TWIN ENG PLT HAD A TXWY EXCURSION; AND THE L PROP HIT ROCKS AT GON.

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I DEPARTED GROTON; CT (GON). I FLEW TO MY HOME ARPT 44N (ABOUT A 35 MIN FLT) AND AFTER SHUTDOWN I NOTICED DAMAGE TO THE L ENG PROP. I HAD 3 PAX IN THE ACFT DURING THE FLT AND ASKED THEM IF THEY HAD NOTICED ANYTHING; WHICH COULD HAVE CAUSED THE DAMAGE. THE PAX IN THE L REAR SEAT STATED SHE OBSERVED WHAT LOOKED LIKE DIRT FLYING AROUND DURING THE TAXI; WHILE ON THE GND AT GROTON. DURING THE TAXI AT GROTON; THERE WAS A LOT OF NOISE IN THE ACFT. I HAD THE OVERHEAD SPEAKER ON FOR THE PAX TO LISTEN. THEY WERE TALKING TO EACH OTHER RATHER LOUDLY TRYING TO TALK ABOVE THE RADIO NOISE (THEY WERE EXCITED ABOUT GOING FLYING) AND ASKING ME QUESTIONS ABOUT THE PLANE; THE FLT; ETC. I WAS WEARING A HEADSET AND THERE WAS A LOT OF CHATTER ON THE RADIO; WHICH ALSO CONTRIBUTED TO THE NOISE. AFTER GOING OVER THE FLT IN MY HEAD; I RECALL BEING L OF THE TXWY MARKINGS FOR A FEW SECONDS AND MOVING BACK OVER TO THE R. THE ENGS RAN UP NORMALLY DURING THE PRE-TKOF CHK AND I DID NOT NOTICE ANY ABNORMAL INDICATIONS (VIBRATIONS; NOISE; UNUSUAL PERFORMANCE). THE ENGS PERFORMED NORMALLY DURING THE TKOF; CLB AND REST OF THE FLT. I AM NOT SURE WHERE THE DAMAGE OCCURRED; BUT THE MOST LIKELY ANSWER IS WHEN I WANDERED OFF TO THE L OF THE TXWY AT GROTON; THE L PROP STRUCK STONES; GRAVEL; OR POSSIBLY A TXWY MARKER; OR LIGHT OFF THE L SIDE OF THE TXWY; CAUSING THE DAMAGE. I FEEL THAT THE NOISE AND DISTRS INSIDE THE ACFT CAUSED ME TO LOSE MY AWARENESS OF WHERE I WAS DURING THE TAXI AT GROTON. I WILL IN THE FUTURE BRIEF ALL MY PAX ABOUT NOISE AND DISTRS WHILE IN THE AIRPLANE.