In　this　paper,　the　electrically　limited　permeable　piezoelectric　cracks　considering　the　induced　Coulomb　tractions　on　the　crack　faces　are　studied　with　respect　to　the　dielectric　constant　of　the　crack　medium　by　BEM.　As　limiting　cases,　the　permeable　and　impermeable　electric　crack-face　boundary　conditions　are　also　considered.　Based　on　the　dual　boundary　integral　equations,　the　crack-tip　field　intensity　factors　and　the　energy　release　rate　are　evaluated　by　the　displacement　extrapolation　method　and　the　J-integral　method,　respectively.　The　crack-face　part　of　the　contour　integral　is　then　handled　by　two　approaches,　namely　numerical　quadrature　and　approximate　formula.　The　analytical　solutions　for　a　Griffith　crack　are　also　presented　for　verification　purpose.　Three　examples　are　presented　to　check　the　efficiency　and　the　accuracy　of　these　approaches.　The　effects　of　the　dielectric　constant　of　the　crack　medium　and　the　induced　Coulomb　tractions　on　the　crack-tip　field　intensity　factors　and　the　energy　release　rate　are　also　discussed.　(C)　2015　Elsevier　Ltd.　All　rights　reserved.