The phrase "spend much effort" is correct and usable in written English.
You can use it to indicate a significant amount of time and effort being put into something. For example, "She spent much effort studying for her final exams and was rewarded with top marks."
Proponents spend much effort convincing people that this or that popular diet is the best.
Inductive engineers spend much effort trying to understand business goals in order to inductively generate the models that matter the most.
And in a time when most newspaper publishers spend much effort figuring out how to profit from the Web, The Daily Post is proudly print-only.
Malagasy pay a lot of attention to their dead and spend much effort on ancestral tombs, which are opened from time to time so the remains can be carried in procession, before being rewrapped in fresh shrouds.
You probably won't have to spend much effort educating them on the benefits of a connected home because they have already done their homework and are impressed by the variety and capabilities of available options.
Although the patient was able to perform the motor task in the localizer experiment, he mentioned that he needed to spend much effort and concentration to execute the conscious movements of the alien hand.
The illegitimate daughter who resulted - Sand's grandmother - spent much effort covering these tracks.
I've spent much effort on this letter, but perhaps you will read it with a shaking head, thinking that it is full of fallacies.
Science fiction writers have spent much effort conceiving societies that are neither perfect nor horrific but excitingly different, alien to human experience.
Currently general secretary of the ruling Congress Party, he has spent much effort democratising its youth wing while avoiding taking up a cabinet position.
As director, Joe initially spent much effort trying to smooth over departmental feuding, which had been fierce during the 1950s and 1960s.
