A C550 CPR JET HAS A CRITICAL GND CONFLICT WITH LNDG TFC ON RWY 20 AT RIC. THE C550 HAD BEEN CLRED TO CROSS RWY 20; HOLD SHORT OF RWY 16.

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AT APPROX XA25 LCL ON MAY/XA/99 OUR CE550 DEPARTED FBO WITH TAXI INSTRUCTIONS FROM RIC GND CTL TO 'TAXI TO RWY 16; CROSS RWY 20; HOLD SHORT OF RWY 16 DUE TO TFC LNDG RWY 34' (OPPOSITE DIRECTION). BOTH THE PIC AND FO AGREED THAT THE FO/PNF'S READBACK OF THE TAXI INSTRUCTIONS REFLECTED THE ABOVE XMISSION FROM GND CTL. IF THERE WAS AN ERROR IN THE READBACK; NO CORRECTION WAS MADE BY GND CTL. THE LAYOUT OF THE RIC ARPT HAS THE APCH ENDS OF RWY 20 AND RWY 16 IN VERY CLOSE PROX WHICH FROM AN APEX. AS WE TAXIED; WE CONTINUED TO MONITOR GND CTL. I; THE PIC/PF; TAXIED ON TXWY R TOWARDS RWY 20 AND RWY 16. MY ATTN WAS DIRECTED TOWARDS COMPLETING THE TAXI CHKLIST; LOOKING FOR THE RWY MARKING LIGHTS; HOLD SHORT LINE FOR RWY 16; AND LOOKING FOR THE LNDG TFC ON RWY 34. BOTH THE PIC AND FO AGREED THAT GND CTL NEVER CALLED TFC FOR RWY 20 AND THAT WE DID NOT ACKNOWLEDGE ANY XMISSION CONCERNING TFC FOR RWY 20. JUST AS THE NOSE OF OUR ACFT WAS ABOUT TO CROSS THE EDGE OF RWY 20; THE FO SAW THE LNDG LIGHTS OF THE ACFT WHICH WAS LNDG ON RWY 20. HE CALLED THE TFC; I IMMEDIATELY STOPPED; AND THE ACFT LANDED WITHOUT INCIDENT. WE HAD REMAINED ON GND CTL WITH NO ADVISORY XMISSIONS FROM THE TWR TO HOLD SHORT OF RWY 20 DUE TO LNDG TFC. HOWEVER; WHEN I SWITCHED THE #2 RADIO TO THE TWR FREQ; WHILE CONTINUING TO MONITOR GND ON THE #1 RADIO; WE HEARD ATC CALLING US ON THE TWR FREQ. MOMENTARILY; THEY CALLED US ON THE GND FREQ AND ASKED US IF WE DID NOT SEE THE HOLD SHORT FOR RWY 20. I REPLIED; 'WE UNDERSTOOD OUR INSTRUCTIONS TO CROSS RWY 20 AND HOLD SHORT OF RWY 16.' GND CTL RESPONDED; 'NEGATIVE; HOLD SHORT OF RWY 20.' AT APPROX THE SAME TIME; THE OTHER ARRIVING ACFT LANDED ON RWY 34. SHORTLY THEREAFTER; GND CTL TOLD US TO 'EXECUTE A 180 DEG TURN AND HOLD SHORT ON RWY 20 DUE TO LNDG TFC ON RWY 2.' WE IMMEDIATELY COMPLIED WITH THOSE INSTRUCTIONS. AFTER THE ACFT CLRED RWY 2; WE WERE INSTRUCTED TO TAXI INTO POS ON RWY 16 AND CLRED FOR TKOF. NO OTHER COMMENTS WERE FORTHCOMING FROM THE TWR. IT APPEARS THAT RIC TWR/GND ELECTED TO HAVE 3 ACFT; ALL WITHIN THE ATA; LAND ON 3 DIFFERENT RWYS; AND IN 3 DIFFERENT DIRECTIONS WITHIN A FEW MINS OF ONE ANOTHER. GND CTL NEVER ADVISED US; AS THEY MONITORED OUR TAXI PROGRESS; TO HOLD SHORT OF RWY 20 OR TFC ON SHORT FINAL TO RWY 20. THIS LACK OF ADVISORIES; AS WELL AS ANOTHER ACFT LNDG OPPOSITE DIRECTION ON OUR DEP RWY 16; CONTRIBUTED TO THE CONFLICT. IF AN ERROR WAS MADE IN OUR INITIAL READBACK OF THE TAXI INSTRUCTIONS; GND CTL NEVER ADVISED US; NEGATING THE PRIMARY PURPOSE FOR THE READBACK OF INSTRUCTIONS. IT ALSO APPEARS THAT TWR WAS ATTEMPTING TO COM WITH US ON THE TWR FREQ; WHILE WE REMAINED ON THE GND FREQ. WE RECEIVED NO INSTRUCTIONS TO MONITOR TWR FREQ; AND WE WERE NOT IN A POS TO CHANGE OVER TO THE TWR FREQ; IE; HOLDING SHORT OF RWY 16.