18.2.9 Basic Material Parameters via Code Regulations

The basic material properties of concrete, Young's modulus, tensile strength, and fracture energy, can be derived from the compressive strength according to international code regulations.

18.2.9.1 CEB-FIP Model Code 1990

The European CEB-FIP Model Code 1990 [16] gives relationships between the compressive strength and the tensile strength, but also between the compressive strength and the fracture energy. In order to facilitate the usage of the Total Strain crack models, you may input the concrete grade and the maximum aggregate size, and DIANA derives the basic material properties from this input according to the Model Code 1990 regulations. The concrete grade according to the Model Code 1990 defines the characteristic compressive strength, e.g. C60: f_ck = 60  [MPa] .

The Young's modulus is estimated from the mean compressive strength, f_cm , according to the following CEB-FIP Model Code relationship,

$$\left(\vphantom{ \dfrac{f_{\mathrm{cm}}}{f_{\mathrm{cm0}}} }\right. {\dfrac{{f_{\mathrm{cm}}}}{{f_{\mathrm{cm0}}}}} \left.\vphantom{ \dfrac{f_{\mathrm{cm}}}{f_{\mathrm{cm0}}} }\right)^{{\tfrac{1}{3}}}_{}$$ (18.120)

with the value E_c0 equal to 2.15  10⁴  [MPa] . The reference mean compressive strength, f_cm0 , is equal to 10  [MPa] . The mean compressive strength is given by

$$\Delta$$ (18.121)

where $\Delta$f = 8  [MPa] . The mean tensile strength is related to the characteristic compressive strength according to

$$\left(\vphantom{ \dfrac{f_{\mathrm{ck}}}{f_{\mathrm{ck0}}} }\right. {\dfrac{{f_{\mathrm{ck}}}}{{f_{\mathrm{ck0}}}}} \left.\vphantom{ \dfrac{f_{\mathrm{ck}}}{f_{\mathrm{ck0}}} }\right)^{{\tfrac{2}{3}}}_{}$$ (18.122)

with f_{ctk0, m} equal to 1.40  [MPa] and f_ck0 equal to 10  [MPa] . The fracture energy is related to the compressive strength and the maximum aggregate size. The relationship according to the Model Code reads

$$\left(\vphantom{ \dfrac{f_{\mathrm{cm}}}{f_{\mathrm{cm0}}} }\right. {\dfrac{{f_{\mathrm{cm}}}}{{f_{\mathrm{cm0}}}}} \left.\vphantom{ \dfrac{f_{\mathrm{cm}}}{f_{\mathrm{cm0}}} }\right)^{{0.7}}_{}$$ (18.123)

with f_cm0 equal to 10  [MPa] and the value of G_f0 related to the maximum aggregate size [Table 18.1].

Table 18.1: COEFFICIENTS FOR DETERMINATION OF THE FRACTURE ENERGY

		dmax
		8	16	32	mm
Fracture energy	Gf0	25	30	58	J/m2