Hello amati,
I just completed a SLAM on my very gross pool, it took 19 days, and 76 gallons of 10% liquid shock to get it clean and clear. (Hopefully your pool will take less, but I just want you to know how long, and how much bleach it Could take).
My pool is only 15,200 gal which is less than half the size of yours. 1 gallon of 10% Liquid Shock was added to mine Several times a day, and I was just able to maintain the appropriate Slam/Shock levels.
The point I'm trying to make is I personally do Not believe that a mere 1 gallon of 10%, and especially a lower % of bleach, will be near enough to adequately maintain your 35K gallon pool at Slam/Shock levels all day while your at work.
Trust me, I totally understand when you are currently at Shock/Slam levels how confusing it can be to try to decide exactly how much bleach is enough to maintain your current level. If your levels are low then pool math will tell you to add X amount to increase to your Goal, but if you're on your goal already, it doesn't say how much is required to stay there.
So that's when you have to do some of the estimated calculations yourself. You have to take into account how much will one gallon of whatever percent you are planning to use raise your FC level, and then compensate for how much of the added chlorine the sun, and your 70 CYA, will eat back up in the process. Putting a cover on your pool during the day will help you not lose as much too.
In your case, since your FC level can't be checked but once a day you need to raise the number up during the time your away to prevent dropping below SLAM/SHOCK level while your at work. Then come home, check the levels, and add more bleach in the appropriate amount per
http://www.troublefreepool.com/calc.html. to maintain 28ppm throughout the night. (which of course should be some less needed than during the day because there is no sun).
Here is the chlorine/cya chart
http://www.troublefreepool.com/content/128-chlorine-cya-chart-slam-shock SWG pool ranges are at the bottom. With a CYA of 70 your pool needs to remain at Least 28ppm all the time.
I'm not certain on how high the level really needs to be to kill Black Algae, but I do know Black algae is one bad boy to get rid of, but here is an article that says you need to maintain the higher end of normal to the shock level of 28ppm in your case.
http://www.troublefreepool.com/content/180-Black-Algae
Perhaps someone with a lot more experience than me can give you an exact levels on the black algae you are trying to kill, but I'd recommend you continue to shoot for at, or above the 28ppm range you are now at when you can check it often, and possible bump that during the day to a higher Goal range of say 31-32ppm to start when you Can't be there to routinely check it, and see how close that keeps you, and then adjust the amount of chlorine you add up, or down, accordingly the next time.
According to Pool Math to take you from your current 28ppm to say 31-32 ppm level will take close to a gallon and half of 10% and a little over a gallon and a half of 8.25% to get you there. If that doesn't hold you to at least 28ppm until you get home, then you may need to add 1 3/4 gallon-2gallons. You might want to just go ahead and add 2 gallons before work to see where your levels are upon returning home then adjust the level the next day accordingly? Only you can decide how you chose to add your chlorine, but I promise if the levels don't stay high enough, the ENTIRE TIME, the Slam will Not work properly.
(NOTE: THESE ARE GALLONS, so if you are using QUARTS of BLEACH etc you have to add more to =the full needed amount. Use POOL MATH to tell you how much you will need if using quarts etc.
(The important thing to remember is a SLAM can NOT be done properly playing hit and miss- (with FC levels up high, then allowed to drop way down low), you MUST maintain the appropriate level, or higher without ever going below the level, at ALL times during the entire SLAM, or you're merely wasting your time, along with a whole lot of money on bleach, and you'll end up not killing the algae, and having to start all over again). Doing it Correct the 1st time is way better than having to RESLAM multiple times.
And like Dom suggested you need to check those levels again at night 30-60 mins after adding the chlorine, and it will tell you a lot about what's going on in there, and how much chlorine your pool is actually consuming. If need be get started an hour earlier than you usually would.
(FYI-MUSTARD ALGAE takes 39ppm of FC on a SWG pool to kill it, and I suspect Black algae may be harder to kill then mustard algae from what I've read, so hopefully the 28ppm will be high enough to kill it, if not you'll need to increase the FC level more).
If you don't have a cover, or don't wish to cover it, and it gets a lot of direct sunlight then you Might have to compensate your levels up for that.
You should be able to get pretty close to knowing what you'll need to add after testing the 1st couple days. Again like Dom suggested you need to check those levels again at night 30-60 mins after adding the chlorine, and it will tell you a lot about what's going on in there, and how much chlorine your pool is actually consuming.
Doing this will get you to where you want to be quicker.
Anyway, I hope this helps get your SLAM started, and Maintained appropriately to get that black algae killed out once, and for all. Good Luck and Happy Slamming