On the scale of a concrete structure, where the typical structural element has a smallest dimension (width) at least 1 and often 2 or 3 orders of magnitude greater than the maximum anistropy (coarse aggregate size), it can be considered isotropic for the purposes of structural calculations and design. On the microstructural scale, when considering e.g. transport properties for water, gases, ions etc., this is not the case. 

The discrepancy between the tensile and compressive strength is common to most brittle materials but is extremely complex to explain properly. Put simply, failure is due to the rapid growth of existing microcracks when the stress reaches a critical level. In compression, the stress state tends to close up cracks as the stress increases, preventing their rapid growth and generally delaying failure until the shear stress has built up to a sufficient level to cause shear failure. However, in tension, these microcracks are pulled apart instead, which causes them to grow very rapidly and a tensile failure state is reached long before significant shear stress can build up. Things are complicated by the fact that most concrete structures are in complex 3-D stress states.

However, the modulus (i.e. the slope of the initial stress-strain relationship) in tension and compression is the same for practical purposes at least until significant microstructural damage builds up; it's just that the failure state will be reached much at much lower loading in tension than in compression.

A full answer would take up several pages: I will try to find a suitable reference.

[EDIT: https://www.researchgate.net/publication/248811634_A_Failure_Criterion_for_Concrete]

Article A Failure Criterion for Concrete

In its uncracked state, concrete is homogeneous and isotropic material and can be considered to have the same modulus in all directions whether compression or tension. In its cracked state, it is orthotropic and have different modulus in different directions. In the direction parallel to the cracks, the modulus is maximum, and minimum in the perpendicular direction.  

With all respect, I disagree with Prof. Saad, Actually, concrete is not homogeneous nor isotropic, it is  very complicated material  and its proprieties depend on its randomly arranged components. But for design purpose, concrete always considered homogeneous and isotropic even in cracked condition.

Cracked sections of reinforced concrete are designed as composite section and the concrete part is also considered as  homogeneous and isotropic. Even in cube compression test, it is allowed to test the cube in any direction. Hence, for structural design purpose, concrete is always considered homogeneous and isotropic.

From the theoretical point of view, concrete is considered isotropic and homogenious, but in reality, it is not. that is why we test the cubes in a direction perpendicular to thecasting direction, actually aggregates prefered particle orientation is a big deal to be considered when investigating the modulus.

I can't accept that concrete is isotropic in the microstrutural case like it is stated by Saad Ataan in the uncracked state. Please find in the attached image a cracked specimen of concrete made of (sands, cement and gravels). You can see that the cracked section is not planar to correspond to a nearly perfect cracked isotropic material. Composite material researchers have defined mixtures properties in the chapter of micromechanics. In the coarse aggregate size I agree with Phil Purnell using his assumptions. 

By gravity effect,  cement paste content is higher at the bottom. By non-destructive testing, as ultrasound, it is easy to survey setting and hardening of the concrete. Cubic specimen of 150 mm side and transducers of 45-54 kHz (with 30 mm diameter or exponencial section) allows surveying simultaneously concrete hardening at several points, according to the axis x, y and z.

I agree with  Saad Altaan, also the presence of reinf with different ratios in both directions affect the isotropic properties of RC.

the existence of reinforcement with different ratios in both directions affect the isotropic properties of concrete 

Dear Albayati and Allawi,

I have asked a question about concrete and not about reinforced-concrete. But if you want to analyse a practical case with reinforced-concrete this will lead you to the orthotropic case which is specific (see my scientific papers) to this mixture of materials. You can find poisson's ratios with positive values and negative values (R.S. Lakes paper and K. Bertoldi blog in imechanica.org). The material properties have been computed in this specific case.

Theory tells us that concrete is an isotropic material with different strength properties with respect to the type of imposed loadings.

Dear Tchakalova, thank you for your comment about the strength properties. But an isotropic material has the same properties along its three principal direction this is not the same case with concrete which is a complex mixture made of arbitrary located cement, gravels and sands with respect to its principal directions. This concrete material has been considered by researchers as an homogeneous one which is like an isotropic material but not having the same properties.

The smaller the maximum aggregate size, the nearer to isotropicity a concrete becomes.

Indeed, a concrete is a mixture of several materials. It is considered by researchers as a paste that satisfies the isotropicity. On the other side, concrete taken as a matrix is an heteregeneous material.

Dear Pr Chabaat,

We have together decided to call the concrete mixture a homogeneous material why have you changed your opinion ?

The name homogeneous or heterogeneous isn't important in our study but the fact of a paste that satisfies the isotropicity that you have cited is the important hypothesis which is commonly used by the majority of researchers in engineering.

i agree ok!

Le béton ne saurait être considéré comme un matériau isotrope. Pour s'en convaincre, il suffit de considérer individuellement les propriétés des différents composants du mélange (gravier, Sable, Ciment, Eau) dans les trois directions principales.

Mais Mr Sohounhloue le module d'elasticité logitudinal et le module d'elasticité transversal du béton ont toujours été considérés les mêmes selon toutes les directions x, y et z (ou principales 1, 2 et 3) par les chercheurs : ce qui est une propriété de l'isotropie. Sinon on devrait avoir un matériau anisotrope avec Ex, Ey, Ez, Gyz, Gzx et Gxy et après simplification orthotrope. La réalité eszt une autre dimension où il faudrait aussi considérer la diposition aléatoire (ou arbitraire) des formes et des emplacements des composants de ce matériau. Mais il y'a aussi la façon de voir les choses de façon globale ou par ce qu'on appelle de manière grossière comme dans le cas des maillages grossiers non raffinés qui peuvent suffire dans certains cas.

I agree with Phil Purnell