Final answer:
Sandstone is the type of natural solid mineral matter that can be excavated with vertical sides and remain intact, due to its clastic sedimentary structure and the cementation of sand grains.
Step-by-step explanation:
The question pertains to the properties of natural solid mineral matter that can be excavated with vertical sides and remain intact while exposed. The options provided are granite, sandstone, marl, and shale. Of these, sandstone is a clastic sedimentary rock composed of sand-sized minerals or rock fragments that can often be quarried with vertical sides and remain intact due to the cementation of the sand grains. Sandstone can display various sedimentary structures such as cross-bedding, mud cracks, and ripple marks, making it a stable rock for extraction and construction. Granite is an igneous rock that is also very durable and could be extracted this way, but it is not typically referred to in terms of sedimentary layering or bedding, which seems to be the context of this question. Shale, though sedimentary, is extremely fine-grained and usually splits along bedding planes, which can make it less stable when excavated with vertical sides. Therefore, the best answer from the given options would be sandstone.