Appendices – Microsoft Excel Workbooks on Compact Disk

Appendices – Microsoft Excel Workbooks on Compact Disk The MS Excel spreadsheet format is used for maximum portability. Microsoft provides MS Excel viewer free of charge at its Internet web site. The spreadsheets are kept as simple as possible. If MS Excel complains at the start about the security level of macros please click on Tools then Macro then Security button and adjust the security level to at least medium. The spreadsheet must be exited and re-entered for the change made to take place. The spreadsheets are applicable to the case studies and examples considered in this monograph. A.1 Coordinates of Earthquake Hypocentre and Site-to-Epicentre Distance The coordinates x, y, z are calculated by solution of three equations: 2 2 2 2 (x − xi ) + (y − yi ) + (z − zi ) = di , (A.1.1) where xi , yi , zi are coordinates of seismograph stations, i = 1...3, di is the source to station distance calculated from Equation (1.1). Depending on the orientation of the vertical z axis, the hypocentral depth could have positive or negative sign. A view of the spreadsheet results is shown below (Fig. A1.1). The site to epicentre distance in km and azimuth (the angle measured clockwise from North direction) between them are calculated from the formulae 180 1 − [sin(EN)∗ sin(SN) + cos(EN)∗ cos(SN)∗ cos(SE−EE)]2 Dis tan ce = 111 · · Atn π sin(EN)∗ sin(SN) + cos(EN)∗ cos(SN)∗ cos(SE-EE) ∗ = cos(SN) sin(SE-EE ) , Azimuth Arc sin Dis tan ce·π (A.1.2) sin 111·180 where EN and EE are the northings and eastings (in degrees) of an earthquake epicentre, SN and SE are the northings and eastings (in degrees) of a seismic station. For 211 212 Appendices Fig. A1.1 Spreadsheet ‘Coordinates of the hypocentre’ in workbook Appendix A.1 distance and azimuth between two stations, it is simply necessary to input the station northings and eastings in place of those data for an earthquake. Equation (A.1.2) is valid when the differences between two locations on Earth’s surface (stations or epicentres) does not exceed geographical 12◦, in which case Earth’s curvature has to be taken into account. A view of the spreadsheet results is shown below (Fig. A1.2). A.2 Limit Equilibrium Method for Northolt Slope Stability The Excel macro solves 2nw-1 equations of equilibrium of forces in the horizontal and vertical direction and nw equations of equilibrium of the rotating moments, where nw is the number of wedges into which a potential sliding mass is subdivided. From Fig. 4.1 it follows for the horizontal x direction: nw Ni sin αi − Ti cos αi + Nn+i−1 cos αn+i−1 − Tn+i−1 sin αn+i−1 − Nn+i i=1 cos αn+i + Tn+i sin αn+i + ch Wi + Fxi + GWi sin αi +GWi−1 cos αn+i−1 − GWi+1 cos αn+i = 0 (A.2.1) Appendices 213 Fig. A1.2 Spreadsheet ‘Site-to-epicentre distance’ in workbook Appendix A.1 For the vertical y direction: nw −1 −Ni cos αi − Ti sin αi + Nn+i−1 sin αn+i−1 + Tn+i−1 cos αn+i−1 i=1 − Nn+i sin αn+i − Tn+i cos αn+i + (1 ± cvm)Wi + Fyi − GWi cos αi + GWi−1 sin αn+i−1 − GWi+1 sin αn+i = 0 (A.2.2) For the moments around the centroids of wedges: nw + + + + + Ni dni Ti dti Nn+i−1dnn+i−1 Tn+i−1dtn+i−1 Nn+i dnn+i Tn+i dtn+i i=1 + + + + + = , Fxid fxi Fyid fyi GWi dwi GWi−1dwn+i−1 GWi+1dwn+i 0 (A.2.3) where dn,tf,w are the shortest distances between the lines of actions of the forces and wedge centroids. The procedure starts with a factor of safety of 1, calculates all axial and transver- th sal forces along wedge boundaries and checks the nw equation of equilibrium of 214 Appendices forces in the vertical direction. If the absolute value of the sum of all vertical forces th th actingonthenw wedge is greater than 2% of the nw wedge weight then the factor of safety is increased by 0.5 and the checking procedure continued. If after 15 th checks the sign of the sum of all vertical forces acting on the nw wedge has not been changed then the slope is considered unstable. If the sign of the sum of all vertical th forces acting on the nw wedge has been changed during stepping procedure then the last considered factor of safety is decreased by 0.05 until the absolute value of the th th sum of vertical forces acting on the nw wedge is smaller than 2% of the nw wedge weight. The axial forces at the bases of wedges are assumed at the centers of the bases except at the base of the last wedge and therefore the turning moments of the axial forces with respect to the centers of the bases are zero (shown as blanks). When a local factor of safety equals to 1.00 then shown number of steps of soil shear strength drops below the peak strength equals to the number of degrees below soil peak friction angle. Similarly, the peak cohesion value is decreased for the number of steps of strength drops times the difference between the peak and residual cohesion over the difference between the peak and residual friction angle. A number of iterations to deﬁne local factors of safety are performed at each step −1 because of a recursive dependence of the rate of joint thickness change (dt j,eγ j,e ) on local factor of safety Fj (i.e. the number of steps of strength drop below the peak value) and the local factor of safety Fj on the rate of joint thickness change (i.e. on −1 γ j(i),e in Equation 4.8, where γ j(i),e =dtj(i),e(tanαj(i)) . A view of the spreadsheet results is shown below (Fig. A2). A.3 Single Wedge for Three-Dimensional Slope Stability The spreadsheet provides: r Factor of safety against sliding of the wedge with/ without external resultant load r and anchor (cable) resultant force Factor of safety and most unfavorable azimuth and dip angle for given resultant r external load Minimal resultant anchor (cable) force and most favorable azimuth and dip angle for required factor of safety Critical acceleration acting on the wedge is determined by trial and error until the factor of safety against sliding of the wedge equals to 1.0 under applied resultant external load. A view of the spreadsheet results is shown below (Fig. A3). Appendices 215 Fig. A2 Spreadsheet ‘Results’ in workbook Appendix A.2 A.4 Co-Seismic Sliding Block The spreadsheets performs double integration in time of the difference between the base and critical acceleration of a sliding block in order to calculate permanent block sliding at time intervals (whenever the base acceleration exceeds the critical acceleration) and to calculate cumulative permanent block sliding. Down slope and level ground sliding can be considered. A view of the spreadsheet results is shown below (Fig. A4). A.5a Post-Seismic Sliding Blocks for Maidipo Slip in Frictional Soil The formulae used for the calculation are given in Appendix B of the paper by Ambraseys and Srbulov (1995). A view of the spreadsheet results is shown below (Fig. A5a). 216 Appendices Fig. A3 Spreadsheet ‘Results’ in workbook Appendix A.3 A.5b Post-Seismic Sliding Blocks for Catak Slip in Cohesive Soil The formulae used for the calculation are given in Appendix A of the paper by Ambraseys and Srbulov (1995). A view of the spreadsheet results is shown below (Fig. A5b). A.6 Bouncing Block Model of Rock Falls A view of the spreadsheet results is shown below (Fig. A6). A.7 Simpliﬁed Model for Soil and Rock Avalanches, Debris Run-Out and Fast Spreads A view of the spreadsheet results is shown below. No macros are used for the calcu- lations (Fig. A7). Appendices 217 Fig. A4 Spreadsheet ‘Results’ in workbook Appendix A.4 Fig. A5a Spreadsheet ‘Results’ in workbook Appendix A.5a 218 Appendices Fig. A5b Spreadsheet ‘Results’ in workbook Appendix A.5b Fig. A6 Spreadsheet ‘Bedrina 1’ in workbook Appendix A.6 Appendices 219 Fig. A7 Spreadsheet ‘Pandemonium Creek Avalanches’ in workbook Appendix A.7 A.8 Closed-Form Solution for Gravity Walls A view of the spreadsheet results is shown below (Fig. A8). A.9a Time Stepping Procedure for Kobe Wall A view of the spreadsheet results is shown below (Fig. A9a). A.9b Time Stepping Procedure for Kalamata Wall A view of the spreadsheet results is shown below (Fig. A9b). A.10 Accelerogram Averaging and Acceleration Response Spectra The averaging is performed according to Equation (6.57). A view of the spreadsheet results is shown below (Fig. A10.1). 220 Appendices Fig. A8 Spreadsheet ‘Results’ in workbook Appendix A.8 Fig. A9a Spreadsheet ‘Out’ in workbook Appendix A.9a Appendices 221 Fig. A9b Spreadsheet ‘Out’ in workbook Appendix A.9b Fig. A10.1 Spreadsheet ‘Averaged acceleration’ in workbook Appendix A.10 222 Appendices Acceleration response spectra represent the peak values of the absolute accelerations of single degree of freedom oscillators (SDOFO) with different peri- ods (frequencies) of vibrations. The absolute accelerations are obtained from the formula t 1 − 2 · ς 2 −ς·ωs ·(t−τ) Abs.acc.(t) = ωs · · Ground acc.(τ) · e · 1 − ς 2 0 2 sin ωs · 1 − ς · (t − τ) · dτ + t −ς·ωs ·(t−τ) 2 · ωs · ς · Ground acc.(τ) · e · 0 2 cos ωs · 1 − ς · (t − τ) · dτ (A.10.1) where the circular frequency of a SDOFO ωs is according to Equation (6.59), ζ is a part of the critical damping, t is time.

Load more