Why are you protecting him/her from rain?
Unless your enclosure can flood, I wouldn't worry.
That tarp is likely to hold a bunch of rain, like a pond, and then fall into the enclosure.
Along with those bricks.
In asking this question, you've exposed some bigger problems that need to be addressed.
1. Is this an adult Russian? If yes, that enclosure is too small. I initially thought we were looking at the night box, not the entire enclosure.
2. Rabbit hutches don't work. You need an insulated, sealed night box, and this is where your tortoise will take shelter form the rain. The rest of the enclosure can get rained on and hopelfully this will make some nice weeds grow up in there for him to eat when the weather warms back up.
3. Which leads me to: Is your tortoise not hibernating? Its cold in San Jose. Nights in the 30s. He should be hibernating this time of year. Why would you have heat on him, and if you had heat on him, what kind and how much? Heat in an uninsulated rabbit hutch isn't going to work. If he is hibernating, then he should be in a fridge somewhere with stable cold temperatures, and not outside in the rain and unpredictable elements of a CA winter.
This is why we can't simply answer yes or no to your tarp question and we were all scratching our heads in wonderment. You shouldn't need a tarp or rain protection for your enclosure, if your shelter and enclosure are built how they should be built.
Here is the current and correct care info to explain what is needed:
The Best Way To Raise Any Temperate Species Of Tortoise
I chose the title of this care sheet very carefully. Are there other ways to raise babies and care for adults? Yes. Yes there are, but those ways are not as good. What follows is the BEST way, according to 30 years of research and experimentation with hundreds of babies of many species. What is...tortoiseforum.org