Get document by document url

What is the use case? Where are you getting the URL from? I would recommend using the document query API as shown in the API examples to work with pages.

Along with Juraj's API Examples documentation a simple query should work:

var docs = DocumentHelper.GetDocuments("CMS.MenuItem").Where("NodeAliasPath LIKE '/your/path/here/%'");

Of course you'll want to optimize this to use caching, set column names, etc.

If you need to find a page based on a URL, you could try PageInfoProvider.GetPageInfoForUrl()

You may try get NodeID from DocumentAlias then get node by NodeID

TreeNode GetNodeFromAlias(string aliasPath)
{
    TreeProvider tree = new TreeProvider(MembershipContext.AuthenticatedUser);
    TreeNode page = null;
    page = tree.SelectNodes()
        .Path(nodePath, PathTypeEnum.Explicit)
        .OnCurrentSite()
        .FirstOrDefault();

    if(page != null){
        return page;
    }
    // try get NodeID from DocumentAliases
    var alias = DocumentAliasInfoProvider.GetDocumentAliases()
        .WhereEquals("AliasURLPath", aliasPath)
        .FirstOrDefault();
    if(alias == null)
    {
        return null;
    }
    return tree.SelectNodes()
        .WhereEquals("NodeID", alias.AliasNodeID)
        .OnCurrentSite()
        .FirstOrDefault();
}