They all look the same

With all the stacks lined up in a row, take $1$ marble from the first stack, two from the second, and in general $n$ marbles from the $n$ th stack for $1 \le n \le 10,$ and then no marbles from the $11$ th stack.

If all the stacks were composed of glass marbles then we would expect this set of $55$ marbles to have a mass of $550$ grams. If this is the measurement then we can conclude that the $11$ th stack is composed of clay marbles. But if the $n$ th stack (for some $n$ such that $1 \le n \le 10$ ) is composed of clay marbles, then the digital scale will read $(550 - n)$ grams. Thus only $\boxed{1}$ measurement is required.