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Let ${\Delta }_{n,d}$ (resp. ${\Delta }_{n,d}^{\text{'}}$) be the simplicial complex and the facet ideal $I_{n,d}=(x_1\cdots x_d,x_{d-k+1}\cdots x_{2d-k},...,x_{n-d+1}\cdots x_n)$ (resp. $J_{n,d}=(x_1\cdots x_d,x_{d-k+1}\cdots x_{2d-k},...,x_{n-2d+2k+1}\cdots x_{n-d+2k},x_{n-d+k+1}\cdots x_n{x}_1\cdots x_k)$). When $d\ge 2k+1$, we give the exact formulas to compute the depth and Stanley depth of quotient rings $S/J_{n,d}$ and $S/I_{n,d}^t$ for all $t\ge 1$. When $d=2k$, we compute the depth and Stanley depth of quotient rings $S/J_{n,d}$ and $S/I_{n,d}$, and give lower bounds for the depth and Stanley depth of quotient rings $S/I_{n,d}^t$ for all $t\ge 1$.