinese Journal of Mechanical Engineering, 27, 1178-1185