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 IIIc‐ CEM III‐ Cs=2%‐ R=4 cm.. -----------------------------------------------------------------------------Job name ............ : 2r4 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 22:11 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................ = 2.000 ( 0.200000000000000E+01) Standard deviation........ = 0.4000 ( 0.400000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 2.000 ( 0.200000000000000E+01) Distr.Param.no.2 : sigma = 0.4000 ( 0.400000000000000E+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) = 0.5500 ( 0.550000000000000E+00) = 0.1100 ( 0.110000000000000E+00) = 0.2000 ( 0.200000000000000E+00) = 0.5500 ( 0.550000000000000E+00) = 0.1100 ( 0.110000000000000E+00). 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 IIIc‐ CEM III‐ Cs=2%‐ 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; 2.000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.5500. (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) = 1.696 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.134 Corresponding approximate prob.of failure = 0.1284 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= -0.1737E-08 and Vector u-* (beta-point) : (x ; 1; -0.5181 ) (cx ; 2; -0.2234 ) (cs ; 3; 0.2050 ) (n ; 4; -0.8276 ) (T ; 5; 0.4906 ) Normalized U-space gradient (alfa-U) with norm = 1.032 : (x ; 1; 0.4568 ) (cx ; 2; 0.1970 ) (cs ; 3; -0.1808 ) (n ; 4; 0.7298 ) (T ; 5; -0.4327 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.4568 ) (cx ; 2; 0.1970 ) (cs ; 3; -0.1808 ) (n ; 4; 0.7298 ) (T ; 5; -0.4327 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 3.586 ) (cx ; 2; 0.4777 ) (cs ; 3; 2.082 ) (n ; 4; 0.4590 ) (T ; 5; 19.77 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.5896 ) (cx ; 2; 2.034 ) (cs ; 3; -0.4667 ) (n ; 4; 6.850 ) (T ; 5; -0.1241 ) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(4) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2%‐ 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 : 4 Calls of state-function : 25 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -12.750 -34.397 59.751. 12.769. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.135 Corresponding prob. of failure = 0.12825. ----- 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)=. 0.987 0.996 1.00 0.997 1.00 1.00 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.=. 4.23 3.00 2.54 2.10 1.96 1.98 2.17 2.03 1.89. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.124 Corresponding prob. of failure = 0.13058 Correction factor by simulation = 1.018 Coefficient of Variation in % = 1.869 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 3.58529 4.00000 0.896 (cx : 2) 0.477641 0.500000 0.955 (cs : 3) 2.08207 2.00000 1.041 (n : 4) 0.458910 0.550000 0.834 (T : 5) 19.7674 18.0000 1.098 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 2.213 1.34E-02 -0.9964 -0.4436 1.250 1.995 2.30E-02 -0.8036 -0.4965 1.500 1.816 3.47E-02 -0.6733 -0.5491 1.750 1.663 4.82E-02 -0.5794 -0.6023 2.000 1.530 6.30E-02 -0.5084 -0.6570 2.250 1.412 7.89E-02 -0.4530 -0.7138 2.500 1.307 9.56E-02 -0.4084 -0.7733 2.750 1.211 0.11 -0.3718 -0.8361 3.000 1.124 0.13 -0.3413 -0.9028 3.250 1.043 0.15 -0.3153 -0.9739 3.500 0.9684 0.17 -0.2930 -1.051 3.750 0.8988 0.18 -0.2736 -1.134 4.000 0.8337 0.20 -0.2567 -1.224 4.250 0.7724 0.22 -0.2417 -1.323 4.500 0.7147 0.24 -0.2284 -1.431 4.750 0.6600 0.25 -0.2164 -1.552 5.000 0.6082 0.27 -0.2057 -1.687 5.250 0.5588 0.29 -0.1959 -1.838 5.500 0.5117 0.30 -0.1870 -2.011 5.750 0.4667 0.32 -0.1789 -2.208 6.000 0.4237 0.34 -0.1715 -2.438 6.250 0.3823 0.35 -0.1646 -2.707 6.500 0.3426 0.37 -0.1583 -3.029 6.750 0.3044 0.38 -0.1525 -3.420 7.000 0.2676 0.39 -0.1470 -3.906 7.250 0.2321 0.41 -0.1419 -4.522 7.500 0.1978 0.42 -0.1372 -5.341 7.750 0.1646 0.43 -0.1328 -6.476 8.000 0.1324 0.45 -0.1286 -8.153. Análisis Probabilista. E. Mosquera..
(5) 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. 0.1013 0.7108E-01 0.4175E-01 0.1324E-01 0.2206E-02 -0.2476E-01 -0.5103E-01 -0.7662E-01 -0.1016 -0.1259 -0.1497 -0.1729 -0.1956 -0.2178 -0.2395 -0.2608 -0.2816 -0.3020 -0.3219 -0.3415 -0.3607 -0.3796 -0.3981 -0.4162 -0.4340 -0.4516 -0.4688 -0.4857. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=4 cm.. 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.59 0.60 0.61 0.62 0.63 0.63 0.64 0.65 0.65 0.66 0.67 0.67 0.68 0.69. -0.1247 -0.1210 -0.1176 -0.1143 -0.1112 -0.1083 -0.1055 -0.1028 -0.1003 -0.9793E-01 -0.9564E-01 -0.9346E-01 -0.9137E-01 -0.8938E-01 -0.8746E-01 -0.8563E-01 -0.8387E-01 -0.8218E-01 -0.8056E-01 -0.7899E-01 -0.7749E-01 -0.7604E-01 -0.7465E-01 -0.7330E-01 -0.7201E-01 -0.7075E-01 -0.6954E-01 -0.6837E-01. -10.89 -16.13 -30.29 -207.0 -44.29 -20.30 -13.29 -9.943 -7.982 -6.694 -5.782 -5.103 -4.577 -4.158 -3.817 -3.532 -3.292 -3.086 -2.908 -2.751 -2.614 -2.492 -2.383 -2.284 -2.195 -2.114 -2.040 -1.972. Representative Alphas of Variables FLIM(1), 2r4.pti. x 0.46 cx 0.20 cs -0.18 n 0.73 T -0.43 Sum of a²1.00. Análisis Probabilista. E. Mosquera..
(6) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=4 cm.. Reliability Index FLIM(1), 2r4.pti. Beta 3.00 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. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. 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. D0 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. Failure Probability FLIM(1), 2r4.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. 8.0. 9.0. 10.0. D0. Análisis Probabilista. E. Mosquera..
(7) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=5 cm.. -----------------------------------------------------------------------------Job name ............ : 2r5 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 22:11 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................ = 2.000 ( 0.200000000000000E+01) Standard deviation........ = 0.4000 ( 0.400000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 2.000 ( 0.200000000000000E+01) Distr.Param.no.2 : sigma = 0.4000 ( 0.400000000000000E+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) = 0.5500 ( 0.550000000000000E+00) = 0.1100 ( 0.110000000000000E+00) = 0.2000 ( 0.200000000000000E+00) = 0.5500 ( 0.550000000000000E+00) = 0.1100 ( 0.110000000000000E+00). 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 IIIc‐ CEM III‐ Cs=2%‐ 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; 2.000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.5500. (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) = 2.696 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.589 Corresponding approximate prob.of failure = 5.5991E-02 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= -0.1423E-08 and Vector u-* (beta-point) : (x ; 1; -0.7622 ) (cx ; 2; -0.3072 ) (cs ; 3; 0.2734 ) (n ; 4; -1.151 ) (T ; 5; 0.6714 ) Normalized U-space gradient (alfa-U) with norm = 0.7734 : (x ; 1; 0.4796 ) (cx ; 2; 0.1933 ) (cs ; 3; -0.1720 ) (n ; 4; 0.7243 ) (T ; 5; -0.4224 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.4796 ) (cx ; 2; 0.1933 ) (cs ; 3; -0.1720 ) (n ; 4; 0.7243 ) (T ; 5; -0.4224 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 4.238 ) (cx ; 2; 0.4693 ) (cs ; 3; 2.109 ) (n ; 4; 0.4234 ) (T ; 5; 20.42 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.3709 ) (cx ; 2; 1.495 ) (cs ; 3; -0.3326 ) (n ; 4; 5.093 ) (T ; 5; -9.0753E-02) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(9) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2%‐ 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 : 5 Calls of state-function : 31 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -13.550 -36.352 59.778. 11.806. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.582 Corresponding prob. of failure = 5.68040E-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)=. 0.987 0.993 1.00 0.996 1.00 0.996 1.02 1.03 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.=. 5.48 3.81 3.19 2.63 2.43 2.44 2.76 2.65 2.45. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.571 Corresponding prob. of failure = 5.81309E-02 Correction factor by simulation = 1.023 Coefficient of Variation in % = 2.406 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 4.24121 5.00000 0.848 (cx : 2) 0.469414 0.500000 0.939 (cs : 3) 2.10887 2.00000 1.054 (n : 4) 0.423945 0.550000 0.771 (T : 5) 20.4061 18.0000 1.134 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 2.641 4.13E-03 -0.9741 -0.3626 1.250 2.429 7.57E-03 -0.7890 -0.3997 1.500 2.253 1.21E-02 -0.6631 -0.4349 1.750 2.103 1.77E-02 -0.5718 -0.4691 2.000 1.972 2.43E-02 -0.5026 -0.5027 2.250 1.856 3.17E-02 -0.4483 -0.5364 2.500 1.752 3.99E-02 -0.4047 -0.5702 2.750 1.657 4.87E-02 -0.3687 -0.6044 3.000 1.571 5.81E-02 -0.3387 -0.6393 3.250 1.491 6.80E-02 -0.3131 -0.6749 3.500 1.417 7.83E-02 -0.2912 -0.7115 3.750 1.348 8.89E-02 -0.2721 -0.7491 4.000 1.283 0.10 -0.2554 -0.7880 4.250 1.222 0.11 -0.2405 -0.8282 4.500 1.165 0.12 -0.2274 -0.8701 4.750 1.110 0.13 -0.2155 -0.9138 5.000 1.059 0.14 -0.2049 -0.9593 5.250 1.010 0.16 -0.1952 -1.007 5.500 0.9627 0.17 -0.1865 -1.057 5.750 0.9178 0.18 -0.1784 -1.110 6.000 0.8749 0.19 -0.1711 -1.165 6.250 0.8337 0.20 -0.1643 -1.224 6.500 0.7941 0.21 -0.1580 -1.286 6.750 0.7559 0.22 -0.1522 -1.352 7.000 0.7192 0.24 -0.1468 -1.422 7.250 0.6837 0.25 -0.1418 -1.497 7.500 0.6494 0.26 -0.1371 -1.578 7.750 0.6163 0.27 -0.1327 -1.664 8.000 0.5842 0.28 -0.1285 -1.757. 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. 0.5530 0.5228 0.4935 0.4650 0.4373 0.4103 0.3840 0.3583 0.3333 0.3090 0.2851 0.2619 0.2391 0.2169 0.1951 0.1738 0.1529 0.1324 0.1124 0.9274E-01 0.7347E-01 0.5455E-01 0.3598E-01 0.1775E-01 0.1652E-01 -0.1069E-02 -0.1836E-01 -0.3535E-01. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=5 cm.. 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.41 0.42 0.43 0.44 0.45 0.46 0.46 0.47 0.48 0.49 0.49 0.49 0.50 0.51 0.51. -0.1247 -0.1210 -0.1176 -0.1143 -0.1112 -0.1083 -0.1055 -0.1029 -0.1004 -0.9800E-01 -0.9572E-01 -0.9355E-01 -0.9147E-01 -0.8948E-01 -0.8758E-01 -0.8575E-01 -0.8400E-01 -0.8232E-01 -0.8071E-01 -0.7915E-01 -0.7766E-01 -0.7622E-01 -0.7483E-01 -0.7349E-01 -0.7220E-01 -0.7095E-01 -0.6974E-01 -0.6858E-01. -1.858 -1.967 -2.086 -2.217 -2.360 -2.519 -2.696 -2.893 -3.116 -3.367 -3.657 -3.993 -4.387 -4.856 -5.422 -6.121 -7.005 -8.160 -9.733 -12.00 -15.56 -21.94 -36.73 -108.6 -117.7 -38.63 -23.26 -16.72. Representative Alphas of Variables FLIM(1), 2r5.pti. x 0.48 cx 0.19 cs -0.17 n 0.72 T -0.42 Sum of a²1.00. Análisis Probabilista. E. Mosquera..
(11) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=5 cm.. Reliability Index FLIM(1), 2r5.pti. Beta 3.00 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. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. 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. D0 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. Failure Probability FLIM(1), 2r5.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. 8.0. 9.0. 10.0. D0. Análisis Probabilista. E. Mosquera..
(12) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=6 cm.. -----------------------------------------------------------------------------Job name ............ : 2r6 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 22:12 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................ = 2.000 ( 0.200000000000000E+01) Standard deviation........ = 0.4000 ( 0.400000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 2.000 ( 0.200000000000000E+01) Distr.Param.no.2 : sigma = 0.4000 ( 0.400000000000000E+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) = 0.5500 ( 0.550000000000000E+00) = 0.1100 ( 0.110000000000000E+00) = 0.2000 ( 0.200000000000000E+00) = 0.5500 ( 0.550000000000000E+00) = 0.1100 ( 0.110000000000000E+00). 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 IIIc‐ CEM III‐ Cs=2%‐ 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; 2.000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.5500. (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) = 3.696 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.958 Corresponding approximate prob.of failure = 2.5101E-02 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= -0.2142E-08 and Vector u-* (beta-point) : (x ; 1; -0.9810 ) (cx ; 2; -0.3720 ) (cs ; 3; 0.3234 ) (n ; 4; -1.405 ) (T ; 5; 0.8096 ) Normalized U-space gradient (alfa-U) with norm = 0.6481 : (x ; 1; 0.5009 ) (cx ; 2; 0.1900 ) (cs ; 3; -0.1651 ) (n ; 4; 0.7175 ) (T ; 5; -0.4134 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.5009 ) (cx ; 2; 0.1900 ) (cs ; 3; -0.1651 ) (n ; 4; 0.7175 ) (T ; 5; -0.4134 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 4.823 ) (cx ; 2; 0.4628 ) (cs ; 3; 2.129 ) (n ; 4; 0.3954 ) (T ; 5; 20.91 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.2706 ) (cx ; 2; 1.231 ) (cs ; 3; -0.2676 ) (n ; 4; 4.227 ) (T ; 5; -7.4430E-02) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(14) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2%‐ 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 : 6 Calls of state-function : 37 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -14.225 -38.020 59.966. 11.012. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.944 Corresponding prob. of failure = 2.59490E-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)=. 0.987 0.990 0.997 0.993 0.996 0.992 1.02 1.03 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.=. 6.72 4.59 3.80 3.14 2.87 2.86 3.34 3.31 3.04. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.932 Corresponding prob. of failure = 2.66810E-02 Correction factor by simulation = 1.028 Coefficient of Variation in % = 2.955 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 4.83142 6.00000 0.805 (cx : 2) 0.463073 0.500000 0.926 (cs : 3) 2.12841 2.00000 1.064 (n : 4) 0.396575 0.550000 0.721 (T : 5) 20.8932 18.0000 1.161 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 2.980 1.44E-03 -0.9472 -0.3119 1.250 2.774 2.77E-03 -0.7718 -0.3417 1.500 2.603 4.62E-03 -0.6509 -0.3689 1.750 2.456 7.02E-03 -0.5628 -0.3947 2.000 2.328 9.97E-03 -0.4956 -0.4194 2.250 2.213 1.34E-02 -0.4428 -0.4435 2.500 2.111 1.74E-02 -0.4001 -0.4671 2.750 2.018 2.18E-02 -0.3650 -0.4906 3.000 1.932 2.67E-02 -0.3355 -0.5140 3.250 1.853 3.19E-02 -0.3104 -0.5373 3.500 1.780 3.76E-02 -0.2888 -0.5608 3.750 1.711 4.35E-02 -0.2701 -0.5844 4.000 1.647 4.98E-02 -0.2536 -0.6083 4.250 1.587 5.63E-02 -0.2390 -0.6325 4.500 1.530 6.30E-02 -0.2260 -0.6570 4.750 1.476 7.00E-02 -0.2143 -0.6820 5.000 1.425 7.71E-02 -0.2038 -0.7074 5.250 1.376 8.44E-02 -0.1942 -0.7332 5.500 1.329 9.19E-02 -0.1856 -0.7597 5.750 1.285 9.94E-02 -0.1776 -0.7869 6.000 1.242 0.11 -0.1703 -0.8147 6.250 1.201 0.11 -0.1636 -0.8432 6.500 1.162 0.12 -0.1574 -0.8726 6.750 1.124 0.13 -0.1517 -0.9027 7.000 1.087 0.14 -0.1463 -0.9338 7.250 1.052 0.15 -0.1413 -0.9659 7.500 1.018 0.15 -0.1367 -0.9990 7.750 0.9845 0.16 -0.1323 -1.033 8.000 0.9525 0.17 -0.1282 -1.069. 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. 0.9215 0.8914 0.8621 0.8337 0.8060 0.7791 0.7528 0.7272 0.7023 0.6779 0.6541 0.6309 0.6082 0.5859 0.5642 0.5429 0.5220 0.5016 0.4815 0.4619 0.4426 0.4237 0.4051 0.3869 0.3689 0.3513 0.3340 0.3170. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=6 cm.. 0.18 0.19 0.19 0.20 0.21 0.22 0.23 0.23 0.24 0.25 0.26 0.26 0.27 0.28 0.29 0.29 0.30 0.31 0.32 0.32 0.33 0.34 0.34 0.35 0.36 0.36 0.37 0.38. -0.1244 -0.1207 -0.1173 -0.1141 -0.1110 -0.1081 -0.1054 -0.1028 -0.1003 -0.9790E-01 -0.9563E-01 -0.9347E-01 -0.9140E-01 -0.8943E-01 -0.8753E-01 -0.8572E-01 -0.8397E-01 -0.8230E-01 -0.8069E-01 -0.7914E-01 -0.7765E-01 -0.7622E-01 -0.7482E-01 -0.7349E-01 -0.7221E-01 -0.7096E-01 -0.6976E-01 -0.6860E-01. -1.105 -1.143 -1.183 -1.224 -1.267 -1.311 -1.358 -1.406 -1.457 -1.510 -1.566 -1.625 -1.687 -1.752 -1.820 -1.893 -1.970 -2.052 -2.139 -2.232 -2.331 -2.438 -2.551 -2.674 -2.807 -2.951 -3.108 -3.280. Representative Alphas of Variables FLIM(1), 2r6.pti. x 0.50 cx 0.19 cs -0.17 n 0.72 T -0.41 Sum of a²1.00. Análisis Probabilista. E. Mosquera..
(16) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=6 cm.. Reliability Index FLIM(1), 2r6.pti. Beta 3.00 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. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. 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. D0 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. Failure Probability FLIM(1), 2r6.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. 8.0. 9.0. 10.0. D0. Análisis Probabilista. E. Mosquera..
(17) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=7 cm.. -----------------------------------------------------------------------------Job name ............ : 2r7 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 22:13 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) = 7.000 ( 0.700000000000000E+01) = 1.400 ( 0.140000000000000E+01) = 0.2000 ( 0.200000000000000E+00) = 7.000 ( 0.700000000000000E+01) = 1.400 ( 0.140000000000000E+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................ = 2.000 ( 0.200000000000000E+01) Standard deviation........ = 0.4000 ( 0.400000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 2.000 ( 0.200000000000000E+01) Distr.Param.no.2 : sigma = 0.4000 ( 0.400000000000000E+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) = 0.5500 ( 0.550000000000000E+00) = 0.1100 ( 0.110000000000000E+00) = 0.2000 ( 0.200000000000000E+00) = 0.5500 ( 0.550000000000000E+00) = 0.1100 ( 0.110000000000000E+00). 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 IIIc‐ CEM III‐ Cs=2%‐ R=7 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; 7.000 ) (cx ; 3; 2.000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.5500. (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) = 4.696 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 2.267 Corresponding approximate prob.of failure = 1.1696E-02 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= -0.3151E-07 and Vector u-* (beta-point) : (x ; 1; -1.183 ) (cx ; 2; -0.4234 ) (cs ; 3; 0.3614 ) (n ; 4; -1.609 ) (T ; 5; 0.9183 ) Normalized U-space gradient (alfa-U) with norm = 0.5715 : (x ; 1; 0.5217 ) (cx ; 2; 0.1868 ) (cs ; 3; -0.1594 ) (n ; 4; 0.7096 ) (T ; 5; -0.4051 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.5217 ) (cx ; 2; 0.1868 ) (cs ; 3; -0.1594 ) (n ; 4; 0.7096 ) (T ; 5; -0.4051 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 5.344 ) (cx ; 2; 0.4577 ) (cs ; 3; 2.145 ) (n ; 4; 0.3731 ) (T ; 5; 21.31 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.2129 ) (cx ; 2; 1.067 ) (cs ; 3; -0.2278 ) (n ; 4; 3.686 ) (T ; 5; -6.4304E-02) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(19) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=7 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 : 6 Calls of state-function : 37 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -14.820 -39.502 60.300. 10.330. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 2.246 Corresponding prob. of failure = 1.23537E-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)=. 0.987 0.987 0.993 0.990 0.991 0.986 1.02 1.04 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.=. 7.97 5.37 4.41 3.64 3.31 3.26 3.94 4.00 3.66. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 2.233 Corresponding prob. of failure = 1.27581E-02 Correction factor by simulation = 1.033 Coefficient of Variation in % = 3.530 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 5.35970 7.00000 0.766 (cx : 2) 0.458056 0.500000 0.916 (cs : 3) 2.14322 2.00000 1.072 (n : 4) 0.374700 0.550000 0.681 (T : 5) 21.2752 18.0000 1.182 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 3.256 5.65E-04 -0.9147 -0.2752 1.250 3.058 1.12E-03 -0.7514 -0.3013 1.500 2.891 1.92E-03 -0.6368 -0.3244 1.750 2.748 3.00E-03 -0.5523 -0.3457 2.000 2.622 4.37E-03 -0.4876 -0.3657 2.250 2.510 6.03E-03 -0.4364 -0.3848 2.500 2.410 7.98E-03 -0.3949 -0.4033 2.750 2.318 1.02E-02 -0.3606 -0.4214 3.000 2.234 1.28E-02 -0.3318 -0.4391 3.250 2.156 1.56E-02 -0.3073 -0.4566 3.500 2.083 1.86E-02 -0.2861 -0.4739 3.750 2.016 2.19E-02 -0.2677 -0.4911 4.000 1.952 2.55E-02 -0.2515 -0.5083 4.250 1.893 2.92E-02 -0.2371 -0.5254 4.500 1.836 3.32E-02 -0.2243 -0.5426 4.750 1.783 3.73E-02 -0.2128 -0.5598 5.000 1.732 4.17E-02 -0.2024 -0.5772 5.250 1.683 4.61E-02 -0.1930 -0.5946 5.500 1.637 5.08E-02 -0.1845 -0.6122 5.750 1.593 5.56E-02 -0.1766 -0.6300 6.000 1.551 6.05E-02 -0.1694 -0.6480 6.250 1.510 6.55E-02 -0.1628 -0.6660 6.500 1.471 7.07E-02 -0.1566 -0.6844 6.750 1.433 7.59E-02 -0.1509 -0.7031 7.000 1.397 8.13E-02 -0.1456 -0.7221 7.250 1.361 8.67E-02 -0.1407 -0.7413 7.500 1.327 9.22E-02 -0.1361 -0.7608 7.750 1.295 9.77E-02 -0.1318 -0.7807 8.000 1.263 0.10 -0.1277 -0.8010. 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. 1.232 1.202 1.173 1.144 1.117 1.090 1.064 1.038 1.013 0.9892 0.9655 0.9423 0.9196 0.8974 0.8757 0.8545 0.8337 0.8133 0.7933 0.7737 0.7544 0.7355 0.7170 0.6988 0.6809 0.6633 0.6460 0.6290. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=7 cm.. 0.11 0.11 0.12 0.13 0.13 0.14 0.14 0.15 0.16 0.16 0.17 0.17 0.18 0.18 0.19 0.20 0.20 0.21 0.21 0.22 0.23 0.23 0.24 0.24 0.25 0.25 0.26 0.26. -0.1239 -0.1203 -0.1169 -0.1137 -0.1107 -0.1078 -0.1051 -0.1025 -0.1000 -0.9765E-01 -0.9540E-01 -0.9326E-01 -0.9120E-01 -0.8924E-01 -0.8736E-01 -0.8555E-01 -0.8382E-01 -0.8216E-01 -0.8056E-01 -0.7902E-01 -0.7754E-01 -0.7611E-01 -0.7474E-01 -0.7341E-01 -0.7213E-01 -0.7090E-01 -0.6970E-01 -0.6855E-01. -0.8216 -0.8427 -0.8641 -0.8860 -0.9084 -0.9313 -0.9546 -0.9786 -1.003 -1.028 -1.054 -1.080 -1.108 -1.135 -1.164 -1.194 -1.224 -1.255 -1.287 -1.320 -1.355 -1.390 -1.427 -1.464 -1.504 -1.544 -1.586 -1.630. Representative Alphas of Variables FLIM(1), 2r7.pti. x 0.52 cx 0.19 cs -0.16 n 0.71 T -0.41 Sum of a²1.00. Análisis Probabilista. E. Mosquera..
(21) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=7 cm.. Reliability Index FLIM(1), 2r7.pti. Beta 3.00 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. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. 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. D0 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. Failure Probability FLIM(1), 2r7.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. 8.0. 9.0. 10.0. D0. Análisis Probabilista. E. Mosquera..
(22) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=8 cm.. -----------------------------------------------------------------------------Job name ............ : 2r8 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 22:13 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) = 8.000 ( 0.800000000000000E+01) = 1.600 ( 0.160000000000000E+01) = 0.2000 ( 0.200000000000000E+00) = 8.000 ( 0.800000000000000E+01) = 1.600 ( 0.160000000000000E+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................ = 2.000 ( 0.200000000000000E+01) Standard deviation........ = 0.4000 ( 0.400000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 2.000 ( 0.200000000000000E+01) Distr.Param.no.2 : sigma = 0.4000 ( 0.400000000000000E+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) = 0.5500 ( 0.550000000000000E+00) = 0.1100 ( 0.110000000000000E+00) = 0.2000 ( 0.200000000000000E+00) = 0.5500 ( 0.550000000000000E+00) = 0.1100 ( 0.110000000000000E+00). 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 IIIc‐ CEM III‐ Cs=2%‐ R=8 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; 8.000 ) (cx ; 3; 2.000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.5500. (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) = 5.696 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 2.531 Corresponding approximate prob.of failure = 5.6829E-03 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= -0.1558E-07 and Vector u-* (beta-point) : (x ; 1; -1.372 ) (cx ; 2; -0.4648 ) (cs ; 3; 0.3910 ) (n ; 4; -1.774 ) (T ; 5; 1.005 ) Normalized U-space gradient (alfa-U) with norm = 0.5183 : (x ; 1; 0.5420 ) (cx ; 2; 0.1836 ) (cs ; 3; -0.1545 ) (n ; 4; 0.7007 ) (T ; 5; -0.3971 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.5420 ) (cx ; 2; 0.1836 ) (cs ; 3; -0.1545 ) (n ; 4; 0.7007 ) (T ; 5; -0.3971 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 5.805 ) (cx ; 2; 0.4535 ) (cs ; 3; 2.156 ) (n ; 4; 0.3549 ) (T ; 5; 21.62 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.1756 ) (cx ; 2; 0.9516 ) (cs ; 3; -0.2001 ) (n ; 4; 3.301 ) (T ; 5; -5.7169E-02) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(24) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=8 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 : -15.363 -40.865 60.776. 9.737. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 2.504 Corresponding prob. of failure = 6.14649E-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)=. 0.987 0.983 0.988 0.986 0.984 0.979 1.02 1.04 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.=. 9.23 6.15 5.02 4.15 3.74 3.66 4.57 4.75 4.32. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 2.491 Corresponding prob. of failure = 6.37303E-03 Correction factor by simulation = 1.037 Coefficient of Variation in % = 4.141 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 5.82887 8.00000 0.729 (cx : 2) 0.454032 0.500000 0.908 (cs : 3) 2.15469 2.00000 1.077 (n : 4) 0.357031 0.550000 0.649 (T : 5) 21.5792 18.0000 1.199 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 3.474 2.56E-04 -0.8750 -0.2455 1.250 3.295 4.93E-04 -0.7272 -0.2702 1.500 3.134 8.63E-04 -0.6204 -0.2911 1.750 2.995 1.37E-03 -0.5404 -0.3099 2.000 2.872 2.04E-03 -0.4784 -0.3271 2.250 2.763 2.87E-03 -0.4291 -0.3434 2.500 2.664 3.86E-03 -0.3890 -0.3589 2.750 2.574 5.03E-03 -0.3557 -0.3739 3.000 2.491 6.37E-03 -0.3277 -0.3884 3.250 2.414 7.89E-03 -0.3037 -0.4025 3.500 2.343 9.57E-03 -0.2830 -0.4163 3.750 2.276 1.14E-02 -0.2649 -0.4300 4.000 2.213 1.34E-02 -0.2491 -0.4435 4.250 2.154 1.56E-02 -0.2350 -0.4568 4.500 2.099 1.79E-02 -0.2224 -0.4701 4.750 2.046 2.04E-02 -0.2111 -0.4833 5.000 1.995 2.30E-02 -0.2009 -0.4965 5.250 1.947 2.57E-02 -0.1916 -0.5096 5.500 1.902 2.86E-02 -0.1832 -0.5227 5.750 1.858 3.16E-02 -0.1754 -0.5359 6.000 1.816 3.47E-02 -0.1683 -0.5491 6.250 1.775 3.79E-02 -0.1618 -0.5623 6.500 1.736 4.12E-02 -0.1557 -0.5755 6.750 1.699 4.47E-02 -0.1501 -0.5889 7.000 1.663 4.82E-02 -0.1449 -0.6023 7.250 1.628 5.18E-02 -0.1400 -0.6157 7.500 1.594 5.54E-02 -0.1354 -0.6294 7.750 1.562 5.92E-02 -0.1311 -0.6431 8.000 1.530 6.30E-02 -0.1271 -0.6569. 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. 1.499 1.469 1.440 1.412 1.385 1.358 1.332 1.307 1.282 1.258 1.234 1.211 1.189 1.166 1.145 1.124 1.103 1.083 1.063 1.043 1.024 1.005 0.9866 0.9684 0.9506 0.9330 0.9158 0.8988. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=8 cm.. 6.69E-02 7.09E-02 7.49E-02 7.89E-02 8.30E-02 8.72E-02 9.14E-02 9.56E-02 0.10 0.10 0.11 0.11 0.12 0.12 0.13 0.13 0.14 0.14 0.14 0.15 0.15 0.16 0.16 0.17 0.17 0.18 0.18 0.18. -0.1233 -0.1198 -0.1164 -0.1132 -0.1102 -0.1074 -0.1047 -0.1021 -0.9965E-01 -0.9732E-01 -0.9509E-01 -0.9296E-01 -0.9092E-01 -0.8897E-01 -0.8710E-01 -0.8531E-01 -0.8359E-01 -0.8194E-01 -0.8035E-01 -0.7883E-01 -0.7735E-01 -0.7594E-01 -0.7457E-01 -0.7325E-01 -0.7198E-01 -0.7075E-01 -0.6956E-01 -0.6842E-01. -0.6709 -0.6850 -0.6993 -0.7138 -0.7284 -0.7431 -0.7581 -0.7733 -0.7886 -0.8042 -0.8200 -0.8361 -0.8523 -0.8689 -0.8857 -0.9028 -0.9201 -0.9378 -0.9558 -0.9741 -0.9927 -1.012 -1.031 -1.051 -1.071 -1.091 -1.112 -1.134. Representative Alphas of Variables FLIM(1), 2r8.pti. x 0.54 cx 0.18 cs -0.15 n 0.70 T -0.40 Sum of a²1.00. Análisis Probabilista. E. Mosquera..
(26) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2%‐ R=8 cm.. Reliability Index FLIM(1), 2r8.pti. Beta 3.00 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. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. 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. D0 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. Failure Probability FLIM(1), 2r8.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. 8.0. 9.0. 10.0. D0. Análisis Probabilista. E. Mosquera..
(27) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2,5%‐ R=4 cm.. -----------------------------------------------------------------------------Job name ............ : 25r4 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 22:14 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................ = 2.500 ( 0.250000000000000E+01) Standard deviation........ = 0.5000 ( 0.500000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 2.500 ( 0.250000000000000E+01) Distr.Param.no.2 : sigma = 0.5000 ( 0.500000000000000E+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) = 0.5500 ( 0.550000000000000E+00) = 0.1100 ( 0.110000000000000E+00) = 0.2000 ( 0.200000000000000E+00) = 0.5500 ( 0.550000000000000E+00) = 0.1100 ( 0.110000000000000E+00). 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 IIIc‐ CEM III‐ Cs=2,5%‐ 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; 2.500 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.5500. (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) = 1.453 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 0.941 Corresponding approximate prob.of failure = 0.1734 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= -0.2884E-08 and Vector u-* (beta-point) : (x ; 1; -0.4271 ) (cx ; 2; -0.1545 ) (cs ; 3; 0.1455 ) (n ; 4; -0.6961 ) (T ; 5; 0.4156 ) Normalized U-space gradient (alfa-U) with norm = 1.213 : (x ; 1; 0.4541 ) (cx ; 2; 0.1643 ) (cs ; 3; -0.1547 ) (n ; 4; 0.7401 ) (T ; 5; -0.4418 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.4541 ) (cx ; 2; 0.1643 ) (cs ; 3; -0.1547 ) (n ; 4; 0.7401 ) (T ; 5; -0.4418 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 3.658 ) (cx ; 2; 0.4845 ) (cs ; 3; 2.573 ) (n ; 4; 0.4734 ) (T ; 5; 19.50 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.6883 ) (cx ; 2; 1.992 ) (cs ; 3; -0.3752 ) (n ; 4; 8.159 ) (T ; 5; -0.1488 ) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(29) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2,5%‐ 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 : 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 : -15.373 -33.274 67.691. 13.038. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 0.938 Corresponding prob. of failure = 0.17406. ----- 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)=. 0.992 0.996 1.00 0.999 1.00 0.998 1.01 1.02 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.=. 3.64 2.54 2.13 1.74 1.62 1.68 1.79 1.69 1.58. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 0.928 Corresponding prob. of failure = 0.17663 Correction factor by simulation = 1.015 Coefficient of Variation in % = 1.575 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 3.65918 4.00000 0.915 (cx : 2) 0.484586 0.500000 0.969 (cs : 3) 2.57257 2.50000 1.029 (n : 4) 0.473622 0.550000 0.861 (T : 5) 19.4923 18.0000 1.083 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 2.036 2.09E-02 -1.012 -0.4890 1.250 1.815 3.48E-02 -0.8156 -0.5533 1.500 1.632 5.14E-02 -0.6831 -0.6187 1.750 1.476 6.99E-02 -0.5877 -0.6866 2.000 1.341 8.99E-02 -0.5157 -0.7582 2.250 1.222 0.11 -0.4594 -0.8345 2.500 1.114 0.13 -0.4142 -0.9166 2.750 1.017 0.15 -0.3771 -1.006 3.000 0.9283 0.18 -0.3460 -1.104 3.250 0.8464 0.20 -0.3197 -1.212 3.500 0.7705 0.22 -0.2971 -1.332 3.750 0.6998 0.24 -0.2775 -1.468 4.000 0.6336 0.26 -0.2603 -1.623 4.250 0.5714 0.28 -0.2451 -1.801 4.500 0.5127 0.30 -0.2316 -2.009 4.750 0.4572 0.32 -0.2195 -2.255 5.000 0.4044 0.34 -0.2086 -2.550 5.250 0.3543 0.36 -0.1987 -2.914 5.500 0.3064 0.38 -0.1897 -3.371 5.750 0.2607 0.40 -0.1815 -3.967 6.000 0.2169 0.41 -0.1740 -4.773 6.250 0.1749 0.43 -0.1670 -5.919. 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. 0.1346 0.9572E-01 0.5829E-01 0.2216E-01 0.1792E-02 -0.3198E-01 -0.6468E-01 -0.9638E-01 -0.1271 -0.1570 -0.1860 -0.2142 -0.2417 -0.2684 -0.2945 -0.3199 -0.3447 -0.3689 -0.3925 -0.4157 -0.4383 -0.4604 -0.4821 -0.5033 -0.5240 -0.5444 -0.5643 -0.5839 -0.6031 -0.6220 -0.6405 -0.6587 -0.6765 -0.6941 -0.7113. Ambiente IIIc‐ CEM III‐ Cs=2,5%‐ R=4 cm.. 0.45 0.46 0.48 0.49 0.50 0.51 0.53 0.54 0.55 0.56 0.57 0.58 0.60 0.61 0.62 0.63 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.69 0.70 0.71 0.71 0.72 0.73 0.73 0.74 0.74 0.75 0.76 0.76. -0.1606 -0.1547 -0.1491 -0.1440 -0.1392 -0.1347 -0.1305 -0.1266 -0.1229 -0.1193 -0.1160 -0.1129 -0.1099 -0.1071 -0.1044 -0.1018 -0.9941E-01 -0.9709E-01 -0.9488E-01 -0.9276E-01 -0.9073E-01 -0.8880E-01 -0.8694E-01 -0.8516E-01 -0.8344E-01 -0.8180E-01 -0.8022E-01 -0.7870E-01 -0.7723E-01 -0.7582E-01 -0.7446E-01 -0.7314E-01 -0.7187E-01 -0.7064E-01 -0.6946E-01. -7.711 -10.88 -18.01 -49.02 -73.97 -21.59 -12.81 -9.186 -7.209 -5.962 -5.105 -4.478 -3.998 -3.621 -3.317 -3.066 -2.855 -2.675 -2.520 -2.384 -2.265 -2.160 -2.066 -1.981 -1.905 -1.835 -1.772 -1.714 -1.661 -1.611 -1.566 -1.523 -1.484 -1.447 -1.412. Representative Alphas of Variables FLIM(1), 25r4.pti. x 0.45 cx 0.16 cs -0.15 n 0.74 T -0.44 Sum of a²1.00. Análisis Probabilista. E. Mosquera..
(31) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2,5%‐ R=4 cm.. Reliability Index FLIM(1), 25r4.pti. Beta 3.00 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. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. 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. D0 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. Failure Probability FLIM(1), 25r4.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. 8.0. 9.0. 10.0. D0. Análisis Probabilista. E. Mosquera..
(32) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2,5%‐ R=5 cm.. -----------------------------------------------------------------------------Job name ............ : 25r5 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 22:15 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................ = 2.500 ( 0.250000000000000E+01) Standard deviation........ = 0.5000 ( 0.500000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 2.500 ( 0.250000000000000E+01) Distr.Param.no.2 : sigma = 0.5000 ( 0.500000000000000E+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) = 0.5500 ( 0.550000000000000E+00) = 0.1100 ( 0.110000000000000E+00) = 0.2000 ( 0.200000000000000E+00) = 0.5500 ( 0.550000000000000E+00) = 0.1100 ( 0.110000000000000E+00). 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 IIIc‐ CEM III‐ Cs=2,5%‐ 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; 2.500 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.5500. (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) = 2.453 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.402 Corresponding approximate prob.of failure = 8.0390E-02 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= -0.4894E-08 and Vector u-* (beta-point) : (x ; 1; -0.6673 ) (cx ; 2; -0.2267 ) (cs ; 3; 0.2078 ) (n ; 4; -1.030 ) (T ; 5; 0.6045 ) Normalized U-space gradient (alfa-U) with norm = 0.8569 : (x ; 1; 0.4758 ) (cx ; 2; 0.1617 ) (cs ; 3; -0.1482 ) (n ; 4; 0.7347 ) (T ; 5; -0.4310 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.4758 ) (cx ; 2; 0.1617 ) (cs ; 3; -0.1482 ) (n ; 4; 0.7347 ) (T ; 5; -0.4310 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 4.333 ) (cx ; 2; 0.4773 ) (cs ; 3; 2.604 ) (n ; 4; 0.4367 ) (T ; 5; 20.18 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.4077 ) (cx ; 2; 1.385 ) (cs ; 3; -0.2539 ) (n ; 4; 5.723 ) (T ; 5; -0.1026 ) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(34) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM III‐ Cs=2,5%‐ 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 : 4 Calls of state-function : 25 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -16.225 -35.252 67.762. 12.084. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.393 Corresponding prob. of failure = 8.18057E-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)=. 0.993 0.995 1.00 0.998 0.999 0.995 1.01 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.=. 4.82 3.30 2.74 2.24 2.06 2.12 2.32 2.26 2.09. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.383 Corresponding prob. of failure = 8.34036E-02 Correction factor by simulation = 1.020 Coefficient of Variation in % = 2.069 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 4.33719 5.00000 0.867 (cx : 2) 0.477480 0.500000 0.955 (cs : 3) 2.60320 2.50000 1.041 (n : 4) 0.437426 0.550000 0.795 (T : 5) 20.1616 18.0000 1.120 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 2.473 6.70E-03 -0.9913 -0.3939 1.250 2.256 1.20E-02 -0.8020 -0.4370 1.500 2.077 1.89E-02 -0.6735 -0.4787 1.750 1.924 2.72E-02 -0.5805 -0.5198 2.000 1.791 3.67E-02 -0.5101 -0.5610 2.250 1.673 4.72E-02 -0.4549 -0.6028 2.500 1.567 5.86E-02 -0.4106 -0.6455 2.750 1.471 7.07E-02 -0.3741 -0.6895 3.000 1.383 8.34E-02 -0.3435 -0.7349 3.250 1.301 9.66E-02 -0.3176 -0.7821 3.500 1.226 0.11 -0.2953 -0.8314 3.750 1.156 0.12 -0.2759 -0.8829 4.000 1.090 0.14 -0.2589 -0.9372 4.250 1.028 0.15 -0.2439 -0.9946 4.500 0.9700 0.17 -0.2306 -1.055 4.750 0.9147 0.18 -0.2186 -1.120 5.000 0.8623 0.19 -0.2078 -1.189 5.250 0.8123 0.21 -0.1980 -1.263 5.500 0.7647 0.22 -0.1891 -1.343 5.750 0.7191 0.24 -0.1810 -1.429 6.000 0.6755 0.25 -0.1735 -1.522 6.250 0.6336 0.26 -0.1666 -1.623 6.500 0.5934 0.28 -0.1603 -1.734 6.750 0.5546 0.29 -0.1544 -1.856 7.000 0.5173 0.30 -0.1489 -1.991 7.250 0.4812 0.32 -0.1438 -2.141 7.500 0.4464 0.33 -0.1390 -2.309 7.750 0.4127 0.34 -0.1346 -2.499 8.000 0.3801 0.35 -0.1304 -2.715. Análisis Probabilista. E. Mosquera..
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