We present electrical conductivity measurements (at a fixed frequency of 1kHz) performed on three directions on limestone samples from the quarry of Meriel, during uniaxial tests of deformation up to failure. Samples were saturated from 100% to 80% by drainage. The samples showed brittle fracture with Young's modulus in the range 10-13 MPa. Formation factor (sample resistivity divided by water resistivity) values range between 2 and 4. In saturated conditions the electrical measurements reflect the initial rock compaction, followed by dilatancy due to new axial cracks formation and finally crack coalescence, fracture localization and failure. The conductivity increase is related to the crack porosity Phi_c which starts to increase at relatively low stress (31% of strength). The magnitude of the electrical conductivity variation is 1 - 4 % of the initial value. We show that when saturation is decreased the conductivity increase occurs earlier during the deformation process, from 68% to 17% of strength for 100% to 80% of water saturation respectively, so that the decrease in conductivity at low stress is less and less present. The induced relative rock conductivity variation in non saturated and undrained conditions is the result of two competing effects : the relative porosity variation, and the relative saturation variation during the deformation process. During compaction the electrical conductivity can show either a small decrease or a small increase : since the size of the partially saturated pores and cracks is reduced, the water occupies a larger percentage of the pore space, and then conductivity can be increased at this stage. We show a continuous increase of the conductivity both during the compaction and the dilatancy phases when the initial saturation is about 80-85%. Finally a power law is shown between conductivity and stress, so that the relative electrical conductivity increase is larger as one goes along the compression process. Just before failure, at 90-95% of strength, the rate increase in horizontal conductivity drops, so that the anisotropy between axial and radial conductivity is about 0.5-2%. At failure a drastic increase of this anisotropy can be seen, up to 5-6%.