Some examples of almost GCD-domains

Let D be an integral domain, X be an indeterminate over D, and D[X] be the polynomial ring over D. We show that D is an almost weakly factorial PMD if and only if is an integrally closed almost GCD-domain for each (saturated) multiplicative subset S of D, if and only if is an integrally closed almost GCD-domain for any t-linked overring of D, if and only if is an integrally closed almost GCD-domain for all t-linked overrings of D.