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Improved method to measure the strength and elastic modulus of single aggregate particles


The standard methods used to determine the mechanical properties of single aggregate particles have shortcomings. Indeed, methods that are commonly used to measure the strength of irregular particles do not provide their elastic modulus and are also only semi-quantitative. The aim of this work is to determine more accurately both the tensile strength and the elastic modulus of single coarse aggregate particles using the point load test fitted with tungsten carbide semi-spheres and coupled with a linear transducer. In the experiment, the poles of the particles are made flat and parallel at the points of contact with the semi-spheres of the apparatus, allowing to estimate the elastic modulus of aggregates in accordance to Hertz contact theory. Glass particles of different shapes (spheres, cubes, and prisms) were used as reference material to validate the experimental method and establish the optimal conditions to conduct the test. These conditions consisted of a deformation rate of 0.2 mm/min, a blunt 4.0-mm diameter cylinder piston for spherical particles, while two 14.0-mm diameter semi-spheres in the case of rectangular particles (cubes/prisms). It is also hereby proposed to measure the tensile strength of irregularly-shaped particles by a modified version of Hiramatsu and Oka’s formula using the equivalent core diameter. The proposed method was then applied to measure the strength and modulus of coarse granite aggregate particles (25.0 to 9.5 mm). It demonstrated that the variability of the elastic modulus and tensile strengths of the individual aggregate particles was quite significant, confirming the importance of using the proposed improved method to qualify materials for structural (high strength) concrete, or to simulate/predict the mechanical behavior of concrete.

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Change history

  • 30 July 2019

    This article was published with an erroneous name of one of the authors and therefore has been corrected.


A c :

Minimum cross-sectional area

B :

Breakage point

C :

Emprirical constant

D :

Diameter of spherical body

D :

Distance between loading points

D n :

Nominal diameter

D e :

Equivalent core diameter

E * :

Effective modulus of contact

E t :

Elastic modulus of the punch

E p :

Elastic modulus of the particle

E n :

Fracture energy

E v :

Specific-volume fracture energy

F :

Applied force

F b :

Breakage force

F el :

Force during elastic deformation

k p :

Particle stiffness

k t :

Punch stiffness

K N-el :

Contact stiffness during elastic deformation

m p :

Particle mass

s :


S :

Total displacement

s :

Displacement variation

V p :

Volume of the particle

W :

Minimum width

Y :

Yield point

σ t :

Tensile strength

μ p :

Poisson’s coefficient of the particle

μ t :

Poisson’s coefficient of the punch

β :

Shape factor

ρ p :

Particle density


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Natalia V. Silva and Sérgio C. Angulo received research scholarship grants of FAPESP Numbers 2016/02902-0 and 2016/19974-3, respectively. Sérgio C. Angulo also received a research grant from CNPq, process 305564/2018-8. The information and views set out in this study are those of the authors and do not necessarily reflect the opinion of FAPESP or CNPq. Luís Marcelo Tavares received the research grant from CNPq process 310293/2017-0. David A. Lange received support from the RECAST University Transportation Center established at Missouri University of Science and Technology.


The study was funded by a research project entitled “Granulometric concepts and advanced processing applied to ecoefficient concrete” between the University of Sao Paulo (USP) and InterCement S.A, as well as by the National Institute of Science and Technology “Advanced Eco-Efficient Cement-Based Technologies”, between USP and CNPq agency.

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Correspondence to Sérgio C. Angulo.

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This article was published with an erroneous name of one of the authors and therefore has been corrected.

Appendix 1

Appendix 1

See Figs. 7, 8, 9 and 10.

Fig. 7

Schematic illustration showing nominal diameter and length of particle

Fig. 8

Typical compression force–displacement curve until breakage (left axis) and calculated contact stiffness (right axis)

Fig. 9

The pattern of rupture of the glass particles: spheres, cubes and prisms

Fig. 10

Aggregate particles after the mechanical test. Most particles broke into two pieces

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Silva, N.V., Angulo, S.C., da Silva Ramos Barboza, A. et al. Improved method to measure the strength and elastic modulus of single aggregate particles. Mater Struct 52, 77 (2019).

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  • Aggregates
  • Single particle
  • Elastic modulus
  • Hertz contact theory
  • Tensile strength
  • Point load test