We derive the fraction of substructure in the Galactic halo using a sample of over 10,000 spectroscopically confirmed halo giant stars from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) spectroscopic survey. By observing 100 synthetic models along each line of sight with the LAMOST selection function in that sky area, we statistically characterize the expected halo populations. We define as Stellar Halo Accretion Related Debris Structures (SHARDS) any stars in $\gt 3\sigma$ excesses above the model predictions. We find that at least 10% of the Milky Way (MW) halo stars from LAMOST are part of SHARDS. By running our algorithm on smooth halos observed with the LAMOST selection function, we show that the LAMOST data contain excess substructure over all Galactocentric radii $R_{\rm GC} \lt 40$ kpc, beyond what is expected due to statistical fluctuations and incomplete sampling of a smooth halo. The level of substructure is consistent with the fraction of stars in SHARDS in model halos created entirely from accreted satellites. This work illustrates the potential of vast spectroscopic surveys with high filling factors over large sky areas to recreate the merging history of the MW.