The 2nd Bianchi identity is an essential step in proving energy conservation from Einstein's extended field equation

(1)
R_{μν} − ½ R g_{μν} = Σ_{μν}

where R_{μν} is the Ricci tensor, R is the scalar curvature and
Σ_{μν} denotes the energy-momentum-tensor.
The 2nd Bianchi identity runs as follows

(2)
D_{λ}R_{ρσμν}
+
D_{ρ}R_{σλμν}
+
D_{σ}R_{λρμν}
= 0 ,

derived under the assumption of **zero torsion**. In [1, p.81, (3.88)]
and [2, p.128, (3.140)] we find the remark:

*For a general connection there would be additional terms
involving the torsion tensor.*

However, M.W. Evans knows more: In his GCUFT book [3, p.325,(D.8)]and in [3a, (D.8)] we find:

D_{ρ}R^{α}_{σμν}
+
D_{μ}R^{α}_{σνρ}
+
D_{ν}R^{α}_{σρμ}
= 0 .
(D.8)

. . . The second Bianchi identity is true for ANY gamma connection.

DÙR^{a}_{b}
=
dÙR^{a}_{b}
+ ω^{a}_{c}
ÙR^{c}_{b}
+ ω^{c}_{b}
ÙR^{a}_{c}
= 0
(D.1)

which can be found also in [1, (3.141)] and [2, (J.32)] and can hence be considered as confirmed. However, the following equation

D_{ρ}R^{a}_{bμν}
=
∂_{ρ}R^{a}_{bμν}
+ ω^{a}_{ρc}
R^{c}_{bμν}
+ ω^{c}_{ρb}
R^{a}_{cμν}
(D.3)

*et cyclicum*.

has evidently missing terms since due to the rules of covariant differentiation each index should produce an additional term besides the partial derivative, but there exist no terms corresponding to the indices μ and ν. The sum

(3)
− Γ_{ρ}^{α}_{μ}
R^{a}_{bαν}
− Γ_{ρ}^{α}_{ν}
R^{a}_{bμα}

is missing which under cyclical summation most likely gives rise to terms containing the torsion tensor.

Evans in [3, p.302], [3a, (D.8)]:

In contrast, note carefully that the second Bianchi identity (17.4) (= (D.8)) is ALWAYS true for any type of connection, because it is fundamentally the cyclic sum of commutators of covariant derivatives [2]:

[[D_{λ},D_{ρ}],D_{σ}]
+
[[D_{ρ},D_{σ}],D_{λ}]
+
[[D_{σ},D_{λ}],D_{ρ}]
:= 0.
(17.9)/(D.9)

Equ. (17.9) is true but NOT so its application to R^{a}_{bμν}
as performed by (D.3) and yielding the **invalid** eqns. (D.8) and (17.4).

[1] S.M. Carroll, Lecture Notes on General Relativity, arXiv 1997

[2] S.M. Carroll, Spacetime and Geometry, Addison Wesley 2004

[3] M.W. Evans, GENERALLY COVARIANT UNIFIED FIELD THEORY, Arima 2006

[3a] M.W. Evans, The Spinning and Curving of Spacetime ..., Preprint

http://www.aias.us/documents/uft/a15thpaper.pdf