Cement strength equation

Intense ion-ion interactions which are characteristic of salt solutions occur in the concentrated aqueous solutions from which AB cements are prepared. As we have seen, in such solutions the simple Debye-Hiickel limiting law that describes the strength goes up so the repulsive force between the ions becomes increasingly important. This is taken account of in the full Debye-Hiickel equation by the inclusion of a parameter related to ionic size and hence distance of closest approach (Marcus, 1988). 

Many empirical relations between compressive strength and one or more of these variables have been proposed. Thus, Feret s law (1892) states that the strength is proportional to [c/(c -I- w -h a)], where c, w and a are the volumes of cement, water and air, respectively, and various authors have reported equations based on regression analyses relating strength to cement composition and other variables (e.g. AI7,A18). The generality of such equations appears to be limited, probably because of the difficulty of taking into account all the relevant parameters. 

Figure 8 exhibits the carbon fiber content vs. compressive strength of artificial woods. The compressive strength of the artificial woods decreases with increasing in the carbon fiber content, HPMC content and shirasu balloon content. Such compressive strength decrease may be explained by increases in both water-(cement+silica fume) ratio and voids in the artificial woods according to the water-cement ratio theory and voids theory, and is expressed by the following empirical equation ... 

By using the above-mentioned equations for slump and compressive strength predictions and nomographs for water-cement ratio and unit cement content estimations, an appropriate mix design system is proposed as represented in Fig. 3.4.I 1... 

The polymer-cement ratio (P/C) to give the required secondary properties is determined on the basis of information shown in catalogs and technical data by the manufacturers of polymer latexes for cement modifiers. Simultaneously, the binder-void ratio (a) to satisfy the required oc and P/C is determined by using an equation for compressive strength prediction. 

For the purpose of developing the equations for the compressive strength prediction for latex-modified mortars and concretes, all-inclusive consideration of various factors such as polymer-cement ratio, water-cement ratio, and air content is required. Expanding Talbot s void theoryP on ordinary cement mortar and concrete, OhamaP P l defined binder-void ratio (a) or void-binder ratio (P), and empirically proposed the equations using a and p to predict the compressive strength of the latex-modified mortars and concretes as follows ... 

As seen in Fig. 4.22,1 ° the addition of steel fibers into latex-modified systems has a positive effect on the strength with increasing polymer-cement ratio and steel fiber content. In general, the flexural and compressive strengths can be predicted by the following equations f391... 

Empirically, a number of equations have been used to link carbonation rates, concrete quality and environment. Table 3.1 summarizes some of those equations and shows the factors that have been included. Generally there is a dependence. As discussed earlier the other factors are exposure, water/cement ratio, strength and CaO content (both functions of cement and, that is, alkali content). 

A number of empirical calculations have been used to derive values of A and n based on such variables as exposure conditions (indoors and outdoors, sheltered, unsheltered), 28 day strength and water cement ratio. A wider range of empirically derived equations is given in Table 3.1. These cover different exposure conditions, curing and concrete properties. The easiest solution for a given structure is to take some measurements of carbonation depth, assume n = 1/2 and calculate A. This can be used to predict the rate of progression of the carbonation front. The time taken to reach the steel can then be estimated and the rate of depassivation calculated. 

The tensile strength of classic cement pastes conforms to the curve plotted on the basis of the Griffith s equation, at the assumption that the width of crack is about 1 mm. The further part of this curve corresponds to the data obtained by Birchall [97], for the specially prepared macro defects free pastes (Fig. 5.40). These pastes are discussed in Chap. 9. They exhibit significantly higher strength because the macropores do not exceed 90 pm. 

With the help of these equations the uniaxial compressive strength/elastic modulus of jointed rocks can be determined for known values ofjoint factor and uniaxial compressive strength/elastic modulus of intact rock. It is observed that the ratios of both static and dynamic elastic modulus decreases with an increase inthe jointfactorunder unconfinement. The test results of POP and the POP-cement mix specimens are given in Table 5. Figure 14 shows the experimental values of uniaxial compressive strength ratio versus joint factor along with a fitted curve. 

Using a somewhat different approach, Knbfel (1989) reliably predicted the 28-day mortar strength with a simple formula containing microscopically determined percentages of alite, belite, aluminate, and ferrite. The equation is F28 = 3(alite) + 2(belite) + aluminate - ferrite. F28 is termed the characteristic strength. The equation is designed for use within a cement plant where production conditions over the period of investigation are virtually identical. 

Variations in predicted 28-day mortar strength among cement producers led Moir (1997) to study the burnabilities of kiln feeds from 15 cement plants in the laboratory, using a horizontal programmable tube furnace. An equation to calculate the temperature required for 1% free lime was given as ... 

The bound or higher stiffness materials such as stabilised bases and asphalt concrete are characterised by the elastic modulus, . The elastic modulus, , of the cement-treated aggregates may be determined according to ASTM C 469 (2010) or, alternatively, from the compressive strength, (AASHTO T 22 2011 or ASTM C 39 2012), and using the correlation equation... 

This equation shows that the strength of a gel can be high enough for stractural applications if the particle size is small enough. For example, a cement gel with particle size of lOnm and a work of adhesion of 0.1 would have a... 

Electrostatic precipitation is a widely nsed process for removing polluting particles from gas streams, for example, in power station fines or in cement kilns. The effluent dust grains become charged as the gas flows between two electrodes, then deposit in a cake on the electrode snrface. This cake sticks to the electrode with a force that rises with the electric field bnt not simply proportional to the square of field strength as expected from the basic electrostatic equation for the cohesive stress a in a dielectric ... 

Effective stress of unsaturated soil will change with the variation of saturation. Ning (2006 and 2008) proposed that it is unreasonable to use matric suction as stress variable. He defined suction stress as a inter particle physico-chemical stresses contributed by cementation, van der Waals attraction, double layer repulsion, capillary stress arising from surface tension, and negative pore water pressure. Shear strength for unsaturated soil based on suction stress conception can be expressed as equation 4 ... 

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