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The BTW sandpile model is considered on three dimensional percolation latticewhich is tunned with the occupation parameter $p$. Along with thethree-dimensional avalanches, we study the energy propagation intwo-dimensional cross-sections. We use the moment analysis to extract theexponents for two separate cases: the critical ($p=p_c\equiv p_c^{3D}$) and theoff-critical ($p_c<p\leq 1$) cases. The three-dimensional avalanches at $p=p_c$has exponents like the regular 2D BTW model, whereas the exponents for the 2Dcross-sections have serious similarities with the 2D critical Ising model. Themoment analysis show that finite size scaling theory is the fulfilled, and somehyper-scaling relations are confirmed. For the off-critical lattice, theexponents change logarithmically with $p-p_c$, for which the cut-off exponents$\nu$ drop discontinuously from $p=p_c$ to the other values. The analysis forthe 2D cross-sections show a singular behavior at some $p_0\approx p_c^{2D}$($p_c^{3D}$ and $p_c^{2D}$ being three- and two-dimensional percolationthresholds). We argue that there are two separate phases in the cross-sections,namely $p_c^{3D}\leq p<p_c^{2D}$ which, due to lack of 2D percolation cluster,has no thermodynamic limit, and $p\geq p_c^{2D}$ having the chance to involvepercolated clusters.

Sandpile on uncorrelated site-diluted percolation lattice; From three to two dimensions