TítuloProbabilismo explícito en la corrosión de armaduras en las estructuras de hormigón sometidas al ambiente marino de la costa gallega
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(2) Propuesta Probabilista a 50 años. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=2 cm.. -----------------------------------------------------------------------------Job name ............ : 8r2 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 24.02.2011 Time(hh:mm) ........ : 13:43 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: DEFFUNC(1)()=D0*(t0/t)^n DEFFUNC(2)()=5725*(1/293-1/(T+273)) DEFFUNC(3)()=(T/20)*exp(FUNC(2)) FLIM(1)=x-2*(1-sqrt(cx/cs))*sqrt(3*0.315*FUNC(1)*FUNC(3)*t*ke*ka) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************. Variable: x ; No. on Comment : Recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector = 1 cm : Normal (2) : Mean & Std.Dev. (0) = 2.000 ( 0.200000000000000E+01) = 0.4000 ( 0.400000000000000E+00) = 0.2000 ( 0.200000000000000E+00) = 2.000 ( 0.200000000000000E+01) = 0.4000 ( 0.400000000000000E+00). Variable: cx ; No. on X-vector = 2 Comment : Conc. Critica Cloruros en % cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.1000 ( 0.100000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.1000 ( 0.100000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 3 Comment : Conc. Super. Cloruros en% cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.8000 ( 0.800000000000000E+00) Standard deviation........ = 0.1600 ( 0.160000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.8000 ( 0.800000000000000E+00) Distr.Param.no.2 : sigma = 0.1600 ( 0.160000000000000E+00) ------------------------Variable: n ; No. on Comment : Factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 4. : Normal (2) : Mean & Std.Dev. (0) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01) = 0.2000 ( 0.200000000000000E+00) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01). Variable: T ; No. on X-vector = 5 Comment : Temperatura en ºC Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev.. (0). Análisis Probabilista. E. Mosquera..
(3) Propuesta Probabilista a 50 años. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. = = = = =. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=2 cm.. 18.00 3.600 0.2000 18.00 3.600. ( 0.180000000000000E+02) ( 0.360000000000000E+01) ( 0.200000000000000E+00) ( 0.180000000000000E+02) ( 0.360000000000000E+01). -- Constant (deterministic) Parameters -Parameter :t0 ; No. on PVEC= Comment : tiempo inicial en años. 1 with value =. Parameter :t ; No. on PVEC= Comment : tiempo final en años. 2 with value =. 50.00. Parameter :ke ; No. on PVEC= 3 with value = Comment : Param de Ejecución y curado. 2.400. Parameter :ka ; No. on PVEC= Comment : Param de microclima. 0.7670E-01. 4 with value =. 0.7000. Parameter :D0 ; No. on PVEC= 5 with value = Comment : Coef. de Difusión en m2/s 10^-12 -------------------------. 3.000. (x (cs (T. ; ; ;. (Lower bounds on U-space variables) 1; -36.69 ) (cx ; 2; 3; -36.69 ) (n ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (x (cs (T. ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (cx ; 2; 0.000 ; 3; 0.000 ) (n ; 4; 0.000 ; 5; 0.000 ). ) ). (x (cs (T. --; ; ;. ) ). X-start: Median values from U=0 1; 2.000 ) (cx ; 3; 0.8000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.4500. (Upper bounds on U-space variables) (x ; 1; 36.69 ) (cx ; 2; 36.69 ) (cs ; 3; 36.69 ) (n ; 4; 36.69 ) (T ; 5; 36.69 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E-03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 0.6657 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 0.648 Corresponding approximate prob.of failure = 0.2586 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.1388E-07 and Vector u-* (beta-point) : (x ; 1; -0.2317 ) (cx ; 2; -0.3399 ) (cs ; 3; 0.2989 ) (n ; 4; -0.3222 ) (T ; 5; 0.2391 ) Normalized U-space gradient (alfa-U) with norm = 1.680 : (x ; 1; 0.3578 ) (cx ; 2; 0.5247 ) (cs ; 3; -0.4615 ) (n ; 4; 0.4974 ) (T ; 5; -0.3692 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.3578 ) (cx ; 2; 0.5247 ) (cs ; 3; -0.4615 ) (n ; 4; 0.4974 ) (T ; 5; -0.3692 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 1.907 ) (cx ; 2; 0.4660 ) (cs ; 3; 0.8478 ) (n ; 4; 0.4210 ) (T ; 5; 18.86 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 1.502 ) (cx ; 2; 8.813 ) (cs ; 3; -4.845 ) (n ; 4; 9.283 ) (T ; 5; -0.1722 ) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(4) Propuesta Probabilista a 50 años. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=2 cm.. Constant Parameters (PVEC): (t0 ; 1; 7.6700E-02) (t ; 2; 50.00 ) (ke ; 3; 2.400 ) (ka ; 4; 0.7000 ) (D0 ; 5; 3.000 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 5 Calls of state-function : 31 -----------------------------------------------------------------------------***************************************************** Report of an error by traceback facility (*YERR*) : Error in module :YSOMHO Warning from 2nd-order improvement: Absolute value of 1st-order beta(FORMBE) < 1 . 2nd-order improvement by Hohenbichlers formula might be inaccurate because it is based on asymptotic theory ! ----- Second-Order Improvement : ----radii of curvature in U-space : -4.860 -42.854 44.546. 17.218. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 0.708 Corresponding prob. of failure = 0.23942. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 30 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 50 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 70 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 90 E(Sim)=. 0.925 0.961 0.941 0.955 0.982 0.997 1.05 1.03 1.02. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 3.63 3.68 4.14 3.33 2.91 3.08 3.65 3.31 3.07. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 0.693 Corresponding prob. of failure = 0.24400 Correction factor by simulation = 1.019 Coefficient of Variation in % = 2.868 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 1.89866 2.00000 0.949 (cx : 2) 0.462840 0.500000 0.926 (cs : 3) 0.852290 0.800000 1.065 (n : 4) 0.418298 0.450000 0.930 (T : 5) 18.9411 18.0000 1.052 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 1.651 4.94E-02 -0.9315 -0.5698 1.250 1.450 7.35E-02 -0.7370 -0.6451 1.500 1.287 9.90E-02 -0.6073 -0.7224 1.750 1.152 0.12 -0.5147 -0.8033 2.000 1.035 0.15 -0.4454 -0.8892 2.250 0.9339 0.18 -0.3915 -0.9817 2.500 0.8455 0.20 -0.3486 -1.083 2.750 0.7656 0.22 -0.3135 -1.193 3.000 0.6934 0.24 -0.2843 -1.317 3.250 0.6278 0.27 -0.2597 -1.456 3.500 0.5677 0.29 -0.2387 -1.614 3.750 0.5123 0.30 -0.2205 -1.797 4.000 0.4610 0.32 -0.2046 -2.011 4.250 0.4134 0.34 -0.1907 -2.265 4.500 0.3689 0.36 -0.1783 -2.575 4.750 0.3272 0.37 -0.1673 -2.960 5.000 0.2881 0.39 -0.1574 -3.453 5.250 0.2512 0.40 -0.1485 -4.110 5.500 0.2164 0.41 -0.1404 -5.021 5.750 0.1834 0.43 -0.1330 -6.397 6.000 0.1521 0.44 -0.1263 -8.697 6.250 0.1224 0.45 -0.1202 -13.33. Análisis Probabilista. E. Mosquera..
(5) Propuesta Probabilista a 50 años. 6.500 6.750 7.000 7.250 7.500 7.750 8.000 8.250 8.500 8.750 9.000 9.250 9.500 9.750 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00. 0.9403E-01 0.8602E-01 0.6007E-01 0.3525E-01 0.1146E-01 -0.1136E-01 -0.3328E-01 -0.5436E-01 -0.7465E-01 -0.9420E-01 -0.1131 -0.1313 -0.1488 -0.1658 -0.1823 -0.1982 -0.2137 -0.2286 -0.2431 -0.2572 -0.2709 -0.2842 -0.2972 -0.3098 -0.3220 -0.3340 -0.3456 -0.3570 -0.3680 -0.3788 -0.3894 -0.3996 -0.4097 -0.4195 -0.4291. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=2 cm.. 0.46 0.47 0.48 0.49 0.50 0.50 0.51 0.52 0.53 0.54 0.55 0.55 0.56 0.57 0.57 0.58 0.58 0.59 0.60 0.60 0.61 0.61 0.62 0.62 0.63 0.63 0.64 0.64 0.64 0.65 0.65 0.66 0.66 0.66 0.67. -0.1145 -0.1093 -0.1044 -0.9995E-01 -0.9577E-01 -0.9188E-01 -0.8824E-01 -0.8484E-01 -0.8165E-01 -0.7865E-01 -0.7583E-01 -0.7317E-01 -0.7066E-01 -0.6829E-01 -0.6605E-01 -0.6392E-01 -0.6190E-01 -0.5996E-01 -0.5813E-01 -0.5640E-01 -0.5475E-01 -0.5317E-01 -0.5167E-01 -0.5023E-01 -0.4886E-01 -0.4754E-01 -0.4629E-01 -0.4508E-01 -0.4392E-01 -0.4281E-01 -0.4175E-01 -0.4073E-01 -0.3974E-01 -0.3880E-01 -0.3788E-01. -27.58 -743.8 -26.38 -13.61 -9.242 -7.038 -5.708 -4.817 -4.178 -3.697 -3.322 -3.020 -2.773 -2.567 -2.391 -2.240 -2.109 -1.993 -1.891 -1.800 -1.718 -1.645 -1.578 -1.517 -1.461 -1.409 -1.362 -1.318 -1.277 -1.239 -1.203 -1.170 -1.138 -1.109 -1.081. Representative Alphas of Variables FLIM(1), 8r2.pti. x cx cs n T Sum of a². Análisis Probabilista. 0.36 0.52 -0.46 0.50 -0.37 1.00. E. Mosquera..
(6) Propuesta Probabilista a 50 años. 3.00. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=2 cm.. Reliability Index FLIM(1), 8r2.pti. Beta. 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00. 0.0. 1.0. Failure Probability 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0 1.0. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. 11.0. 12.0. 13.0. 14.0. 15.0. 11.0. 12.0. 13.0. 14.0. 15.0. Failure Probability FLIM(1), 8r2.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. Análisis Probabilista. E. Mosquera..
(7) Propuesta Probabilista a 50 años. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=3 cm.. -----------------------------------------------------------------------------Job name ............ : 8r3 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 24.02.2011 Time(hh:mm) ........ : 13:44 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: DEFFUNC(1)()=D0*(t0/t)^n DEFFUNC(2)()=5725*(1/293-1/(T+273)) DEFFUNC(3)()=(T/20)*exp(FUNC(2)) FLIM(1)=x-2*(1-sqrt(cx/cs))*sqrt(3*0.315*FUNC(1)*FUNC(3)*t*ke*ka) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************. Variable: x ; No. on Comment : Recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector = 1 cm : Normal (2) : Mean & Std.Dev. (0) = 3.000 ( 0.300000000000000E+01) = 0.6000 ( 0.600000000000000E+00) = 0.2000 ( 0.200000000000000E+00) = 3.000 ( 0.300000000000000E+01) = 0.6000 ( 0.600000000000000E+00). Variable: cx ; No. on X-vector = 2 Comment : Conc. Critica Cloruros en % cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.1000 ( 0.100000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.1000 ( 0.100000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 3 Comment : Conc. Super. Cloruros en% cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.8000 ( 0.800000000000000E+00) Standard deviation........ = 0.1600 ( 0.160000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.8000 ( 0.800000000000000E+00) Distr.Param.no.2 : sigma = 0.1600 ( 0.160000000000000E+00) ------------------------Variable: n ; No. on Comment : Factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 4. : Normal (2) : Mean & Std.Dev. (0) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01) = 0.2000 ( 0.200000000000000E+00) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01). Variable: T ; No. on X-vector = 5 Comment : Temperatura en ºC Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev.. (0). Análisis Probabilista. E. Mosquera..
(8) Propuesta Probabilista a 50 años. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. = = = = =. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=3 cm.. 18.00 3.600 0.2000 18.00 3.600. ( 0.180000000000000E+02) ( 0.360000000000000E+01) ( 0.200000000000000E+00) ( 0.180000000000000E+02) ( 0.360000000000000E+01). -- Constant (deterministic) Parameters -Parameter :t0 ; No. on PVEC= Comment : tiempo inicial en años. 1 with value =. Parameter :t ; No. on PVEC= Comment : tiempo final en años. 2 with value =. 50.00. Parameter :ke ; No. on PVEC= 3 with value = Comment : Param de Ejecución y curado. 2.400. Parameter :ka ; No. on PVEC= Comment : Param de microclima. 0.7670E-01. 4 with value =. 0.7000. Parameter :D0 ; No. on PVEC= 5 with value = Comment : Coef. de Difusión en m2/s 10^-12 -------------------------. 3.000. (x (cs (T. ; ; ;. (Lower bounds on U-space variables) 1; -36.69 ) (cx ; 2; 3; -36.69 ) (n ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (x (cs (T. ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (cx ; 2; 0.000 ; 3; 0.000 ) (n ; 4; 0.000 ; 5; 0.000 ). ) ). (x (cs (T. --; ; ;. ) ). X-start: Median values from U=0 1; 3.000 ) (cx ; 3; 0.8000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.4500. (Upper bounds on U-space variables) (x ; 1; 36.69 ) (cx ; 2; 36.69 ) (cs ; 3; 36.69 ) (n ; 4; 36.69 ) (T ; 5; 36.69 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E-03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 1.666 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.369 Corresponding approximate prob.of failure = 8.5548E-02 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.1058E-07 and Vector u-* (beta-point) : (x ; 1; -0.5668 ) (cx ; 2; -0.6754 ) (cs ; 3; 0.5284 ) (n ; 4; -0.7327 ) (T ; 5; 0.5290 ) Normalized U-space gradient (alfa-U) with norm = 0.8698 : (x ; 1; 0.4141 ) (cx ; 2; 0.4935 ) (cs ; 3; -0.3860 ) (n ; 4; 0.5353 ) (T ; 5; -0.3865 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.4141 ) (cx ; 2; 0.4935 ) (cs ; 3; -0.3860 ) (n ; 4; 0.5353 ) (T ; 5; -0.3865 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 2.660 ) (cx ; 2; 0.4325 ) (cs ; 3; 0.8845 ) (n ; 4; 0.3841 ) (T ; 5; 19.90 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.6004 ) (cx ; 2; 4.292 ) (cs ; 3; -2.099 ) (n ; 4; 5.174 ) (T ; 5; -9.3392E-02) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(9) Propuesta Probabilista a 50 años. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=3 cm.. Constant Parameters (PVEC): (t0 ; 1; 7.6700E-02) (t ; 2; 50.00 ) (ke ; 3; 2.400 ) (ka ; 4; 0.7000 ) (D0 ; 5; 3.000 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 7 Calls of state-function : 43 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -5.524 -42.914 40.687. 14.343. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.408 Corresponding prob. of failure = 7.95541E-02. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 30 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 50 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 70 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 90 E(Sim)=. 0.948 0.988 0.998 0.988 1.01 1.01 1.04 1.04 1.04. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 5.64 4.67 4.29 3.63 3.61 3.31 3.93 3.50 3.21. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.392 Corresponding prob. of failure = 8.19240E-02 Correction factor by simulation = 1.030 Coefficient of Variation in % = 3.123 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 2.65014 3.00000 0.883 (cx : 2) 0.430515 0.500000 0.861 (cs : 3) 0.886974 0.800000 1.109 (n : 4) 0.382161 0.450000 0.849 (T : 5) 19.9593 18.0000 1.109 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 2.392 8.38E-03 -0.9454 -0.3942 1.250 2.188 1.44E-02 -0.7561 -0.4321 1.500 2.020 2.17E-02 -0.6286 -0.4679 1.750 1.880 3.01E-02 -0.5369 -0.5024 2.000 1.758 3.94E-02 -0.4678 -0.5362 2.250 1.651 4.94E-02 -0.4139 -0.5697 2.500 1.556 5.99E-02 -0.3708 -0.6031 2.750 1.470 7.08E-02 -0.3354 -0.6367 3.000 1.392 8.19E-02 -0.3060 -0.6706 3.250 1.321 9.33E-02 -0.2810 -0.7050 3.500 1.255 0.10 -0.2596 -0.7401 3.750 1.195 0.12 -0.2411 -0.7759 4.000 1.138 0.13 -0.2249 -0.8126 4.250 1.085 0.14 -0.2106 -0.8504 4.500 1.035 0.15 -0.1979 -0.8893 4.750 0.9887 0.16 -0.1866 -0.9295 5.000 0.9446 0.17 -0.1764 -0.9711 5.250 0.9039 0.18 -0.1672 -1.014 5.500 0.8645 0.19 -0.1588 -1.059 5.750 0.8270 0.20 -0.1512 -1.106 6.000 0.7913 0.21 -0.1442 -1.155 6.250 0.7572 0.22 -0.1378 -1.206 6.500 0.7246 0.23 -0.1318 -1.260 6.750 0.6935 0.24 -0.1264 -1.317 7.000 0.6635 0.25 -0.1213 -1.376 7.250 0.6348 0.26 -0.1166 -1.439 7.500 0.6072 0.27 -0.1122 -1.506 7.750 0.5806 0.28 -0.1080 -1.577 8.000 0.5550 0.29 -0.1042 -1.652. Análisis Probabilista. E. Mosquera..
(10) Propuesta Probabilista a 50 años. 8.250 8.500 8.750 9.000 9.250 9.500 9.750 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00. 0.5303 0.5064 0.4834 0.4611 0.4394 0.4185 0.3983 0.3786 0.3595 0.3409 0.3228 0.3052 0.2881 0.2714 0.2552 0.2394 0.2239 0.2089 0.1942 0.1798 0.1658 0.1521 0.1387 0.1256 0.1128 0.1002 0.8791E-01 0.7588E-01. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=3 cm.. 0.30 0.31 0.31 0.32 0.33 0.34 0.35 0.35 0.36 0.37 0.37 0.38 0.39 0.39 0.40 0.41 0.41 0.42 0.42 0.43 0.43 0.44 0.44 0.45 0.46 0.46 0.46 0.47. -0.1006 -0.9717E-01 -0.9397E-01 -0.9095E-01 -0.8810E-01 -0.8541E-01 -0.8282E-01 -0.8040E-01 -0.7810E-01 -0.7591E-01 -0.7383E-01 -0.7184E-01 -0.6995E-01 -0.6814E-01 -0.6641E-01 -0.6475E-01 -0.6317E-01 -0.6165E-01 -0.6019E-01 -0.5879E-01 -0.5744E-01 -0.5615E-01 -0.5490E-01 -0.5370E-01 -0.5255E-01 -0.5143E-01 -0.5036E-01 -0.4932E-01. -1.733 -1.819 -1.911 -2.010 -2.118 -2.235 -2.360 -2.499 -2.652 -2.820 -3.007 -3.217 -3.452 -3.719 -4.025 -4.378 -4.792 -5.282 -5.874 -6.601 -7.518 -8.709 -10.32 -12.62 -16.17 -22.40 -36.10 -91.20. Representative Alphas of Variables FLIM(1), 8r3.pti. x cx cs n T Sum of a². Análisis Probabilista. 0.41 0.49 -0.39 0.54 -0.39 1.00. E. Mosquera..
(11) Propuesta Probabilista a 50 años. 3.00. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=3 cm.. Reliability Index FLIM(1), 8r3.pti. Beta. 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00. 0.0. 1.0. Failure Probability 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0 1.0. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. 11.0. 12.0. 13.0. 14.0. 15.0. 11.0. 12.0. 13.0. 14.0. 15.0. Failure Probability FLIM(1), 8r3.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. Análisis Probabilista. E. Mosquera..
(12) Propuesta Probabilista a 50 años. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=4 cm.. -----------------------------------------------------------------------------Job name ............ : 8r4 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 24.02.2011 Time(hh:mm) ........ : 19:22 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: DEFFUNC(1)()=D0*(t0/t)^n DEFFUNC(2)()=5725*(1/293-1/(T+273)) DEFFUNC(3)()=(T/20)*exp(FUNC(2)) FLIM(1)=x-2*(1-sqrt(cx/cs))*sqrt(3*0.315*FUNC(1)*FUNC(3)*t*ke*ka) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************. Variable: x ; No. on Comment : Recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector = 1 cm : Normal (2) : Mean & Std.Dev. (0) = 4.000 ( 0.400000000000000E+01) = 0.8000 ( 0.800000000000000E+00) = 0.2000 ( 0.200000000000000E+00) = 4.000 ( 0.400000000000000E+01) = 0.8000 ( 0.800000000000000E+00). Variable: cx ; No. on X-vector = 2 Comment : Conc. Critica Cloruros en % cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.1000 ( 0.100000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.1000 ( 0.100000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 3 Comment : Conc. Super. Cloruros en% cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.8000 ( 0.800000000000000E+00) Standard deviation........ = 0.1600 ( 0.160000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.8000 ( 0.800000000000000E+00) Distr.Param.no.2 : sigma = 0.1600 ( 0.160000000000000E+00) ------------------------Variable: n ; No. on Comment : Factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 4. : Normal (2) : Mean & Std.Dev. (0) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01) = 0.2000 ( 0.200000000000000E+00) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01). Variable: T ; No. on X-vector = 5 Comment : Temperatura en ºC Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev.. (0). Análisis Probabilista. E. Mosquera..
(13) Propuesta Probabilista a 50 años. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. = = = = =. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=4 cm.. 18.00 3.600 0.2000 18.00 3.600. ( 0.180000000000000E+02) ( 0.360000000000000E+01) ( 0.200000000000000E+00) ( 0.180000000000000E+02) ( 0.360000000000000E+01). -- Constant (deterministic) Parameters -Parameter :t0 ; No. on PVEC= Comment : tiempo inicial en años. 1 with value =. Parameter :t ; No. on PVEC= Comment : tiempo final en años. 2 with value =. 50.00. Parameter :ke ; No. on PVEC= 3 with value = Comment : Param de Ejecución y curado. 2.400. Parameter :ka ; No. on PVEC= Comment : Param de microclima. 0.7670E-01. 4 with value =. 0.7000. Parameter :D0 ; No. on PVEC= 5 with value = Comment : Coef. de Difusión en m2/s 10^-12 -------------------------. 3.000. (x (cs (T. ; ; ;. (Lower bounds on U-space variables) 1; -36.69 ) (cx ; 2; 3; -36.69 ) (n ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (x (cs (T. ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (cx ; 2; 0.000 ; 3; 0.000 ) (n ; 4; 0.000 ; 5; 0.000 ). ) ). (x (cs (T. --; ; ;. ) ). X-start: Median values from U=0 1; 4.000 ) (cx ; 3; 0.8000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.4500. (Upper bounds on U-space variables) (x ; 1; 36.69 ) (cx ; 2; 36.69 ) (cs ; 3; 36.69 ) (n ; 4; 36.69 ) (T ; 5; 36.69 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E-03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 2.666 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.904 Corresponding approximate prob.of failure = 2.8442E-02 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.1336E-07 and Vector u-* (beta-point) : (x ; 1; -0.8666 ) (cx ; 2; -0.9001 ) (cs ; 3; 0.6528 ) (n ; 4; -1.045 ) (T ; 5; 0.7401 ) Normalized U-space gradient (alfa-U) with norm = 0.6594 : (x ; 1; 0.4551 ) (cx ; 2; 0.4727 ) (cs ; 3; -0.3428 ) (n ; 4; 0.5485 ) (T ; 5; -0.3886 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.4551 ) (cx ; 2; 0.4727 ) (cs ; 3; -0.3428 ) (n ; 4; 0.5485 ) (T ; 5; -0.3886 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 3.307 ) (cx ; 2; 0.4100 ) (cs ; 3; 0.9044 ) (n ; 4; 0.3560 ) (T ; 5; 20.66 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.3751 ) (cx ; 2; 3.117 ) (cs ; 3; -1.413 ) (n ; 4; 4.019 ) (T ; 5; -7.1193E-02) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(14) Propuesta Probabilista a 50 años. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=4 cm.. Constant Parameters (PVEC): (t0 ; 1; 7.6700E-02) (t ; 2; 50.00 ) (ke ; 3; 2.400 ) (ka ; 4; 0.7000 ) (D0 ; 5; 3.000 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 8 Calls of state-function : 49 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -6.101 -44.119 38.907. 12.626. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.928 Corresponding prob. of failure = 2.69405E-02. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 30 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 50 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 70 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 90 E(Sim)=. 0.938 0.985 0.999 0.987 1.01 1.01 1.04 1.05 1.05. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 7.06 5.71 5.15 4.36 4.25 3.93 4.86 4.34 3.94. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.913 Corresponding prob. of failure = 2.78889E-02 Correction factor by simulation = 1.035 Coefficient of Variation in % = 3.816 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 3.29814 4.00000 0.825 (cx : 2) 0.408874 0.500000 0.818 (cs : 3) 0.905737 0.800000 1.132 (n : 4) 0.354830 0.450000 0.789 (T : 5) 20.6972 18.0000 1.150 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 2.906 1.83E-03 -0.9311 -0.3168 1.250 2.713 3.33E-03 -0.7515 -0.3440 1.500 2.547 5.43E-03 -0.6290 -0.3687 1.750 2.406 8.05E-03 -0.5402 -0.3917 2.000 2.284 1.12E-02 -0.4728 -0.4135 2.250 2.176 1.48E-02 -0.4200 -0.4343 2.500 2.080 1.88E-02 -0.3775 -0.4546 2.750 1.992 2.32E-02 -0.3426 -0.4744 3.000 1.913 2.79E-02 -0.3135 -0.4939 3.250 1.840 3.29E-02 -0.2887 -0.5130 3.500 1.772 3.82E-02 -0.2675 -0.5320 3.750 1.710 4.37E-02 -0.2490 -0.5509 4.000 1.651 4.94E-02 -0.2328 -0.5697 4.250 1.596 5.52E-02 -0.2186 -0.5885 4.500 1.545 6.12E-02 -0.2059 -0.6073 4.750 1.496 6.73E-02 -0.1945 -0.6262 5.000 1.450 7.35E-02 -0.1843 -0.6452 5.250 1.406 7.98E-02 -0.1750 -0.6642 5.500 1.365 8.62E-02 -0.1666 -0.6835 5.750 1.325 9.25E-02 -0.1589 -0.7029 6.000 1.288 9.90E-02 -0.1518 -0.7225 6.250 1.251 0.11 -0.1454 -0.7423 6.500 1.217 0.11 -0.1394 -0.7624 6.750 1.184 0.12 -0.1338 -0.7827 7.000 1.152 0.12 -0.1287 -0.8034 7.250 1.121 0.13 -0.1239 -0.8243 7.500 1.091 0.14 -0.1194 -0.8456 7.750 1.063 0.14 -0.1153 -0.8673 8.000 1.035 0.15 -0.1113 -0.8893. Análisis Probabilista. E. Mosquera..
(15) Propuesta Probabilista a 50 años. 8.250 8.500 8.750 9.000 9.250 9.500 9.750 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00. 1.009 0.9830 0.9581 0.9339 0.9115 0.8889 0.8669 0.8455 0.8247 0.8045 0.7848 0.7656 0.7469 0.7286 0.7108 0.6935 0.6765 0.6599 0.6437 0.6278 0.6123 0.5971 0.5823 0.5678 0.5535 0.5395 0.5258 0.5124. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=4 cm.. 0.16 0.16 0.17 0.18 0.18 0.19 0.19 0.20 0.20 0.21 0.22 0.22 0.23 0.23 0.24 0.24 0.25 0.25 0.26 0.27 0.27 0.28 0.28 0.29 0.29 0.29 0.30 0.30. -0.1077 -0.1042 -0.1010 -0.9788E-01 -0.9498E-01 -0.9223E-01 -0.8962E-01 -0.8714E-01 -0.8478E-01 -0.8254E-01 -0.8041E-01 -0.7837E-01 -0.7642E-01 -0.7456E-01 -0.7278E-01 -0.7108E-01 -0.6944E-01 -0.6788E-01 -0.6637E-01 -0.6493E-01 -0.6354E-01 -0.6220E-01 -0.6091E-01 -0.5965E-01 -0.5845E-01 -0.5730E-01 -0.5619E-01 -0.5511E-01. -0.9117 -0.9346 -0.9579 -0.9818 -1.006 -1.031 -1.056 -1.082 -1.109 -1.137 -1.165 -1.193 -1.223 -1.253 -1.285 -1.317 -1.350 -1.384 -1.419 -1.456 -1.493 -1.532 -1.572 -1.613 -1.656 -1.701 -1.748 -1.796. Representative Alphas of Variables FLIM(1), 8r4.pti. x cx cs n T Sum of a². Análisis Probabilista. 0.46 0.47 -0.34 0.55 -0.39 1.00. E. Mosquera..
(16) Propuesta Probabilista a 50 años. 3.00. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=4 cm.. Reliability Index FLIM(1), 8r4.pti. Beta. 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00. 0.0. 1.0. Failure Probability 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0 1.0. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. 11.0. 12.0. 13.0. 14.0. 15.0. 11.0. 12.0. 13.0. 14.0. 15.0. Failure Probability FLIM(1), 8r4.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. Análisis Probabilista. E. Mosquera..
(17) Propuesta Probabilista a 50 años. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=5 cm.. -----------------------------------------------------------------------------Job name ............ : 8r5 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 24.02.2011 Time(hh:mm) ........ : 19:22 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: DEFFUNC(1)()=D0*(t0/t)^n DEFFUNC(2)()=5725*(1/293-1/(T+273)) DEFFUNC(3)()=(T/20)*exp(FUNC(2)) FLIM(1)=x-2*(1-sqrt(cx/cs))*sqrt(3*0.315*FUNC(1)*FUNC(3)*t*ke*ka) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************. Variable: x ; No. on Comment : Recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector = 1 cm : Normal (2) : Mean & Std.Dev. (0) = 5.000 ( 0.500000000000000E+01) = 1.000 ( 0.100000000000000E+01) = 0.2000 ( 0.200000000000000E+00) = 5.000 ( 0.500000000000000E+01) = 1.000 ( 0.100000000000000E+01). Variable: cx ; No. on X-vector = 2 Comment : Conc. Critica Cloruros en % cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.1000 ( 0.100000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.1000 ( 0.100000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 3 Comment : Conc. Super. Cloruros en% cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.8000 ( 0.800000000000000E+00) Standard deviation........ = 0.1600 ( 0.160000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.8000 ( 0.800000000000000E+00) Distr.Param.no.2 : sigma = 0.1600 ( 0.160000000000000E+00) ------------------------Variable: n ; No. on Comment : Factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 4. : Normal (2) : Mean & Std.Dev. (0) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01) = 0.2000 ( 0.200000000000000E+00) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01). Variable: T ; No. on X-vector = 5 Comment : Temperatura en ºC Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev.. (0). Análisis Probabilista. E. Mosquera..
(18) Propuesta Probabilista a 50 años. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. = = = = =. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=5 cm.. 18.00 3.600 0.2000 18.00 3.600. ( 0.180000000000000E+02) ( 0.360000000000000E+01) ( 0.200000000000000E+00) ( 0.180000000000000E+02) ( 0.360000000000000E+01). -- Constant (deterministic) Parameters -Parameter :t0 ; No. on PVEC= Comment : tiempo inicial en años. 1 with value =. Parameter :t ; No. on PVEC= Comment : tiempo final en años. 2 with value =. 50.00. Parameter :ke ; No. on PVEC= 3 with value = Comment : Param de Ejecución y curado. 2.400. Parameter :ka ; No. on PVEC= Comment : Param de microclima. 0.7670E-01. 4 with value =. 0.7000. Parameter :D0 ; No. on PVEC= 5 with value = Comment : Coef. de Difusión en m2/s 10^-12 -------------------------. 3.000. (x (cs (T. ; ; ;. (Lower bounds on U-space variables) 1; -36.69 ) (cx ; 2; 3; -36.69 ) (n ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (x (cs (T. ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (cx ; 2; 0.000 ; 3; 0.000 ) (n ; 4; 0.000 ; 5; 0.000 ). ) ). (x (cs (T. --; ; ;. ) ). X-start: Median values from U=0 1; 5.000 ) (cx ; 3; 0.8000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.4500. (Upper bounds on U-space variables) (x ; 1; 36.69 ) (cx ; 2; 36.69 ) (cs ; 3; 36.69 ) (n ; 4; 36.69 ) (T ; 5; 36.69 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E-03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 3.666 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 2.326 Corresponding approximate prob.of failure = 1.0022E-02 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.4960E-07 and Vector u-* (beta-point) : (x ; 1; -1.139 ) (cx ; 2; -1.062 ) (cs ; 3; 0.7297 ) (n ; 4; -1.283 ) (T ; 5; 0.8967 ) Normalized U-space gradient (alfa-U) with norm = 0.5568 : (x ; 1; 0.4900 ) (cx ; 2; 0.4567 ) (cs ; 3; -0.3138 ) (n ; 4; 0.5516 ) (T ; 5; -0.3856 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.4900 ) (cx ; 2; 0.4567 ) (cs ; 3; -0.3138 ) (n ; 4; 0.5516 ) (T ; 5; -0.3856 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 3.861 ) (cx ; 2; 0.3938 ) (cs ; 3; 0.9168 ) (n ; 4; 0.3346 ) (T ; 5; 21.23 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.2728 ) (cx ; 2; 2.543 ) (cs ; 3; -1.092 ) (n ; 4; 3.412 ) (T ; 5; -5.9634E-02) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(19) Propuesta Probabilista a 50 años. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=5 cm.. Constant Parameters (PVEC): (t0 ; 1; 7.6700E-02) (t ; 2; 50.00 ) (ke ; 3; 2.400 ) (ka ; 4; 0.7000 ) (D0 ; 5; 3.000 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 8 Calls of state-function : 49 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -6.596 -45.541 37.964. 11.387. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 2.336 Corresponding prob. of failure = 9.74157E-03. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 30 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 50 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 70 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 90 E(Sim)=. 0.930 0.979 0.997 0.986 1.01 1.01 1.05 1.05 1.06. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 8.42 6.62 5.90 5.00 4.81 4.46 5.85 5.24 4.73. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 2.322 Corresponding prob. of failure = 1.01288E-02 Correction factor by simulation = 1.040 Coefficient of Variation in % = 4.552 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 3.85538 5.00000 0.771 (cx : 2) 0.393312 0.500000 0.787 (cs : 3) 0.917292 0.800000 1.147 (n : 4) 0.334028 0.450000 0.742 (T : 5) 21.2428 18.0000 1.180 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 3.294 4.94E-04 -0.8994 -0.2686 1.250 3.103 9.59E-04 -0.7344 -0.2918 1.500 2.942 1.63E-03 -0.6193 -0.3120 1.750 2.812 2.46E-03 -0.5347 -0.3303 2.000 2.692 3.55E-03 -0.4701 -0.3471 2.250 2.585 4.88E-03 -0.4190 -0.3630 2.500 2.488 6.42E-03 -0.3777 -0.3781 2.750 2.401 8.17E-03 -0.3437 -0.3926 3.000 2.322 1.01E-02 -0.3152 -0.4066 3.250 2.248 1.23E-02 -0.2909 -0.4202 3.500 2.180 1.46E-02 -0.2700 -0.4336 3.750 2.117 1.71E-02 -0.2518 -0.4466 4.000 2.058 1.98E-02 -0.2359 -0.4594 4.250 2.002 2.26E-02 -0.2218 -0.4721 4.500 1.950 2.56E-02 -0.2092 -0.4846 4.750 1.901 2.87E-02 -0.1979 -0.4970 5.000 1.854 3.19E-02 -0.1878 -0.5092 5.250 1.809 3.52E-02 -0.1786 -0.5214 5.500 1.767 3.86E-02 -0.1702 -0.5336 5.750 1.727 4.21E-02 -0.1625 -0.5456 6.000 1.688 4.57E-02 -0.1555 -0.5577 6.250 1.651 4.94E-02 -0.1490 -0.5697 6.500 1.616 5.31E-02 -0.1430 -0.5817 6.750 1.581 5.69E-02 -0.1375 -0.5938 7.000 1.549 6.07E-02 -0.1324 -0.6058 7.250 1.517 6.46E-02 -0.1276 -0.6179 7.500 1.487 6.86E-02 -0.1231 -0.6300 7.750 1.457 7.25E-02 -0.1189 -0.6421 8.000 1.429 7.65E-02 -0.1150 -0.6543. Análisis Probabilista. E. Mosquera..
(20) Propuesta Probabilista a 50 años. 8.250 8.500 8.750 9.000 9.250 9.500 9.750 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00. 1.401 1.375 1.349 1.324 1.299 1.276 1.253 1.230 1.209 1.188 1.167 1.147 1.127 1.108 1.089 1.071 1.053 1.035 1.018 1.001 0.9850 0.9690 0.9532 0.9377 0.9236 0.9088 0.8942 0.8800. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=5 cm.. 8.06E-02 8.46E-02 8.87E-02 9.28E-02 9.69E-02 0.10 0.11 0.11 0.11 0.12 0.12 0.13 0.13 0.13 0.14 0.14 0.15 0.15 0.15 0.16 0.16 0.17 0.17 0.17 0.18 0.18 0.19 0.19. -0.1113 -0.1079 -0.1046 -0.1015 -0.9858E-01 -0.9581E-01 -0.9319E-01 -0.9069E-01 -0.8832E-01 -0.8606E-01 -0.8391E-01 -0.8185E-01 -0.7989E-01 -0.7801E-01 -0.7622E-01 -0.7450E-01 -0.7285E-01 -0.7126E-01 -0.6974E-01 -0.6828E-01 -0.6687E-01 -0.6552E-01 -0.6421E-01 -0.6295E-01 -0.6174E-01 -0.6057E-01 -0.5944E-01 -0.5835E-01. -0.6665 -0.6788 -0.6912 -0.7037 -0.7162 -0.7288 -0.7415 -0.7543 -0.7672 -0.7803 -0.7934 -0.8067 -0.8201 -0.8336 -0.8473 -0.8612 -0.8751 -0.8893 -0.9036 -0.9181 -0.9328 -0.9476 -0.9627 -0.9779 -0.9934 -1.009 -1.025 -1.041. Representative Alphas of Variables FLIM(1), 8r5.pti. x cx cs n T Sum of a². Análisis Probabilista. 0.49 0.46 -0.31 0.55 -0.39 1.00. E. Mosquera..
(21) Propuesta Probabilista a 50 años. 3.00. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=5 cm.. Reliability Index FLIM(1), 8r5.pti. Beta. 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00. 0.0. 1.0. Failure Probability 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0 1.0. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. 11.0. 12.0. 13.0. 14.0. 15.0. 11.0. 12.0. 13.0. 14.0. 15.0. Failure Probability FLIM(1), 8r5.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. Análisis Probabilista. E. Mosquera..
(22) Propuesta Probabilista a 50 años. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=6 cm.. -----------------------------------------------------------------------------Job name ............ : 8r6 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 24.02.2011 Time(hh:mm) ........ : 19:23 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: DEFFUNC(1)()=D0*(t0/t)^n DEFFUNC(2)()=5725*(1/293-1/(T+273)) DEFFUNC(3)()=(T/20)*exp(FUNC(2)) FLIM(1)=x-2*(1-sqrt(cx/cs))*sqrt(3*0.315*FUNC(1)*FUNC(3)*t*ke*ka) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************. Variable: x ; No. on Comment : Recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector = 1 cm : Normal (2) : Mean & Std.Dev. (0) = 6.000 ( 0.600000000000000E+01) = 1.200 ( 0.120000000000000E+01) = 0.2000 ( 0.200000000000000E+00) = 6.000 ( 0.600000000000000E+01) = 1.200 ( 0.120000000000000E+01). Variable: cx ; No. on X-vector = 2 Comment : Conc. Critica Cloruros en % cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.1000 ( 0.100000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.1000 ( 0.100000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 3 Comment : Conc. Super. Cloruros en% cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.8000 ( 0.800000000000000E+00) Standard deviation........ = 0.1600 ( 0.160000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.8000 ( 0.800000000000000E+00) Distr.Param.no.2 : sigma = 0.1600 ( 0.160000000000000E+00) ------------------------Variable: n ; No. on Comment : Factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 4. : Normal (2) : Mean & Std.Dev. (0) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01) = 0.2000 ( 0.200000000000000E+00) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01). Variable: T ; No. on X-vector = 5 Comment : Temperatura en ºC Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev.. (0). Análisis Probabilista. E. Mosquera..
(23) Propuesta Probabilista a 50 años. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. = = = = =. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=6 cm.. 18.00 3.600 0.2000 18.00 3.600. ( 0.180000000000000E+02) ( 0.360000000000000E+01) ( 0.200000000000000E+00) ( 0.180000000000000E+02) ( 0.360000000000000E+01). -- Constant (deterministic) Parameters -Parameter :t0 ; No. on PVEC= Comment : tiempo inicial en años. 1 with value =. Parameter :t ; No. on PVEC= Comment : tiempo final en años. 2 with value =. 50.00. Parameter :ke ; No. on PVEC= 3 with value = Comment : Param de Ejecución y curado. 2.400. Parameter :ka ; No. on PVEC= Comment : Param de microclima. 0.7670E-01. 4 with value =. 0.7000. Parameter :D0 ; No. on PVEC= 5 with value = Comment : Coef. de Difusión en m2/s 10^-12 -------------------------. 3.000. (x (cs (T. ; ; ;. (Lower bounds on U-space variables) 1; -36.69 ) (cx ; 2; 3; -36.69 ) (n ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (x (cs (T. ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (cx ; 2; 0.000 ; 3; 0.000 ) (n ; 4; 0.000 ; 5; 0.000 ). ) ). (x (cs (T. --; ; ;. ) ). X-start: Median values from U=0 1; 6.000 ) (cx ; 3; 0.8000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.4500. (Upper bounds on U-space variables) (x ; 1; 36.69 ) (cx ; 2; 36.69 ) (cs ; 3; 36.69 ) (n ; 4; 36.69 ) (T ; 5; 36.69 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E-03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 4.666 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 2.670 Corresponding approximate prob.of failure = 3.7947E-03 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.1307E-07 and Vector u-* (beta-point) : (x ; 1; -1.394 ) (cx ; 2; -1.183 ) (cs ; 3; 0.7811 ) (n ; 4; -1.465 ) (T ; 5; 1.014 ) Normalized U-space gradient (alfa-U) with norm = 0.4927 : (x ; 1; 0.5220 ) (cx ; 2; 0.4430 ) (cs ; 3; -0.2926 ) (n ; 4; 0.5489 ) (T ; 5; -0.3799 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.5220 ) (cx ; 2; 0.4430 ) (cs ; 3; -0.2926 ) (n ; 4; 0.5489 ) (T ; 5; -0.3799 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 4.328 ) (cx ; 2; 0.3817 ) (cs ; 3; 0.9250 ) (n ; 4; 0.3181 ) (T ; 5; 21.65 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.2143 ) (cx ; 2; 2.183 ) (cs ; 3; -0.9009 ) (n ; 4; 3.005 ) (T ; 5; -5.1998E-02) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(24) Propuesta Probabilista a 50 años. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=6 cm.. Constant Parameters (PVEC): (t0 ; 1; 7.6700E-02) (t ; 2; 50.00 ) (ke ; 3; 2.400 ) (ka ; 4; 0.7000 ) (D0 ; 5; 3.000 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 9 Calls of state-function : 55 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -7.032 -47.017 37.518. 10.410. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 2.669 Corresponding prob. of failure = 3.80446E-03. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 30 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 50 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 70 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 90 E(Sim)=. 0.922 0.972 0.992 0.982 1.00 0.997 1.05 1.06 1.07. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 9.79 7.50 6.61 5.62 5.32 4.95 6.95 6.24 5.60. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 2.655 Corresponding prob. of failure = 3.97031E-03 Correction factor by simulation = 1.044 Coefficient of Variation in % = 5.367 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 4.32815 6.00000 0.721 (cx : 2) 0.381760 0.500000 0.764 (cs : 3) 0.924935 0.800000 1.156 (n : 4) 0.318148 0.450000 0.707 (T : 5) 21.6504 18.0000 1.203 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 3.591 1.65E-04 -0.8510 -0.2320 1.250 3.412 3.23E-04 -0.7069 -0.2543 1.500 3.259 5.58E-04 -0.6021 -0.2727 1.750 3.127 8.83E-04 -0.5234 -0.2888 2.000 3.010 1.30E-03 -0.4624 -0.3033 2.250 2.906 1.83E-03 -0.4138 -0.3167 2.500 2.820 2.40E-03 -0.3742 -0.3293 2.750 2.734 3.13E-03 -0.3414 -0.3412 3.000 2.655 3.97E-03 -0.3137 -0.3525 3.250 2.582 4.92E-03 -0.2901 -0.3634 3.500 2.514 5.97E-03 -0.2697 -0.3739 3.750 2.451 7.12E-03 -0.2520 -0.3842 4.000 2.392 8.38E-03 -0.2363 -0.3942 4.250 2.337 9.73E-03 -0.2225 -0.4039 4.500 2.284 1.12E-02 -0.2101 -0.4135 4.750 2.235 1.27E-02 -0.1990 -0.4229 5.000 2.188 1.44E-02 -0.1890 -0.4321 5.250 2.143 1.61E-02 -0.1799 -0.4412 5.500 2.100 1.79E-02 -0.1717 -0.4502 5.750 2.059 1.97E-02 -0.1641 -0.4591 6.000 2.020 2.17E-02 -0.1571 -0.4679 6.250 1.983 2.37E-02 -0.1507 -0.4766 6.500 1.947 2.58E-02 -0.1448 -0.4853 6.750 1.913 2.79E-02 -0.1393 -0.4939 7.000 1.880 3.01E-02 -0.1342 -0.5024 7.250 1.848 3.23E-02 -0.1295 -0.5109 7.500 1.817 3.46E-02 -0.1250 -0.5194 7.750 1.787 3.70E-02 -0.1209 -0.5278 8.000 1.758 3.94E-02 -0.1169 -0.5362. Análisis Probabilista. E. Mosquera..
(25) Propuesta Probabilista a 50 años. 8.250 8.500 8.750 9.000 9.250 9.500 9.750 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00. 1.730 1.703 1.677 1.651 1.626 1.602 1.579 1.556 1.534 1.512 1.491 1.470 1.450 1.430 1.411 1.392 1.374 1.356 1.338 1.321 1.304 1.288 1.271 1.255 1.240 1.224 1.209 1.195. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=6 cm.. 4.18E-02 4.43E-02 4.68E-02 4.94E-02 5.20E-02 5.46E-02 5.72E-02 5.99E-02 6.26E-02 6.53E-02 6.80E-02 7.08E-02 7.35E-02 7.63E-02 7.91E-02 8.19E-02 8.47E-02 8.76E-02 9.04E-02 9.33E-02 9.61E-02 9.90E-02 0.10 0.10 0.11 0.11 0.11 0.12. -0.1133 -0.1098 -0.1066 -0.1035 -0.1006 -0.9781E-01 -0.9519E-01 -0.9270E-01 -0.9033E-01 -0.8807E-01 -0.8592E-01 -0.8386E-01 -0.8190E-01 -0.8002E-01 -0.7822E-01 -0.7649E-01 -0.7484E-01 -0.7325E-01 -0.7172E-01 -0.7026E-01 -0.6884E-01 -0.6748E-01 -0.6617E-01 -0.6491E-01 -0.6369E-01 -0.6251E-01 -0.6138E-01 -0.6028E-01. -0.5446 -0.5530 -0.5614 -0.5697 -0.5781 -0.5864 -0.5948 -0.6031 -0.6115 -0.6199 -0.6283 -0.6367 -0.6452 -0.6536 -0.6621 -0.6706 -0.6792 -0.6878 -0.6964 -0.7050 -0.7137 -0.7225 -0.7313 -0.7401 -0.7490 -0.7579 -0.7669 -0.7759. Representative Alphas of Variables FLIM(1), 8r6.pti. x cx cs n T Sum of a². Análisis Probabilista. 0.52 0.44 -0.29 0.55 -0.38 1.00. E. Mosquera..
(26) Propuesta Probabilista a 50 años. 3.00. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.8%‐ R=6 cm.. Reliability Index FLIM(1), 8r6.pti. Beta. 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00. 0.0. 1.0. Failure Probability 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0 1.0. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. 11.0. 12.0. 13.0. 14.0. 15.0. 11.0. 12.0. 13.0. 14.0. 15.0. Failure Probability FLIM(1), 8r6.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. Análisis Probabilista. E. Mosquera..
(27) Propuesta Probabilista a 50 años. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.9%‐ R=2 cm.. -----------------------------------------------------------------------------Job name ............ : 9r2 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 10:40 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: DEFFUNC(1)()=D0*(t0/t)^n DEFFUNC(2)()=5725*(1/293-1/(T+273)) DEFFUNC(3)()=(T/20)*exp(FUNC(2)) FLIM(1)=x-2*(1-sqrt(cx/cs))*sqrt(3*0.315*FUNC(1)*FUNC(3)*t*ke*ka) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************. Variable: x ; No. on Comment : Recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector = 1 cm : Normal (2) : Mean & Std.Dev. (0) = 2.000 ( 0.200000000000000E+01) = 0.4000 ( 0.400000000000000E+00) = 0.2000 ( 0.200000000000000E+00) = 2.000 ( 0.200000000000000E+01) = 0.4000 ( 0.400000000000000E+00). Variable: cx ; No. on X-vector = 2 Comment : Conc. Critica Cloruros en % cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.1000 ( 0.100000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.1000 ( 0.100000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 3 Comment : Conc. Super. Cloruros en% cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.9000 ( 0.900000000000000E+00) Standard deviation........ = 0.1800 ( 0.180000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.9000 ( 0.900000000000000E+00) Distr.Param.no.2 : sigma = 0.1800 ( 0.180000000000000E+00) ------------------------Variable: n ; No. on Comment : Factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 4. : Normal (2) : Mean & Std.Dev. (0) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01) = 0.2000 ( 0.200000000000000E+00) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01). Variable: T ; No. on X-vector = 5 Comment : Temperatura en ºC Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev.. (0). Análisis Probabilista. E. Mosquera..
(28) Propuesta Probabilista a 50 años. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. = = = = =. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.9%‐ R=2 cm.. 18.00 3.600 0.2000 18.00 3.600. ( 0.180000000000000E+02) ( 0.360000000000000E+01) ( 0.200000000000000E+00) ( 0.180000000000000E+02) ( 0.360000000000000E+01). -- Constant (deterministic) Parameters -Parameter :t0 ; No. on PVEC= Comment : tiempo inicial en años. 1 with value =. Parameter :t ; No. on PVEC= Comment : tiempo final en años. 2 with value =. 50.00. Parameter :ke ; No. on PVEC= 3 with value = Comment : Param de Ejecución y curado. 2.400. Parameter :ka ; No. on PVEC= Comment : Param de microclima. 0.7670E-01. 4 with value =. 0.7000. Parameter :D0 ; No. on PVEC= 5 with value = Comment : Coef. de Difusión en m2/s 10^-12 -------------------------. 3.000. (x (cs (T. ; ; ;. (Lower bounds on U-space variables) 1; -36.69 ) (cx ; 2; 3; -36.69 ) (n ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (x (cs (T. ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (cx ; 2; 0.000 ; 3; 0.000 ) (n ; 4; 0.000 ; 5; 0.000 ). ) ). (x (cs (T. --; ; ;. ) ). X-start: Median values from U=0 1; 2.000 ) (cx ; 3; 0.9000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.4500. (Upper bounds on U-space variables) (x ; 1; 36.69 ) (cx ; 2; 36.69 ) (cs ; 3; 36.69 ) (n ; 4; 36.69 ) (T ; 5; 36.69 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E-03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 0.3776 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 0.367 Corresponding approximate prob.of failure = 0.3568 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.9002E-08 and Vector u-* (beta-point) : (x ; 1; -0.1358 ) (cx ; 2; -0.1764 ) (cs ; 3; 0.1647 ) (n ; 4; -0.1927 ) (T ; 5; 0.1443 ) Normalized U-space gradient (alfa-U) with norm = 2.862 : (x ; 1; 0.3702 ) (cx ; 2; 0.4807 ) (cs ; 3; -0.4489 ) (n ; 4; 0.5250 ) (T ; 5; -0.3933 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.3702 ) (cx ; 2; 0.4807 ) (cs ; 3; -0.4489 ) (n ; 4; 0.5250 ) (T ; 5; -0.3933 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 1.946 ) (cx ; 2; 0.4824 ) (cs ; 3; 0.9297 ) (n ; 4; 0.4327 ) (T ; 5; 18.52 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 2.648 ) (cx ; 2; 13.75 ) (cs ; 3; -7.137 ) (n ; 4; 16.69 ) (T ; 5; -0.3127 ) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(29) Propuesta Probabilista a 50 años. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.9%‐ R=2 cm.. Constant Parameters (PVEC): (t0 ; 1; 7.6700E-02) (t ; 2; 50.00 ) (ke ; 3; 2.400 ) (ka ; 4; 0.7000 ) (D0 ; 5; 3.000 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 4 Calls of state-function : 25 -----------------------------------------------------------------------------***************************************************** Report of an error by traceback facility (*YERR*) : Error in module :YSOMHO Warning from 2nd-order improvement: Absolute value of 1st-order beta(FORMBE) < 1 . 2nd-order improvement by Hohenbichlers formula might be inaccurate because it is based on asymptotic theory ! ----- Second-Order Improvement : ----radii of curvature in U-space : -4.900 -39.576 44.554. 16.962. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 0.429 Corresponding prob. of failure = 0.33403. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 30 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 50 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 70 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 90 E(Sim)=. 0.968 0.992 0.995 0.989 1.01 1.01 1.02 1.02 1.03. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 3.42 2.84 2.67 2.29 2.30 2.11 2.44 2.18 2.02. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 0.413 Corresponding prob. of failure = 0.33998 Correction factor by simulation = 1.018 Coefficient of Variation in % = 2.007 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 1.93650 2.00000 0.968 (cx : 2) 0.479387 0.500000 0.959 (cs : 3) 0.934651 0.900000 1.039 (n : 4) 0.429736 0.450000 0.955 (T : 5) 18.6072 18.0000 1.034 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 1.417 7.82E-02 -0.9700 -0.6923 1.250 1.208 0.11 -0.7692 -0.8110 1.500 1.038 0.15 -0.6351 -0.9423 1.750 0.8958 0.19 -0.5392 -1.091 2.000 0.7740 0.22 -0.4674 -1.264 2.250 0.6675 0.25 -0.4115 -1.470 2.500 0.5733 0.28 -0.3669 -1.722 2.750 0.4888 0.31 -0.3304 -2.039 3.000 0.4125 0.34 -0.3001 -2.453 3.250 0.3430 0.37 -0.2744 -3.021 3.500 0.2792 0.39 -0.2525 -3.852 3.750 0.2205 0.41 -0.2335 -5.191 4.000 0.1660 0.43 -0.2169 -7.688 4.250 0.1153 0.45 -0.2023 -14.23 4.500 0.7091E-01 0.47 -0.1894 -74.60 4.750 0.4885E-01 0.48 -0.1779 -24.49 5.000 0.7317E-02 0.50 -0.1675 -10.78 5.250 -0.3183E-01 0.51 -0.1581 -7.012 5.500 -0.6883E-01 0.53 -0.1496 -5.247 5.750 -0.1039 0.54 -0.1419 -4.221 6.000 -0.1371 0.55 -0.1347 -3.546 6.250 -0.1687 0.57 -0.1282 -3.072. Análisis Probabilista. E. Mosquera..
(30) Propuesta Probabilista a 50 años. 6.500 6.750 7.000 7.250 7.500 7.750 8.000 8.250 8.500 8.750 9.000 9.250 9.500 9.750 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00. -0.1989 -0.2276 -0.2551 -0.2814 -0.3066 -0.3308 -0.3540 -0.3763 -0.3978 -0.4186 -0.4385 -0.4578 -0.4765 -0.4945 -0.5119 -0.5288 -0.5451 -0.5610 -0.5764 -0.5913 -0.6058 -0.6199 -0.6336 -0.6470 -0.6599 -0.6726 -0.6849 -0.6969 -0.7086 -0.7200 -0.7311 -0.7420 -0.7526 -0.7630 -0.7731. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.9%‐ R=2 cm.. 0.58 0.59 0.60 0.61 0.62 0.63 0.64 0.65 0.65 0.66 0.67 0.68 0.68 0.69 0.70 0.70 0.71 0.71 0.72 0.72 0.73 0.73 0.74 0.74 0.75 0.75 0.75 0.76 0.76 0.76 0.77 0.77 0.77 0.78 0.78. -0.1222 -0.1167 -0.1116 -0.1068 -0.1024 -0.9821E-01 -0.9433E-01 -0.9071E-01 -0.8730E-01 -0.8409E-01 -0.8108E-01 -0.7823E-01 -0.7554E-01 -0.7300E-01 -0.7059E-01 -0.6830E-01 -0.6613E-01 -0.6407E-01 -0.6211E-01 -0.6024E-01 -0.5846E-01 -0.5676E-01 -0.5514E-01 -0.5359E-01 -0.5210E-01 -0.5068E-01 -0.4932E-01 -0.4801E-01 -0.4676E-01 -0.4556E-01 -0.4441E-01 -0.4330E-01 -0.4223E-01 -0.4120E-01 -0.4021E-01. -2.719 -2.446 -2.228 -2.049 -1.900 -1.774 -1.666 -1.571 -1.489 -1.415 -1.350 -1.291 -1.238 -1.190 -1.146 -1.105 -1.068 -1.033 -1.001 -0.9714 -0.9436 -0.9175 -0.8931 -0.8701 -0.8484 -0.8279 -0.8085 -0.7901 -0.7727 -0.7561 -0.7403 -0.7252 -0.7108 -0.6971 -0.6839. Representative Alphas of Variables FLIM(1), 9r2.pti. x 0.37 cx 0.48 cs -0.45 n 0.53 T -0.39 Sum of a²1.00. Análisis Probabilista. E. Mosquera..
(31) Propuesta Probabilista a 50 años. 3.00. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.9%‐ R=2 cm.. Reliability Index FLIM(1), 9r2.pti. Beta. 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 0.0. 1.0. Failure Probability 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0 1.0. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. 11.0. 12.0. 13.0. 14.0. 15.0. 11.0. 12.0. 13.0. 14.0. 15.0. Failure Probability FLIM(1), 9r2.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. Análisis Probabilista. E. Mosquera..
(32) Propuesta Probabilista a 50 años. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.9%‐ R=3 cm.. -----------------------------------------------------------------------------Job name ............ : 9r3 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 10:41 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: DEFFUNC(1)()=D0*(t0/t)^n DEFFUNC(2)()=5725*(1/293-1/(T+273)) DEFFUNC(3)()=(T/20)*exp(FUNC(2)) FLIM(1)=x-2*(1-sqrt(cx/cs))*sqrt(3*0.315*FUNC(1)*FUNC(3)*t*ke*ka) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************. Variable: x ; No. on Comment : Recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector = 1 cm : Normal (2) : Mean & Std.Dev. (0) = 3.000 ( 0.300000000000000E+01) = 0.6000 ( 0.600000000000000E+00) = 0.2000 ( 0.200000000000000E+00) = 3.000 ( 0.300000000000000E+01) = 0.6000 ( 0.600000000000000E+00). Variable: cx ; No. on X-vector = 2 Comment : Conc. Critica Cloruros en % cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.1000 ( 0.100000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.1000 ( 0.100000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 3 Comment : Conc. Super. Cloruros en% cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.9000 ( 0.900000000000000E+00) Standard deviation........ = 0.1800 ( 0.180000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.9000 ( 0.900000000000000E+00) Distr.Param.no.2 : sigma = 0.1800 ( 0.180000000000000E+00) ------------------------Variable: n ; No. on Comment : Factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 4. : Normal (2) : Mean & Std.Dev. (0) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01) = 0.2000 ( 0.200000000000000E+00) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01). Variable: T ; No. on X-vector = 5 Comment : Temperatura en ºC Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev.. (0). Análisis Probabilista. E. Mosquera..
(33) Propuesta Probabilista a 50 años. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. = = = = =. Ambiente IIIa‐500‐ CEM I/II‐ Cs=0.9%‐ R=3 cm.. 18.00 3.600 0.2000 18.00 3.600. ( 0.180000000000000E+02) ( 0.360000000000000E+01) ( 0.200000000000000E+00) ( 0.180000000000000E+02) ( 0.360000000000000E+01). -- Constant (deterministic) Parameters -Parameter :t0 ; No. on PVEC= Comment : tiempo inicial en años. 1 with value =. Parameter :t ; No. on PVEC= Comment : tiempo final en años. 2 with value =. 50.00. Parameter :ke ; No. on PVEC= 3 with value = Comment : Param de Ejecución y curado. 2.400. Parameter :ka ; No. on PVEC= Comment : Param de microclima. 0.7670E-01. 4 with value =. 0.7000. Parameter :D0 ; No. on PVEC= 5 with value = Comment : Coef. de Difusión en m2/s 10^-12 -------------------------. 3.000. (x (cs (T. ; ; ;. (Lower bounds on U-space variables) 1; -36.69 ) (cx ; 2; 3; -36.69 ) (n ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (x (cs (T. ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (cx ; 2; 0.000 ; 3; 0.000 ) (n ; 4; 0.000 ; 5; 0.000 ). ) ). (x (cs (T. --; ; ;. ) ). X-start: Median values from U=0 1; 3.000 ) (cx ; 3; 0.9000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.4500. (Upper bounds on U-space variables) (x ; 1; 36.69 ) (cx ; 2; 36.69 ) (cs ; 3; 36.69 ) (n ; 4; 36.69 ) (T ; 5; 36.69 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E-03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 1.378 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.124 Corresponding approximate prob.of failure = 0.1306 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.9784E-08 and Vector u-* (beta-point) : (x ; 1; -0.4762 ) (cx ; 2; -0.5063 ) (cs ; 3; 0.4197 ) (n ; 4; -0.6282 ) (T ; 5; 0.4566 ) Normalized U-space gradient (alfa-U) with norm = 1.028 : (x ; 1; 0.4238 ) (cx ; 2; 0.4506 ) (cs ; 3; -0.3736 ) (n ; 4; 0.5591 ) (T ; 5; -0.4064 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.4238 ) (cx ; 2; 0.4506 ) (cs ; 3; -0.3736 ) (n ; 4; 0.5591 ) (T ; 5; -0.4064 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 2.714 ) (cx ; 2; 0.4494 ) (cs ; 3; 0.9756 ) (n ; 4; 0.3935 ) (T ; 5; 19.64 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.7259 ) (cx ; 2; 4.630 ) (cs ; 3; -2.133 ) (n ; 4; 6.384 ) (T ; 5; -0.1160 ) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
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