  In the paper, we analyze some physical properties of static traversable WH
within the framework of $f(R,T)$ modified gravitational theory. Firstly, we
explore the validity of the null, weak, dominant and strong energy conditions
for wormhole matter for the considered $f(R,T)=R+\alpha R^2+\lambda T$ model.
Research shows that it is possible to obtain traversable WH geometry without
bring in exotic matter that violates the null energy condition in the $f(R,T)$
theory. The violation of the dominant energy condition in this model may be
related to quantum fluctuations or indicates the existence of special matter
that violates this EC within the wormhole. Moreover, it is found that in the
$f(R,T)=R+\alpha R^2+\lambda T$ model, relative to the GR, the introduction of
the geometric term $\alpha R^2$ has no remarkable impact on the wormhole matter
components and their properties, while the appearance of the matter-geometry
coupling term $\lambda T$ can resolve the question that WH matter violates the
null, weak and strong energy condition in GR. Additionally, we investigate
dependency of the valid NEC on model parameters and quantify the matter
components within the wormhole using the ``volume integral quantifier". Lastly,
based on the modified Tolman-Oppenheimer-Volkov equation, we find that the
traversable WH in this theory is stable. On the other hand, we use the
classical reconstruction technique to derive wormhole solution in $f(R,T)$
theory and discuss the corresponding ECs of matter. It is found that all four
ECs (NEC, WEC, SEC and DEC) of matter in the traversable wormholes are valid in
this reconstructed $f(R,T)$ model, i.e we provide a wormhole solution without
introducing the exotic matter and special matter in $f(R,T)$ theory.
