Materials and Structures

, 52:77 | Cite as

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

  • Natalia V. Silva
  • Sérgio C. AnguloEmail author
  • Aline da Silva Ramos Barboza
  • David A. Lange
  • Luís M. Tavares
Original Article


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.


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

List of symbols


Minimum cross-sectional area


Breakage point


Emprirical constant


Diameter of spherical body


Distance between loading points


Nominal diameter


Equivalent core diameter


Effective modulus of contact


Elastic modulus of the punch


Elastic modulus of the particle


Fracture energy


Specific-volume fracture energy


Applied force


Breakage force


Force during elastic deformation


Particle stiffness


Punch stiffness


Contact stiffness during elastic deformation


Particle mass




Total displacement


Displacement variation


Volume of the particle


Minimum width


Yield point


Tensile strength


Poisson’s coefficient of the particle


Poisson’s coefficient of the punch


Shape factor


Particle density



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.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© RILEM 2019
corrected publication July 2019

Authors and Affiliations

  1. 1.Department of Construction Engineering, Escola PolitécnicaUniversity of Sao PauloSao PauloBrasil
  2. 2.Center of TechnologyUniversidade Federal de AlagoasMaceióBrazil
  3. 3.Department of Civil and Environmental EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  4. 4.Department of Metallurgical and Materials EngineeringUniversidade Federal do Rio de Janeiro, COPPE/UFRJRio de JaneiroBrazil

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