ACR ACFT ENCOUNTERS MUD AND DIRT LEFT BY A PREVIOUS ACFT THAT HAD A TXWY EXCURSION AT THE INTXN OF TAXIWAY'S A AND C AT CID.

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AFTER NORMAL APPROACH AND LANDING ON RWY 09 AT CEDAR RAPIDS; I TAXIED THE AIRPLANE OFF AT TXWY ALPHA AND PROCEEDED TO TAXI TOWARD TXWY CHARLEY FOR A TURN TO GET US TO GATE. AS WE ROUNDED THE CORNER I FELT A SLIGHT TUG ON THE RIGHT SIDE OF THE AIRPLANE; WHICH WAS BARELY NOTICEABLE. THE AIRPLANE WAS ON THE TXWY CENTERLINE FROM MY VIEW; SO I THOUGHT WE HAD A DRAGGING BRAKE. AFTER PARKING; I INSPECTED THE RIGHT MAIN GEAR AND SAW DIRT ON BOTH TIRES. I THEN ASSUMED THAT WE HAD GONE INTO THE GRASS AND CALLED MAINT WHO HAD THE AIRPLANE INSPECTED. ON ARRIVING AT THE ARPT THE NEXT MORNING I HAD ARPT SECURITY TAKE THE CREW TO THE AREA TO INSPECT IT. THIS WAS AFTER WE HAD BEEN INFORMED THAT THE ARPT AUTHORITIES HAD FOUND DIRT ON THE TXWY AT THE POINT WHERE WE EXPERIENCED THE BUMP. IT APPEARS TO ME THAT ANOTHER AIRPLANE MAY HAVE TAXIED OFF THE TXWY AND LEFT DIRT ON THE TXWY EDGE AND THAT THIS WAS WHAT WE RAN OVER. AFTER VISUAL INSPECTION OF THE TXWY AREA WHERE TXWY A JOINS TXWY C AT CID; IT APPEARS THAT THE CURVING TXWY CENTERLINE CONTRIBUTED TO APPROACHING THE EDGE OF THE TXWY DURING THE TURN FROM A TO C. WHERE THE LINE FROM TXWY A EXTENDED AN ADDITIONAL 15 TO 20 FT BEFORE IT CURVES INTO THE TXWY C CENTERLINE IT WOULD SIGNIFICANTLY INCREASE THE SAFETY MARGIN DURING THE TURN.