ASTM F1554 anchor rods essentially the same as AASHTO M314-90, they conformance with ASTM F1554 "Standard Specification for Anchor Bolts, Steel, 36, 55 and 105 Ksi Yield Strength." ASTM F1554 provides for three different grades of anchor rods: Grade 36 (painted blue on the projecting end), Grade 55 (painted yellow on the projecting end), and Grade 105 (painted red on the projecting end). ASTM F1554 grades 36, 55 and 105 are essentially the anchor-rod equivalents of the generic rod specifications ASTM A36, ASTM A572 grade 55 and A193 grade B7, respectively.
The length of the bolts should be such that the end of the bolt should be at least flush with the outside face of the nut when properly installed. I would consider gouging the concrete and adding extensions. One way to extend anchor bolt lengths without welding is to provide threaded couplers. Another way is to consider limited carbon arc gouging (air arc) of the base plate surface under the nut to provide full thread engagement. Weld is allowable for ASTM F1554 grade 36 or ASTM F1554 grade 55 with weldability supplement S1 and the carbon equivalent formula in ASTM F1554 Section S1.5.2.1 can be specified to allow welded field correction should the anchor rods be placed incorrectly in the field. The weldability supplement is only for Grade 55. Grade 36 does not need it as it is essentially an ASTM A36-like rod material. Grade 105 is heat treated and, therefore, not suitable for welding. The weld joint may have tension loss due to the weld temperature also watch for galvanize contamination. Seismic Applications or a pretensioned joint subject to cyclic fatigue loads, welding cannot be recommended.
AWS standard D1.1:2004 allows the welding, look at para 1.2 Limitations. Item (1) states in essence that the code was not intended for use for steels with a minimum specified yield strength greater than 100 ksi. and 2.9.4 plug and slot welds. In order to create a WPS for welding D1.1:2004 Table 4.7, Essential Variables and look at 4.7.3.
Typically the base plate should be at least as thick as the anchor rod diameter to provide for even distribution of the load and to minimize prying forces. The minimum distance from the center of the anchor rod hole to the edge of the base plate should be two times the nominal diameter of the anchor rod.
Hope this helps