C172 pilot reported striking an obstacle with a main tire during an off field landing; causing the tire to lose pressure. The pilot immediately performed a takeoff and returned to an airport for repairs.

Narrative

The subject flight was initiated from ZZZ1 and departed Runway X at XA38 on Day 0. The purpose of the flight was to fly with a friend and explore the option of fishing at a few off-airport landing locations adjacent to creeks. The first landing spot was planned and occurred at an off-airport location approximately 20 nm southwest of ZZZ. During landing the right main landing gear tire; a 31' Bush wheel; contacted a small unknown object. Upon landing rollout while on the ground; it was determined that the right main tire was likely losing pressure. With the decreasing tire pressure and a few moments to make a decision; combined with uncertainty of access to the location; and unknown cellular service for rescue/assistance; as well as an unknown potential survival situation; the decision was made to depart the area and seek a more suitable location. This decision to takeoff/depart is the primary reason for this report; as a possible violation of CFR 14 91.7 (a) and/or (b) ('Civil Aircraft Airworthiness'); may have occurred albeit completely unintentional and unbeknownst at the time. A normal takeoff and departure occurred and subsequently a general plan was formulated. During flight; the pilot began reducing fuel load to mitigate any possible post-landing fire potential in the event of a ground loop; wing tip strike or prop/engine strike/noseover. The pilot planned to land with VFR minimum fuel reserves of at least 30 minutes; according to 14 CFR 91.151 VFR minimum fuel requirements. However during subsequent plan development; fuel reduction measures; and in multiple practices/attempts to land on the flattening tire; the fuel level may have reached a level below the 30 minute requirement. However; landing with adequate fuel per 91.151 was the planned intent throughout the flight.Finally; during the entire operation of the aircraft - both on the ground and in flight; it was the pilot's intent to operate the aircraft with utmost care and with great caution and prudence. There was never any intentional or known unintentional operation of the aircraft which would have violated 14 CFR 91.13 (a) and (b) Careless or Reckless operation. In fact; the opposite is true. The pilot made great effort to conduct the flight with extreme precautions in order to mitigate any further issues. As an example and to describe the prudence of operation; the pilot conducted the following procedures to attempt a safe outcome of the flight:After takeoff/departure from the first landing; the pilot made cellular contact with 4 people to discuss the situation and determine an appropriate course of action. The first individual that was contacted owns a grass strip near ZZZ1 airport; but it was determined to be unsuitable for landing with the aircraft's situation. The second person contacted owns and operates a very similar aircraft with the same tires; and the owner had recently experienced a blowout of one of his Bushwheels during operations. The pilot discussed at length the considerations and handling which would be experienced in the landing with a potentially flat tire. A final recommendation and decision was made to land on grass surface rather than pavement. The third person contacted owns a hangar and business at ZZZ and provided further information regarding emergency support at ZZZ. The final person contacted was located at ZZZ2 for the purposes of conducting practice approaches there before flying to ZZZ for the intended final/[priority] landing. Before flying to ZZZ2; the pilot flew toward and intended to practice approaches at ZZZ3; but glider operations precluded such action. The pilot then flew to ZZZ2 and conducted a roll-on style practice approach and touchdown to determine handling characteristics of the aircraft on both pavement and grass adjacent to the runway - with permission / supervision of ZZZ2 personnel. This was done without slowing to a speed where directional control might be lost. The pilot used the passenger's visual description of the tire (via the aircraft's 'bubble' style window) while the pilot felt the handling characteristics of the aircraft during rollo-on touch and go. The pilot then departed ZZZ2 to ZZZ; obtained ATIS and contacted ZZZ Approach Control where a request for priority handling was made. How the problem arose:- The problem arose due to tire damage from an unseen object along the off-airport landing/rollout area. Contributing factors:- Contributing factors were the higher than expected grass height which hid the object that caused the tire to begin deflating. However; having landed there before; the pilot believed that the area was free from objects.How was it discovered:- The flattening tire was discovered from a moderate bump felt during landing rollout combined with visual verification.Corrective actions:- In the short duration between occurrence and discovery of the impending tire flat; and within a perceived short-time to decide; the decision to takeoff and depart the area was made as a corrective action. This was done in order to preclude a potential survival situation; combined with unknown distance to roads/civilization; unknown cellular service; etc. - However; in order to prevent potential violation of CFR 14 91.7 and the subsequent necessity to request priority handling for landing; the pilot could have remained on the ground and sought assistance; hiked out; attempted cellular contact; etc.HUMAN PERFORMANCE CONSIDERATIONS:On the ground; the pilot perceived a worsening overall situation and had to make a decision whether to takeoff or remain on the ground. Due to the above mentioned considerations; combined with seemingly time-compressed risk management; the human factor of decision making (under time compression) may have led to a less than optimum decision.Options which may have been omitted from the time-compressed decision making process were: adequate time of day/daylight remaining; moderate/mild weather; actual proximity to civilization; potential cellular service; etc.At the time of the event; the judgment seemed reasonable and prudent when weighing all the perceived factors at hand in the moment. Time and location were a significant factors in the quality of human performance in risk management and decision making. If I had the opportunity to be in the same situation again (or to re-do this occurrence); I would remain on the ground at the off-airport location; and use the tools mentioned above to remedy the situation; find transportation/shelter; seek assistance; repair/replace the tire and fly out sometime later. Additionally; If airborne; I would plan to land approximately 10 minutes earlier to ensure adequate fuel reserves were met as required.