4. Design guidelines

#### 4.1. Theoretical modeling and numerical simulation of rubberized concrete

A typical model for the behavior of TDA concrete is a modification of Holmquist-Johnson-Cook (H-J-C) constitutive model. The original H-J-C model contains 21 modifiable parameters to present characteristics of TDA concrete, which was simplified to ten parameters in the modified form [17].

Numerical simulations using finite element analysis are also available to model mechanical properties of TDA concrete. The basis for these simulations is generally an elastoplastic model for the behavior of materials. Successful modeling of beam specimens has been reported using hexahedron elements with standard shape functions [6]. Using a two-phase composite material helps to define the dispersion of TDA in the cementitious matrix. This model utilized three-node triangular elements to simulate split-tensile tests [16].

#### 4.2. Suggested strength reduction factors

Similarly, the damping ratio of TDA concrete measured by elastic wave method showed a moderate increase because of the increase in the rubber content in concrete [24]. However, the shake-table studies on TDA concrete columns indicated much higher damping ratios [23]. These comparisons indicate how TDA becomes more effective in post-peak performance of concrete specimens. Further, same shake table studies have shown that increasing rubber content in the TDA concrete reduces the natural frequencies and the response acceleration by 28 and 27%, respectively [23].

Non-destructive tests using ultrasonic pulses confirm that rubber reduces the velocity of waves, which is in correlation with lower dynamic modulus of elasticity [14]. Dynamic compression tests confirm the capability of TDA concrete in dissipating energy and show that increasing the load frequency or strain rate increases the dynamic modulus of elasticity [12, 17]. However, the

Nonstructural mechanical properties of TDA concrete have been subject to studies for specific applications. Non-loadbearing wall elements often require proper thermal and electrical insulation as well as sound absorption. Studies indicate that TDA improves the sound absorption of concrete, reduces the thermal conductivity coefficient, and increases the electrical resistivity

A typical model for the behavior of TDA concrete is a modification of Holmquist-Johnson-Cook (H-J-C) constitutive model. The original H-J-C model contains 21 modifiable parameters

age of the specimens has an adverse impact on the energy dissipation [12].

Figure 8. Selected reported relative changes in the absorbed energy of rubberized concrete.

3.7. Thermal conductivity, electrical conductivity and sound absorption

4.1. Theoretical modeling and numerical simulation of rubberized concrete

[13, 18, 27].

144 Cement Based Materials

4. Design guidelines

Figure 9 shows a comparative view of the relationships between mechanical properties of TDA concrete and the TDA content volume. This figure suggests that developing a simple model for practical design of TDA concrete elements may be possible, as various strengths follow similar trends in respect to TDA content.

Eq. (1) presents a proposed model to find the strength reduction factor [15]:

$$SRF = a + b(1 - R)^m \tag{1}$$

In this model, SRF is the "strength reduction factor"; R is the rubber content as a volumetric ratio by the total volume of aggregates; and a, b, and m are modeling parameters. This equation is equal to unity at a rubber content of 0% and reaches an asymptote at higher rubber content values. The m parameter indicates the degree of curvature of the reduction and is a function of the particle size. In addition, parameters a and b must satisfy the relationship a þ b ¼ 1. Table 2 contains suggested modeling parameters from past studies.

Figure 9. Selected reported relative changes in the dynamic properties of rubberized concrete (marked data) and their general trends (trend-lines).


cementitious materials. Enhancing the properties of TDA concrete using these methods require

Tire-Derived Aggregate Cementitious Materials: A Review of Mechanical Properties

http://dx.doi.org/10.5772/intechopen.74313

147

The California State University, Fresno Foundation has partially supported this work.

The authors declare that there is no conflict of interest regarding the publication of this work.

[1] Environmental Protection Agency (EPA). Why are scrap tires an issue? Scrap Tire Man-

[2] Environmental Protection Agency (EPA). Municipal Solid Waste Generation, Recycling, and Disposal in the United States: Facts and Figures for 2012. Annual Report. Washington

[3] Siddique R, Naik TR. Properties of concrete containing scrap-tire rubber - An overview.

[4] Miller NM, Tehrani FM. Mechanical properties of rubberized lightweight aggregate con-

[5] Aiello MA, Leuzzi F. Waste tire rubberized concrete: Properties at fresh and hardened

[6] Al-Tayeb MM, Abu Bakar BH, Akil HM, Ismail H. Performance of rubberized and hybrid rubberized concrete structures under static and impact load conditions. Experimental

crete. Construction and Building Materials. 2017;147:264-271

further research.

Acknowledgements

Conflict of interest

Author details

References

DC: EPA; 2012

Fariborz M. Tehrani\* and Nathan M. Miller

California State University, Fresno, USA

\*Address all correspondence to: ftehrani@csufresno.edu

agement Forum; Rapid City, SD: EPA; 2006

Waste Management. 2004;24:563-569

Mechanics. 2012;53:377-384

state. Waste Management. 2010;30:1696-1704

Table 2. Summary of selected modeling parameters.

#### 4.3. Handling procedures

Another important aspect of concrete design is the handling procedures used when placing the concrete while in the workable state. Care needs to be taken to ensure that segregation of materials does not occur and the mix remains as homogenous as possible while being placed and cured. An uneven distribution of rubber particles has been observed in concrete mixes, particularly when specimens are vibrated during placement causing light TDA to surface [10, 23].
