Experimental Determination of Cohesion and Internal Friction Angle On Conventional Concretes

 

ACI MA MATERI TERIALS ALS JOU JOURNA RNAL L

TECHNI TEC HNICAL CAL PAPER

Title No. 114-M36 114-M36

Experimental Determination Determination of Cohesion and Internal Friction Angle on Conventional Concretes by Selim Pul, Amir Ghaffari, Ertekin Öztekin, Metin Hüsem, and Serhat Demir Various failure criterions have been used for the nonlinear analysis of concrete and reinforced concrete structures. To get more accurate results from the analyses, the selected failure criterion must be appropriate with the characteristics of problem and the assumptions made in the criterion should comply with the characteristics of problem. In this study, an experimental investigation was carried out to determine the cohesion (c) and internal friction angle (ϕ) values, which are in the compressive strength range of 14.4 MPa ≤ f cm cm cube ≤ 47.0 MPa (2.03 ksi ≤ f cm cm cube ≤ 6.82 ksi) that are used in failure criterions such as Mohr-Coulomb and Druck er-Prager preferred in end unit analyses for concrete and rein forced concrete concrete structures. Tests Tests are performed by using the direct direct  shear test system, which is designed and produced for this study study..  Finally,, cohesion and internal friction angle were determined  Finally between 2.94 and 12.34 MPa (0.43 and 1.79 ksi) and 29.8 and

dened as the second deviatory invariant of the Cauchy stress tensor and calculated by Eq. (5).

41.7 degrees, respectively.

(2), both cohesion c  and internal friction angle ϕ must be known to constitute DP and MC failure criterions. Accuracy of the nonlinear analysis, in which DP and MC failure critecrite rions were used, depends on the accuracy of these parameparameters. When the existing technical literature is examined, it can be seen that many different values were proposed for cohesion and internal friction angle by different researchers for concrete. Arslan5  calculated the parameters of c  and ϕ as 3.06 MPa (0.44 ksi) and 33 degrees, respectively, respectively, for the concrete with 22.5 MPa (3.26 ksi) compressive strength. Mahboubi and Ajorloo6  determined the cohesion and internal friction angle as c = 0.73 MPa (0.11 ksi) and ϕ = 30.5 degrees for 2828-day concrete and c = 1.01 MPa (0.15 ksi) and ϕ = 29.7 degrees for 150150 -day concrete, respectively. 7 Moosavi and Bawden   obtained the c  and ϕ parameters as 11.5 MPa (1.67 ksi) and 22.8 degrees for cement paste with a water-cement ratio (w (w/c) of 0.50, respectively. Calayir and 8 Karaton  used c = 2.109 MPa (0.31 ksi) and ϕ = 38 degrees for concrete having 25 MPa (3.6 ksi) compressive strength in their study. Doran et al.9 were proposed Eq. (6) to calcucalculate cohesion of conventional concrete. Two parameters, Young’s modulus ( E   E c) and maximum aggregate size ( D  Dmax) of concrete, were used in this equation. They also proposed ϕ = 25 to 38 degrees for conventional concrete.

Keywords: cohesion; conventional concrete; direct shear test; Drucker-Pra Drucker-Prager ger  parameters  param eters;; internal internal frict friction ion angle; angle; Mohr Mohr-Coul -Coulomb omb failur failuree criterio criterion; n; nonlinea nonlinearr nite element analysis.

INTRODUCTION  Nonlinear analysis is used to get the most sensitive and accurate behavior of a structure or a structural member subjected to different loading conditions. However, selecselec tion of the most appropriate failure criterion according to the structural materials is a prerequisite in nonlinear analysis. Several failure criterion were proposed for different strucstructural materials. Because of their simplicity and obtaining of more accurate results by using them, Mohr and Coulomb1,2  (MC) and Drucker and Prager 3  (DP) criterions became the most commonly used failure criterions for concrete and reinreinforced concrete. MC and DP criterions were represented by the Eq. (1) and Eq. (2), respectively.    

τ = c +  σ tan φ    f ( I1 , J 2 ) = αI1 +

J2

(1)

− K    = 0 

(2)

In Eq. (1), τ, c, σ, and ϕ are dened as shear strength, cohecohesion, normal stress, and internal friction angle, respectively. α and K  and  K  are   are positive material constants, called DP parameparame 3 ters  in Eq. (2). They are obtained as

 

  2 sin φ α = 3 (3 ± sin φ)  and  K  =

 

6c cos φ 3 (3 ± sin φ)  

(3)

 I 1 is the sum of principal stresses (Eq. (4)) and it is dened as rst invariant of the Cauchy stress tensor. Finally,  J 2  is

ACI Materials Journal/May-June 2017

 

 

 I 1

 J 2

=

= σ +σ +σ 1

2

3

 

1

(σ1 − σ 2 ) 2 + (σ 2 −  σ3 ) 2 + (σ3 − σ1 ) 2    6

(4)

(5)

The symbols (±) in Eq. (3) are negative if the DP yield surface surrounded the MC hexagonal pyramid and touches to corners, and is positive if the DP cone passes through inner bound of the pyramid. Figure 1 shows the DP and MC yield surfaces in three-dimensional (3-D) stress space and in the deviatoric (π) plane. 4 As seen from Eq. (1) and

 

c

= 0.23 ln( E

c

2

Dmax )

− 0.6  (MPa)

(6)

Rochette and Labossiére10 were proposed Eq. (7) and (8) to dene c  and ϕ values of conventional concrete conned  ACI Materials Journal , V. 114, No. 3, May-June 2017. MS No. M-2016-047.R1, doi: 10.14359/51689676, was received August 16, 2016, and reviewed under Institute publication policies. Copyright © 2017, American Concrete Institute. All rights reserved, including the making of copies unless  permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.

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