A FUNDAMENTAL FALLACY IN EARTH PRESSURE COMPUTATIONS

RANKINE'S AND COULOMB'S THEORIES OF EARTH PRESSURE COMPUTATIONS ARE ANALYZED. IT IS DETERMINED THAT THE FUNDAMENTAL ASSUMPTIONS OF RANKINE'S EARTH PRESSURE THEORY ARE INCOMPATABLE WITH THE KNOWN RELATION BETWEEN STRESS AND STRAIN IN SOILS, INCLUDING SAND. THE RESULTS OBTAINED FROM THE OTHER CLASSICAL THEORIES CAN ONLY BE ACCEPTED FOR PRACTICAL PURPOSES IF CERTAIN CONDITIONS CONCERNING THE LATERAL EXPANSION OF THE SUPPORTED SAND ARE SATISFIED. THE TOTAL LATERAL PRESSURE OF THE SAND DOES NOT ASSUME THE THEORETICAL VALUE UNLESS THE AVERAGE YIELD OF THE LATERAL SUPPORT EXCEEDS A CERTAIN MINIMUM VALUE. UNDER NORMAL CONDITIONS THIS REQUIREMENT IS SATISFIED BY BOTH THE RETAINING WALLS AND THE TIMBERING IN CUTS. THE DISTRIBUTION OF THE PRESSURE OF SAND ON THE BACK OF A LATERAL SUPPORT DOES NOT AGREE WITH THE THEORY UNLESS THE YIELD OF THE SUPPORT EXCEEDS IN EVERY POINT THE VALUES DETERMINED BY THE COULOMB THEORY. FOR IDENTICAL SOIL CONDITIONS AND EQUAL YIELD OF THE LATERAL SUPPORT, THE TOTAL LATERAL PRESSURE ON THE SUPPORT IS THE SAME. YET THE DISTRIBUTION OF THE PRESSURE OVER THIS SUPPORT VARIES ENORMOUSLY ACCORDING TO THE DISTRIBUTION OF THE YIELD OVER THE FACE OF THE BANK. THE MORE THIS DISTRIBUTION DEPARTS FROM A STRAIGHT LINE TO THE FOOT OF THE BANK, THE MORE IMPORTANT THE DEPARTURE FROM THE HYDROSTATIC PRESSURE DISTRIBUTION IS LIKELY TO BE.