Russellwh:
Here are some comments from ACI CHAPTER 22 — STRUCTURAL PLAIN CONCRETE (concrete without reinforcement).
R22.2 — Limitations
R22.2.2 — Since the structural integrity of plain concrete members depends solely on the properties of the concrete, use of structural plain concrete members should be limited to: members that are primarily in a state of compression; members that can tolerate random cracks without detriment to their structural integrity; and members where ductility is not an essential feature of design. The tensile strength of concrete can be utilized in design of members when the buildup of tensile stresses due to restraint
from creep, shrinkage, or temperature effects are considered and sufficiently reduced by construction techniques to avoid uncontrolled cracks, or when uncontrolled cracks due to such restraint effects can be anticipated to occur in such a manner that will not induce structural failure or collapse.
R22.3 — Joints
Joints in plain concrete construction are an important design consideration. In reinforced concrete, reinforcement is provided to resist the stresses due to restraint of creep, shrinkage, and temperature effects. In plain concrete, joints are the only design means of controlling and thereby relieving the buildup of such tensile stresses. A plain concrete member, therefore, must be small enough, or divided into smaller elements by joints, to control the buildup of internal stresses. The joint may be a contraction joint or an isolation joint. A minimum 25 percent reduction of member thickness is considered sufficient for contraction joints to be effective. The jointing must be such that no axial tension or flexural tension can be developed across a joint after cracking, if applicable, a condition referred to by the code as flexural discontinuity. Where random cracking due to creep, shrinkage, and temperature effects will not affect the structural integrity, and is otherwise acceptable, such as transverse cracks in a continuous wall footing, transverse contraction or isolation joints are not necessary.
So he may be allowed to use plain concrete, as these cracks seem to be minor and are not detrimental to the slab's integrity. He did use joints, just not in a timely manner. But they were too late, and the cracking had already occurred. Hence the use of rebar. May be overkill, but it would have significantly reduced the cracking before the joints were cut.
These comments said, along with everyone else's you can decide your proper course of action.
I recommend you do the following.
Check with your local building official about reinforcement in slabs (particularly slabs on grade). As mentioned before, was he under contract for rebar? That should have been written down on the contract documents, not implied. Check what your actual weather records were 2-3 days before the pour date and the cure dates following (going on 7 days?). And I mean all facets: temp, wind, and humidity. This will show proper knowledge of near freezing temps and that he should have taken means to prevent freezing in the new slab. Is their evidence of a sprayed-on-membrane as the curing agent for the slab (would look sort of like dried milk)? Was he also under contract to do this also?
Other questions for you. What type of fill did you use? How was it compacted? Did you add water while compacting? Did the contractor add water to the fill just before he placed his concrete? These are going to be valid questions from his part or his representatives if it gets that far.
If you are looking for someone to blame, you really only have one person with whom you should be concerned. That would be your general contractor. He is ultimately responsible for all his subs and their work.
As for the comments of a crack free slab. My garage pad is 26x26 @ 5" deep with 6x6 WWF. Concrete was placed at about 50-deg F. and immediately covered and saw cut (1/2 each way). The slab was then wet-cured for 6 days. The joints were then properly sealed (backer-rod is essential in this process or the sealant may fail).
The pad is on its second winter, with lows in the -20s deg F. and highs about 100 deg F. The garage is uninusulated, so the covered slab has easily seen a temperature gradient of 70-deg F. (a common design factor). The pad is crack free. If it would have cracked, it would have done it as yours did - right away or after the first winter. It didn't and I'm sure it won't.
A crack free pad can be done, not as a gamble, but with proper design knowledge, proper construction methods, and a highly skilled and trustworthy general.
Good luck in resolving your problem. You are going to need it!
Dan