Force btBvhTriangleMesh to do single-sided collisions

[SoapyMan]

Hello! This is my first post on the forum. I have experience with Bullet physics, and now got big problems.

I have a static world with btBvhTriangleMesh and some small or thin physics objects (compound and convex shapes only)

Problem 1: When I drop my object flatwise on the ground from actor height (in case weapon), it sometimes goes through ground.

Problem 2: Some differrent situation with the ragdolls. When changing my character's state to "ragdoll" his foots sometimes goes through ground and gets stuck (when object penetrates triangle and object center is behind triangle plane it pushes to back side)

In searching of methods to solve that I've made fixed timestep of physics engine and enabled CCD, but in this purpose it doesn't help to get rid of problem. Also i've tried to tweak some ERP's and thresholds, but it helps a little. Increasing iterations results a performance loss.
Also I've tried to find old solutions on this forum, but seems them doesn't work.

I think that if bullet has support of single-sided collisions we could avoid that issues.

So my question is how to make single-sided collisions? Thanks for advance.

[CireNeikual]

You can use a collision callback and make it ignore collisions if the dot product of the hit normal and a vector pointing to the center of an object is less than 0.