Homogenising MPM test curves by using a hyperbolic model

Development of the interpretation of Ménard pressuremeter (MPM) data using the double hyperbolic model is still progressing. Simultaneously research work is undertaken to improve the starting phase of a test by a drastic decrease of both the stress relief and the remoulding around the borehole wall. Further a new software by the name of Xpressio® was developed which helps obtain MPM parameters in an industrial fashion. These advances now permit to submit MPM plots where the soil response can be modelled by a single hyperbola, a typical feature in the elastic plastic behaviour of an undisturbed soil. Then it becomes possible to characterise a homogeneous geological formation by a single hyperbolic response to cylindrical expansion, after compilation of a large number of hyperbolically modelled MPM tests curves at a job site. This powerful and versatile tool so obtained can be very helpful to the practising geotechnical engineer. ∑ ∑ ∑ ∑ ⋅ ∑ = n V n V p / )2 V 1 ( 2 1 / ) p V 1 ( a n p ∑ ∑ = ) V 1 a. ( b 2 ANALYSIS OF THE DOUBLE HYPERBOLIC BEST FIT 2.1 Statistical treatment of MPM curves The refined analysis of the expansion of such a cavity during one single test is certainly useful for giving to a soil mechanics scientist the opportunity to obtain a stress-strain law which is valid for all levels of strains ranging from rest condition up to failure for a soil at one particular depth. For the geotechnical engineer, the statistical analysis of a large number of tests in a lithologically homogeneous formation investigated by several boreholes drilled throughout its whole thickness is more important. It is one of the fundamental aspects of the pressuremeter method, for which Louis Ménard proposed to take into consideration the reciprocal or harmonic mean of the EM moduli and the geometrical mean for the pLM limit pressures. Whenever possible, histograms of EM and pLM for each geological formation are carefully analysed and compared with the lognormal distribution (Cassan, 1978). The EM/pLM ratio, which, to a greater or lesser extent, reflects the stretched appearance of the MPM second hyperbola, is also a criterion to discriminate between families of tests. 2.2 The help that the hyperbolic modelling can provide Can the next step be a comparison of the modelled curves by superposition? In the case of a site investigation involving several heterogeneous soils, this ambition would soon result in a series of conflicts, not only due to the natural diversity of the limit pressures but also to the shape of the curves (expressed by their EM/pLM value), and the contingencies particular to each type of curve (variable probe volume at borehole wall contact and variable curvature near the contact pressure) related to the quality of the preliminary drilling. The test curves to be compared with each other must therefore be sorted first into categories representing a relevant set from a geotechnical standpoint, or in other words which represent a type of soil and lithology exhibiting a relatively similar behaviour. It is not necessary to say that this selection cannot be automated, it constitutes part of the geotechnical engineer expertise, based firstly on the description of the cuttings during drilling and, if possible, from borehole logs taken from core sample examination at the same site. The statistical analysis referred to above should assist with making this choice. The statistical selection can be largely helped by looking for relatively tight cluster of dots in the [log(p*LM), log(EM/p*LM)] MPM tests Pressiorama® spectral diagram (Baud, 2005), where p*LM = pLM s hs, with s hs being the soil horizontal pressure at rest. Then a synoptical presentation to compare the various curves within one of these cluster can be conducted by assigning common axes to curves in p* and e, where p* = p-s hs and e = (V – V1)/Vp where p is the corrected pressure reading V the corrected volume reading V1 the start volume for the pseudo-elastic phase, Vp the volume of the probe when the contact with the borehole wall is reached. The e value varies between 0 and 1. This change can be done easily by considering the 4 coefficients a1, . a4 which appear in the tags of the final diagram for each MPM test computed with Xpressio® program as single hyperbolic fitting: v=a1 + a2.p + a3 / (a4-p) (2) This equation describes the soil reaction when the start phase of MPM test to the original at rest condition is eliminated when neglecting the first readings.