it depends. Keep in mind that your "nature behavior" (which is not defined in your question) involves with both sediment and groundwater. I would think you need sample both media to figure out what you are looking for. Unless you are looking for a particular thing that only depends on the sediment to live and grow and interact with others.
I have Sedimentary Core samples below ground level and i know the water level from that location. Now, i am trying to think about analysis of core sample to understand the groundwater nature. Is it possible to test core samples for the study?
I would say no although there will be something leaching from the soil to the underlying groundwater. Still it is very difficult to predict anything in groundwater without sampling it.
Could you elaborate more if you just need the groundwater chemistry of the core sample or some other parameters of the core sample (e.g. conductivity, diffusion/dispersion parameters etc.).
Sure, it can be done and identify the groundwater nature and flow/accumulation behavior from coring samples, but you need a considerable number of cores at different depths.
Your question is too broad and unfocussed to be addressed, other than to say that much of the solute load of a groundwater derives from dissolution of/reaction with, the minerals of the aquifer in which it resides. John D. Hem, of the USGS, wrote a classic USGS Water-Supply Paper (No 2254, 1986) on the topic. Although old, it is still a first-class read.
If you are thinking of manganese and arsenic, see the attached.