This relays don't work with RPI, because the gpio output is too weak to drive the inputs of relays. For 1-3 pins works, but if you connect more, the output driver of RPI is out of valid range.
The solution is to use a very cheap driver IC. If you want, I can share the wiring diagram here.
I think the issue is that the sainsmart 12volt relay requires its own 12 power rail.
No dirver chips are needed as this is included on the relay board.
I'm sure it would help!
12Volt power doesn't come from Rpi - only logic level to trigger the relays via transitors onboard.