Although I would not call it "large", there is a quite rich database from TC304, called 304db which you can find here: http://140.112.12.21/issmge/tc304.htm?=6
It has been used quite extensively for Bayesian ML to derive site-specific parameters. One of the most famous is MUSIC-X (Multivariate,Uncertain,Sparse, and Incomplete Site Investigation Data with Spatial Variation).
You can find in my Ph.D Thesis (Appendix B and C, page 187) a database including 1341 boreholes, which contain more than 2000 physical and mechanical laboratory tests, and 489 pressuremeter tests. The database was collected in the Algiers area, and shared for research works. I have already used this Database for 8 papers using Machine Learning modeling.
You can download several such datasets from Kik-Net or K-Net database. I recently downloaded borehole data from the same. Please go through this link to find such data:
The ‘GeoRiskR’ package contains many site-specific datasets, such as the power law regression parameters for piles, the cohesion and friction angle of soils.