The Researches on Slope Stability Evaluation with Inclinometric Measurements

User Rating: / 1
PoorBest 

The Researches on Slope Stability Evaluation with Inclinometric Measurements Authors: D. Domańska, A. Wichur Slopes are encountered either as naturally shaped or artifi cially molded terrain forms (as elements of various structures, e.g. tanks, trenches, heaps, embankments, earth banks); moreover, they are often present in surface mining. Slope stability analysis is usually conducted using the factor (degree) of slope safety or the factor (coeffi cient) of slope stability. Classic calculation methods, e.g. Fellenius’, Taylor’s, Bishop’s, Janbu’s have introduced the notion of slope safety factor in this fi eld, understood as the ratio of the limit value of the force required to induce displacement of the considered body of earth (stabilizing force) to the value of the acting sliding force (destabilizing force) (or the ratio of the moment causing its turn to the actual turning moment). The term of safety factor also functions in contemporary computer programs (e.g. in Z_Soil as Safety Factor SF), while its estimate is assessed during the generation of the medium’s limit state through the fi ctional reduction of its strength parameters, dismissing the arbitrary assumption of the slide surface shape. The defi nition also corresponds to the notion of slope stability factor or stability coeffi cient. The term of slope stability factor is incorporated in this paper and marked with the symbol SF. This work presents the concept of ground media stability evaluation drawn on the basis of horizontal displacement value analysis, measured with the use of inclinometers in the conditions of the „Bełchatów” brown coal pit. Action in this fi eld was undertaken in two fundamental directions: • on the basis of the proposed reduction of the soil elasticity modulus value (ch. 2), • on the basis of the conducted analysis of the state of soil effort in the inclinometer hole axis and its relation to slope stability (ch. 3). Both approaches incorporate computer calculations of slope stability factor made with the Z_Soil program. In order to evolve the slope stability evaluation method on the basis of inclinometric measurements with the use of computer calculations (ch. 2), the conditions of placement and the „in situ” results obtained from ten exploratory bore-holes were analyzed. The estimation procedure of allowable horizontal soil displacements was closely connected with the methodology of numerical determination of the slope stability factor, defi ned during the analysis of the stress and strain state in the modeled soil shield. The stability assessment of the earthen structures was conducted according to the following outline: • creating the computer models of slopes representing the inclinometers’ working conditions in the considered moments, which is exemplifi ed by Fig. 1 (in relation to all models notations containing the time point symbol were implemented, while the symbol served solely an ordinal function and did not denote any physical dimension, that is it did not refl ect any time intervals between particular measurements), • determining the slope stability factor SF in the aforementioned moments with a computer program, • calculation of horizontal displacements along the lines mapping the location of the inclinometer hole axes with a computer program, • estimating horizontal displacement critical values upon the reaching of which the slope instability may occur, • comparing the displacements registered in the inclinometer holes with their critical values and the evaluation of slope stability on the basis of the formulated criterion. While determining the slope stability factor SF with the computer method (the Z_Soil program in particular), it is assumed that the hypothetical slope stability failure will ensue at the reduced values of soil parameters c/SF and tanΦ/SF, not considering the reduction of the elasticity modulus (researches 602 show that this value does not infl uence the SF value). When making this assumption, it is essential to be aware of the fact that if such a state of slope stability failure did occur, then reducing the cohesion value and the shearing resistance angle tangent of the soil would inevitably lead to the decrease of the elasticity modulus value, and the vectors of soil displacements in the moment directly preceding the slope stability failure would be much larger than those specifi ed for the input values (i.e. for SF = 1.0). Owing to this, the reduction of the elasticity modulus value based on the correlatives between cohesion, angle of shearing resistance, soil elasticity modulus and the liquidity index of cohesive soils or the density index of noncohesive soils was proposed for this task. It was assumed that the introduction of the factor SF, reducing the values c and tanΦ, matches the simultaneous decrease of the soil elasticity modulus value E by a certain factor NE, in the consequence of which soil strains, particularly horizontal displacements, increase. A physical interpretation of this simultaneous reduction could be the stipulated plastifi cation of the cohesive soil (the change of the liquidity index from the assumed initial value IL0 to the fi nal IL) or the decrease of the noncohesive soil density index (from the initial value ID0 to the fi nal ID). In the aim of estimating the value of the factor NE reducing the soil elasticity modulus E (a general term, related to the modulus of linear deformation, as well as to oedometer modulus), the standard (PN-81/B-03020) served as a basis. The proposed reductive factor of soil elasticity NE was represented by the formula (3), and as a result of the analysis of the obtained relations, aiming at safety, horizontal displacements estimated on the grounds of the relations (4) were acknowledged as critical. For research purposes, it was assumed that in a given moment of time, characterized by a specifi c geometry of the system, the slope is stable when the horizontal displacement recorded by the inclinometer located within it does not exceed the critical value expressed by the formula (5). The obtained dependences were applied in the area of an example inclinometer hole of slope geometry at the time of inclinometer placement (t = 1) and of geotechnical parameters of soils specifi ed in Fig. 1, also assuming that cohesive soils at the initial state IL0 = 0.5 (Fig. 3) are dealt with. In ch. 3 a diagram of a slope with an inclinometer hole as in Fig. 4 was considered. The further assumption was that the slope material has the unit weight γ and is elastic-plastic at the limit condition described with the dependence (7) (the Coulomb-Mohr criterion). In the fi rst attempt Levy’s solution of the plane problem of the elasticity theory to the infi nite wedge loaded with the dead weight and the hydrostatic pressure of fl uid (Fig. 5) was applied. The solution achieved in this way has a disadvantageous property: for x → –∞ one obtains σx → –∞; which explains the possibility of its use solely in dam calculations. This inconvenience could be bypassed by assuming the application of Levy’s solution only to the right side of the slope (i.e. for x > 0 and α = 0), and for the left side of the slope (i.e. for x ≤ 0) the solution for the primary stress state in the rock mass could be used (see Fig. 4) (the formulae 18-21). After making appropriate calculations (with the assumption of the boundary condition: for y = H and x = x0 the horizontal displacement equals zero ux = 0) the formula (29) was obtained for the horizontal displacement in the hole axis. Zeroing the horizontal shift value ux stands in contradiction with the results of inclinometric measurements, therefore this model may not be used in this case as is. In the physical perspective it is clear, since the presence of the slope edge near the inclinometer hole distorts the primary undisturbed stress state around that hole. It seems obvious that the nearby location of the slope edge will cause the appearance of shearing stresses τxy, which had not occurred in the previously analyzed model. Thus the simplest correction of this model is the introduction of the shearing stress τxy of a constant value in the vicinity of the inclinometer hole (the formula 30). At that time the stress state will be given by the formulae (18), (19), (21) and the formula (30). In this case the horizontal displacements in the hole axis will be represented by the formula (31), and the horizontal displacement of the inclinometer hole head (x = x0, y = 0) – by the formula (32). The linear dependence ux along with the depth corresponds to relations occurring in reality (see Fig. 3), and the quantity t found in the formulae (31) and (32) facilitates their „calibration” in real conditions. Indeed, the measurement results of horizontal displacements in the inclinometer hole axis could be presented in the form of a linear function, for instance using the linear regression apparatus, then deriving the u0 value from this equation, and calculating the value t from the converted formula (32). By marking this value as t0 the formula (33) is obtained. The value determined in this manner could be implemented in further calculations, mainly those aiming at the evaluation of the rock mass effort in the inclinometer hole axis, which will be used for slope monitoring. The expression (34) was employed in the further considerations as an effort measure. After substituting the stress tensor components, one arrives at the function of effort in the inclinometer hole axis – the formula (38), and its value on the surface of the ground (i.e. for y = 0) 603 – the formula (39). After making appropriate calculations (the formulae 40-45) one ultimately arrives at the formula (46) for the critical displacement value of the inclinometer hole head in relation to the hole bottom, corresponding to the slope stability failure. Its application is explained on the example of an inclinometer located in the slope area (acc. to Fig. 1), the stability of which was estimated in ch. 2 on the basis of the method of reducing the soil elasticity modulus value (Fig. 3). The horizontal displacement critical values obtained in this way will be reliable in slope stability evaluation on the basis of inclinometric measurements. In the practical application of the method, it is recommended on the grounds of safety to reduce that value – in the case of the lack of other premises, the principles stated in the technical rules (Rozporządzenie 1996) or applied abroad (Gunaratne et al. 2006) should be assumed.

 

< Prev		Next >