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TítuloProbabilismo explícito en la corrosión de armaduras en las estructuras de hormigón sometidas al ambiente marino de la costa gallega

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(1)Cálculos Probabilistas, en Ambiente IIIa-500, Tipo de Cemento CEM I, Cc=300 Kg/m3, a/c=0.4,t=50 años y recubrimientos 2,2 cm. y 4 cm.. Influencia de la variabilidad conjunta de las variables básicas sobre la probabilidad de fallo.. Anejo nº 6.-. Probabilismo explicito en la corrosión de armaduras en las estructuras de hormigón sometidas al ambiente marino de la costa gallega.. Emilio Mosquera Rey.

(2) 2.50. Beta. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. Reliability Index FLIM(1), DP1.pti. 48.50. 54.25. Emilio Mosquera Rey 2.50. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. Failure Probability FLIM(1), DP1.pti. 48.50. 54.25. 60.00. 60.00. 0.82. 0.85. 0.88. 0.91. 0.95. 0.98. 1.01. 1.04. 1.07. 1.10. 2.50. 8.25. 14.00. 0.00 1.75 -107374184.00 2.53 -151996493463552.00. P.S.F. 1.13. 19.75. 25.50. 31.25 t. 37.00. 42.75. Partial Safety Factors FLIM(1), DP1.pti. 48.50. 54.25. 60.00. n Do cs cx x. Variación de los Coef. parciales de seguridad en función del tiempo o del recubr.. 0.00. 0.08. 0.17. 0.25. 0.34. 0.42. 0.50. 0.59. 0.67. 0.76. Failure Probability 0.84. Variación de la Probabilidad de fallo en función del tiempo o del recubrimiento. -0.99. 4.06. 9.10. 14.15. 19.19. 24.24. 29.29. 34.33. 39.38. 44.42. 49.47. Variación del Índice de fiabilidad en función del tiempo o del recubrimiento. Contenido del anejo 6. Probabilismo explicito en la corrosión de armaduras en las estructuras de hormigón sometidas al ambiente marino de la costa gallega..

(3) Emilio Mosquera Rey. Cosenos directores de la significación de cada variable básica en el análisis efectuado.. n 0.46 Do -0. 14 cs -0. 58 cx 0.59 x 0.29 S um of a²1.00. Representative Alphas of Variables FLIM(1), DP1.pti. Los gráficos que se muestran, de los análisis realizados son:. Índice de fiabilidad según FORM, SORM y muestreo por significación; Coeficientes parciales de seguridad para cada variable. y en función del parámetro de estudio: Índice de fiabilidad; Probabilidad de fallo; y sensibilidad y elasticidad del parámetro.. Los resultados que se obtienen son:. Nombre del trabajo; Tipo de transformación; Algoritmo de optimización; Función de estado límite; Variables básicas estocásticas.. Para cada cálculo efectuado se especifica:. 3.- Denominados.- cv5-R; cv10-R; cv15-R; cv30-R; cv70-R. Son los resúmenes probabilistas para el conjunto paramétrico con t=50 años y recubrimiento variable determinista y variabilidad del resto de las variables básicas de 5%,10%,15%,30% y 70%. 2.- Denominados.- cv5r4; cv10r4; cv15r4; cv30r4; cv70r4. Son los resúmenes probabilistas para el conjunto paramétrico con recubrimiento 4 cm. y variabilidad de todos las variables básicas de 5%,10%,15%,30% y 70%. 1.-Denominados.- cv5; cv10; cv15; cv30; cv70. Son los resúmenes probabilistas para el conjunto paramétrico con recubrimiento 2,2 cm. y variabilidad de todos las variables básicas de 5%,10%,15%,30% y 70%. Los estudios se efectúan sobre un ambiente IIIa-500, un hormigón de relación a/c= 0,4 , Contenido de cemento 300 kg/m3, tiempo 50 años, tipo de cemento CEM I, Se estudian para los recubrimientos 2.2 cm. Y 4 cm. Y en estas condiciones se estudian los siguientes conjuntos de casos:. Resumen de los cálculos probabilistas para conocer la influencia de la variabilidad conjunta de los parámetros utilizados en el anejo 9º de EHE08, sobre la probabilidad de fallo en el estado límite. Su comportamiento en el tiempo y para un periodo de 50 años, su influencia sobre el recubrimiento.. El contenido del anejo es el siguiente:. Referencia del Análisis: Variabilidad del conjunto paramétrico de variables básicas.. Contenido del anejo 6. Probabilismo explicito en la corrosión de armaduras en las estructuras de hormigón sometidas al ambiente marino de la costa gallega..

(4) Estudio Cof. Variación(5%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. -----------------------------------------------------------------------------Job name ............ : cv5 -----------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: FLIM(1)=x-(2*(1-sqrt(cx/cs))*sqrt(3*0.315*Do*(0.0767/t)^n*t)) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************. Variable: x ; No. on X-vector = 1 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 2.200 ( 0.220000000000000E+01) Standard deviation........ = 0.1100 ( 0.110000000000000E+00) Coefficient of Variation.. = 5.0000E-02 ( 0.500000000000000E-01) Distr.Param.no.1 : m = 2.200 ( 0.220000000000000E+01) Distr.Param.no.2 : sigma = 0.1100 ( 0.110000000000000E+00) ------------------------Variable: n ; No. on X-vector = 2 Comment : factor de edad Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 2.5000E-02 ( 0.250000000000000E-01) Coefficient of Variation.. = 5.0000E-02 ( 0.500000000000000E-01) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 2.5000E-02 ( 0.250000000000000E-01) ------------------------Variable: Do ; No. on X-vector = 3 Comment : Coef. Difusión inicial en cm2/s Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 8.900 ( 0.890000000000000E+01) Standard deviation........ = 0.4450 ( 0.445000000000000E+00) Coefficient of Variation.. = 5.0000E-02 ( 0.500000000000000E-01) Distr.Param.no.1 : m = 8.900 ( 0.890000000000000E+01) Distr.Param.no.2 : sigma = 0.4450 ( 0.445000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 4 Comment : contenido superficial (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 1.073 ( 0.107300000000000E+01) Standard deviation........ = 5.3600E-02 ( 0.536000000000000E-01) Coefficient of Variation.. = 4.9953E-02 ( 0.499534016775396E-01) Distr.Param.no.1 : m = 1.073 ( 0.107300000000000E+01) Distr.Param.no.2 : sigma = 5.3600E-02 ( 0.536000000000000E-01) ------------------------Variable: cx ; No. on X-vector = 5 Comment : contenido critico (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.6000 ( 0.600000000000000E+00) Standard deviation........ = 3.0000E-02 ( 0.300000000000000E-01) Coefficient of Variation.. = 5.0000E-02 ( 0.500000000000000E-01) Distr.Param.no.1 : m = 0.6000 ( 0.600000000000000E+00) Distr.Param.no.2 : sigma = 3.0000E-02 ( 0.300000000000000E-01) -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= 1 with value = 50.00 Comment : tiempo en años ------------------------(Lower bounds on U-space variables) (x ; 1; -30.00 ) (n ; 2; -30.00 (Do ; 3; -30.00 ) (cs ; 4; -30.00 (cx ; 5; -30.00 ). (x (Do (cx. ----- U-start as given by user ; 1; 0.000 ) (n ; 3; 0.000 ) (cs ; 5; 0.000 ). ; ;. -----2; 0.000 4; 0.000. ) ). ) ). Análisis Probabilista. E. Mosquera..

(5) Estudio Cof. Variación(5%). (x (Do (cx. Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. ---- X-start computed from U-start ----; 1; 2.200 ) (n ; 2; 0.5000 ; 3; 8.900 ) (cs ; 4; 1.073 ; 5; 0.6000 ). ) ). (Upper bounds on U-space variables) (x ; 1; 30.00 ) (n ; 2; 30.00 ) (Do ; 3; 30.00 ) (cs ; 4; 30.00 ) (cx ; 5; 30.00 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 200 1 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) = 0.1528 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 0.507 Corresponding approximate prob.of failure = 0.3060 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.8936E-08 and Vector u-* (beta-point) : (x ; 1; -0.1824 ) (n ; 2; -0.2929 ) (Do ; 3; 8.9984E-02) (cs ; 4; 0.2516 ) (cx ; 5; -0.2584 ) Normalized U-space gradient (alfa-U) with norm = 2.001 : (x ; 1; 0.3597 ) (n ; 2; 0.5774 ) (Do ; 3; -0.1774 ) (cs ; 4; -0.4962 ) (cx ; 5; 0.5094 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.3597 ) (n ; 2; 0.5774 ) (Do ; 3; -0.1774 ) (cs ; 4; -0.4962 ) (cx ; 5; 0.5094 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 2.180 ) (n ; 2; 0.4927 ) (Do ; 3; 8.940 ) (cs ; 4; 1.086 ) (cx ; 5; 0.5922 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 6.544 ) (n ; 2; 46.22 ) (Do ; 3; -0.7978 ) (cs ; 4; -18.52 ) (cx ; 5; 33.98 ) -----------------------------------------------------------------------------Constant Parameters (PVEC): (t ; 1; 50.00 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 3 Calls of state-function : 19 -----------------------------------------------------------------------------***************************************************** 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 : -19.523 -123.778 175.711. 70.515. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 0.526 Corresponding prob. of failure = 0.29946. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 100 E(Sim)= Importance sampling: Sample no. 120 E(Sim)= Importance sampling: Sample no. 140 E(Sim)= Importance sampling: Sample no. 160 E(Sim)=. 0.989 0.994 1.01 1.01 1.00 0.998 0.998 0.998. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 1.00 0.79 0.67 0.72 0.63 0.56 0.51 0.47. (%) (%) (%) (%) (%) (%) (%) (%). Análisis Probabilista. E. Mosquera..

(6) Estudio Cof. Variación(5%). Importance sampling: Sample no. 180. Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. E(Sim)=. 0.997. C.o.V.=. 0.44 (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 0.528 Corresponding prob. of failure = 0.29870 Correction factor by simulation = 0.997 Coefficient of Variation in % = 0.407 200(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 2.17919 2.20000 0.991 (n : 2) 0.492407 0.500000 0.985 (Do : 3) 8.94153 8.90000 1.005 (cs : 4) 1.08699 1.07300 1.013 (cx : 5) 0.591962 0.600000 0.987 ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 11.78 2.67E-32 -4.737 -0.2012 3.500 6.578 2.39E-11 -0.7751 -0.4129 6.500 4.951 3.70E-07 -0.3909 -0.5143 9.500 4.014 2.99E-05 -0.2535 -0.6020 12.50 3.368 3.79E-04 -0.1846 -0.6881 15.50 2.881 1.98E-03 -0.1437 -0.7771 18.50 2.494 6.32E-03 -0.1168 -0.8723 21.50 2.174 1.49E-02 -0.9793E-01 -0.9762 24.50 1.902 2.86E-02 -0.8399E-01 -1.092 27.50 1.668 4.77E-02 -0.7330E-01 -1.222 30.50 1.461 7.20E-02 -0.6488E-01 -1.372 33.50 1.278 0.10 -0.5808E-01 -1.546 36.50 1.113 0.13 -0.5248E-01 -1.752 39.50 0.9627 0.17 -0.4780E-01 -2.003 42.50 0.8257 0.20 -0.4384E-01 -2.313 45.50 0.6997 0.24 -0.4044E-01 -2.709 48.50 0.5832 0.28 -0.3749E-01 -3.233 51.50 0.4750 0.32 -0.3492E-01 -3.963 54.50 0.3739 0.35 -0.3266E-01 -5.048 57.50 0.2793 0.39 -0.3065E-01 -6.840 60.50 0.1903 0.42 -0.2885E-01 -10.36 63.50 0.1064 0.46 -0.2725E-01 -20.46 66.50 0.2712E-01 0.49 -0.2580E-01 -357.5 69.50 -0.4778E-01 0.52 -0.2448E-01 -24.16 72.50 -0.1192 0.55 -0.2328E-01 -11.92. Representative Alphas of Variables FLIM(1), cv5.pti. x 0.36 n 0.58 Do -0.18 cs -0.50 cx 0.51 Sum of a² 1.00. Análisis Probabilista. E. Mosquera..

(7) Estudio Cof. Variación(5%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. Reliability Index FLIM(1), cv5.pti. Beta 11.78. 10.59 9.40 8.21 7.02 5.83 4.64 3.45 2.26 1.07 -0.12. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. 58.10. 65.30. 72.50. 58.10. 65.30. 72.50. Failure Probability FLIM(1), cv5.pti. Failure Probability 0.55. 0.49 0.44 0.38 0.33 0.27 0.22 0.16 0.11 0.05 0.00. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. Partial Safety Factors FLIM(1), cv5.pti. P.S.F. 1.16 -0.00 2.02 1.10 0.00 1.75 1.03 -107374184.00. x n Do cs cx. 0.97 0.90 0.84 0.78 0.71 0.65 0.58 0.52. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. 58.10. 65.30. 72.50. Análisis Probabilista. E. Mosquera..

(8) Estudio Cof. Variación(10%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. Job name ............ : cv10 -----------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: FLIM(1)=x-(2*(1-sqrt(cx/cs))*sqrt(3*0.315*Do*(0.0767/t)^n*t)) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************ Variable: x ; No. on X-vector = 1 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 2.200 ( 0.220000000000000E+01) Standard deviation........ = 0.2200 ( 0.220000000000000E+00) Coefficient of Variation.. = 0.1000 ( 0.100000000000000E+00) Distr.Param.no.1 : m = 2.200 ( 0.220000000000000E+01) Distr.Param.no.2 : sigma = 0.2200 ( 0.220000000000000E+00) ------------------------Variable: n ; No. on X-vector = 2 Comment : factor de edad Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 5.0000E-02 ( 0.500000000000000E-01) Coefficient of Variation.. = 0.1000 ( 0.100000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 5.0000E-02 ( 0.500000000000000E-01) ------------------------Variable: Do ; No. on X-vector = 3 Comment : Coef. Difusión inicial en cm2/s Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 8.900 ( 0.890000000000000E+01) Standard deviation........ = 0.8900 ( 0.890000000000000E+00) Coefficient of Variation.. = 0.1000 ( 0.100000000000000E+00) Distr.Param.no.1 : m = 8.900 ( 0.890000000000000E+01) Distr.Param.no.2 : sigma = 0.8900 ( 0.890000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 4 Comment : contenido superficial (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 1.073 ( 0.107300000000000E+01) Standard deviation........ = 0.1070 ( 0.107000000000000E+00) Coefficient of Variation.. = 9.9720E-02 ( 0.997204100652377E-01) Distr.Param.no.1 : m = 1.073 ( 0.107300000000000E+01) Distr.Param.no.2 : sigma = 0.1070 ( 0.107000000000000E+00) ------------------------Variable: cx ; No. on X-vector = 5 Comment : contenido critico (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.6000 ( 0.600000000000000E+00) Standard deviation........ = 6.0000E-02 ( 0.600000000000000E-01) Coefficient of Variation.. = 0.1000 ( 0.100000000000000E+00) Distr.Param.no.1 : m = 0.6000 ( 0.600000000000000E+00) Distr.Param.no.2 : sigma = 6.0000E-02 ( 0.600000000000000E-01) -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= 1 with value = 50.00 Comment : tiempo en años ------------------------(Lower bounds on U-space variables) (x ; 1; -30.00 ) (n ; 2; -30.00 (Do ; 3; -30.00 ) (cs ; 4; -30.00 (cx ; 5; -30.00 ). ) ). (x (Do (cx. ----- U-start as given by user ; 1; 0.000 ) (n ; 3; 0.000 ) (cs ; 5; 0.000 ). -----2; 0.000 4; 0.000. ) ). (x (Do. ---- X-start computed from U-start ----; 1; 2.200 ) (n ; 2; 0.5000 ; 3; 8.900 ) (cs ; 4; 1.073. ) ). ; ;. Análisis Probabilista. E. Mosquera..

(9) Estudio Cof. Variación(10%). (cx. ;. 5;. 0.6000. Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. ). (Upper bounds on U-space variables) (x ; 1; 30.00 ) (n ; 2; 30.00 ) (Do ; 3; 30.00 ) (cs ; 4; 30.00 ) (cx ; 5; 30.00 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 200 1 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) = 0.1528 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 0.254 Corresponding approximate prob.of failure = 0.3999 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.8895E-08 and Vector u-* (beta-point) : (x ; 1; -9.1303E-02) (n ; 2; -0.1466 ) (Do ; 3; 4.5031E-02) (cs ; 4; 0.1257 ) (cx ; 5; -0.1293 ) Normalized U-space gradient (alfa-U) with norm = 4.000 : (x ; 1; 0.3599 ) (n ; 2; 0.5777 ) (Do ; 3; -0.1775 ) (cs ; 4; -0.4955 ) (cx ; 5; 0.5097 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.3599 ) (n ; 2; 0.5777 ) (Do ; 3; -0.1775 ) (cs ; 4; -0.4955 ) (cx ; 5; 0.5097 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 2.180 ) (n ; 2; 0.4927 ) (Do ; 3; 8.940 ) (cs ; 4; 1.086 ) (cx ; 5; 0.5922 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 6.544 ) (n ; 2; 46.22 ) (Do ; 3; -0.7978 ) (cs ; 4; -18.52 ) (cx ; 5; 33.98 ) -----------------------------------------------------------------------------Constant Parameters (PVEC): (t ; 1; 50.00 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 3 Calls of state-function : 19 -----------------------------------------------------------------------------***************************************************** 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 : -9.806 -62.025 88.241. 35.277. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 0.290 Corresponding prob. of failure = 0.38599. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 100 E(Sim)= Importance sampling: Sample no. 120 E(Sim)= Importance sampling: Sample no. 140 E(Sim)= Importance sampling: Sample no. 160 E(Sim)= Importance sampling: Sample no. 180 E(Sim)=. 0.981 0.989 1.01 1.01 0.999 0.995 0.996 0.996 0.994. 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.=. 1.67 1.32 1.12 1.22 1.07 0.95 0.86 0.79 0.74. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling --------------------. Análisis Probabilista. E. Mosquera..

(10) Estudio Cof. Variación(10%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. Corrected reliability index = 0.296 Corresponding prob. of failure = 0.38378 Correction factor by simulation = 0.994 Coefficient of Variation in % = 0.688 200(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 2.17706 2.20000 0.990 (n : 2) 0.491630 0.500000 0.983 (Do : 3) 8.94578 8.90000 1.005 (cs : 4) 1.08836 1.07300 1.014 (cx : 5) 0.591138 0.600000 0.985 ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 5.893 1.90E-09 -2.368 -0.2011 3.500 3.302 4.79E-04 -0.3876 -0.4129 6.500 2.493 6.34E-03 -0.1955 -0.5142 9.500 2.027 2.13E-02 -0.1268 -0.6019 12.50 1.706 4.40E-02 -0.9231E-01 -0.6880 15.50 1.464 7.16E-02 -0.7186E-01 -0.7771 18.50 1.272 0.10 -0.5842E-01 -0.8723 21.50 1.113 0.13 -0.4898E-01 -0.9763 24.50 0.9780 0.16 -0.4201E-01 -1.092 27.50 0.8614 0.19 -0.3667E-01 -1.222 30.50 0.7589 0.22 -0.3245E-01 -1.372 33.50 0.6677 0.25 -0.2905E-01 -1.546 36.50 0.5857 0.28 -0.2625E-01 -1.752 39.50 0.5113 0.30 -0.2391E-01 -2.003 42.50 0.4433 0.33 -0.2193E-01 -2.313 45.50 0.3807 0.35 -0.2023E-01 -2.709 48.50 0.3229 0.37 -0.1875E-01 -3.233 51.50 0.2692 0.39 -0.1747E-01 -3.962 54.50 0.2190 0.41 -0.1634E-01 -5.048 57.50 0.1721 0.43 -0.1533E-01 -6.839 60.50 0.1279 0.45 -0.1443E-01 -10.31 63.50 0.8628E-01 0.47 -0.1363E-01 -20.46 66.50 0.4693E-01 0.48 -0.1290E-01 -357.5 69.50 0.1050E-01 0.50 -0.1225E-01 -24.16 72.50 -0.2486E-01 0.51 -0.1165E-01 -11.92. Representative Alphas of Variables FLIM(1), cv10.pti. x 0.36 n 0.58 Do -0.18 cs -0.50 cx 0.51 Sum of a² 1.00. Análisis Probabilista. E. Mosquera..

(11) Estudio Cof. Variación(10%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. Reliability Index FLIM(1), cv10.pti. Beta 5.89. 5.30 4.71 4.12 3.53 2.93 2.34 1.75 1.16 0.57 -0.02. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. 58.10. 65.30. 72.50. 58.10. 65.30. 72.50. Failure Probability FLIM(1), cv10.pti. Failure Probability 0.51. 0.46 0.41 0.36 0.31 0.25 0.20 0.15 0.10 0.05 0.00. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. Partial Safety Factors FLIM(1), cv10.pti. P.S.F. 1.16 -0.00 2.02 1.10 0.00 1.75 1.03 -107374184.00. x n Do cs cx. 0.97 0.90 0.84 0.78 0.71 0.65 0.58 0.52. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. 58.10. 65.30. 72.50. Análisis Probabilista. E. Mosquera..

(12) Estudio Cof. Variación(15%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. Job name ............ : cv15 -----------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: FLIM(1)=x-(2*(1-sqrt(cx/cs))*sqrt(3*0.315*Do*(0.0767/t)^n*t)) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************ Variable: x ; No. on X-vector = 1 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 2.200 ( 0.220000000000000E+01) Standard deviation........ = 0.3300 ( 0.330000000000000E+00) Coefficient of Variation.. = 0.1500 ( 0.150000000000000E+00) Distr.Param.no.1 : m = 2.200 ( 0.220000000000000E+01) Distr.Param.no.2 : sigma = 0.3300 ( 0.330000000000000E+00) ------------------------Variable: n ; No. on X-vector = 2 Comment : factor de edad Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 7.5000E-02 ( 0.750000000000000E-01) Coefficient of Variation.. = 0.1500 ( 0.150000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 7.5000E-02 ( 0.750000000000000E-01) ------------------------Variable: Do ; No. on X-vector = 3 Comment : Coef. Difusión inicial en cm2/s Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 8.900 ( 0.890000000000000E+01) Standard deviation........ = 1.335 ( 0.133500000000000E+01) Coefficient of Variation.. = 0.1500 ( 0.150000000000000E+00) Distr.Param.no.1 : m = 8.900 ( 0.890000000000000E+01) Distr.Param.no.2 : sigma = 1.335 ( 0.133500000000000E+01) ------------------------Variable: cs ; No. on X-vector = 4 Comment : contenido superficial (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 1.073 ( 0.107300000000000E+01) Standard deviation........ = 0.1610 ( 0.161000000000000E+00) Coefficient of Variation.. = 0.1500 ( 0.150046598322460E+00) Distr.Param.no.1 : m = 1.073 ( 0.107300000000000E+01) Distr.Param.no.2 : sigma = 0.1610 ( 0.161000000000000E+00) ------------------------Variable: cx ; No. on X-vector = 5 Comment : contenido critico (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.6000 ( 0.600000000000000E+00) Standard deviation........ = 9.0000E-02 ( 0.900000000000000E-01) Coefficient of Variation.. = 0.1500 ( 0.150000000000000E+00) Distr.Param.no.1 : m = 0.6000 ( 0.600000000000000E+00) Distr.Param.no.2 : sigma = 9.0000E-02 ( 0.900000000000000E-01) -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años -------------------------. (x (Do (cx. (x (Do (cx. ; ; ;. 1 with value =. (Lower bounds on U-space variables) 1; -30.00 ) (n ; 2; 3; -30.00 ) (cs ; 4; 5; -30.00 ). ----- U-start as given by user ; 1; 0.000 ) (n ; 3; 0.000 ) (cs ; 5; 0.000 ) ---- X-start computed from U-start. ; ;. 50.00. -30.00 -30.00. ) ). -----2; 0.000 4; 0.000. ) ). -----. Análisis Probabilista. E. Mosquera..

(13) Estudio Cof. Variación(15%). (x (Do (cx. ; ; ;. 1; 3; 5;. 2.200 8.900 0.6000. ) ) ). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. (n (cs. ; ;. 2; 4;. 0.5000 1.073. ) ). (Upper bounds on U-space variables) (x ; 1; 30.00 ) (n ; 2; 30.00 ) (Do ; 3; 30.00 ) (cs ; 4; 30.00 ) (cx ; 5; 30.00 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 200 1 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) = 0.1528 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 0.169 Corresponding approximate prob.of failure = 0.4329 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.8968E-08 and Vector u-* (beta-point) : (x ; 1; -6.0778E-02) (n ; 2; -9.7560E-02) (Do ; 3; 2.9977E-02) (cs ; 4; 8.3927E-02) (cx ; 5; -8.6067E-02) Normalized U-space gradient (alfa-U) with norm = 6.005 : (x ; 1; 0.3596 ) (n ; 2; 0.5773 ) (Do ; 3; -0.1774 ) (cs ; 4; -0.4966 ) (cx ; 5; 0.5093 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.3596 ) (n ; 2; 0.5773 ) (Do ; 3; -0.1774 ) (cs ; 4; -0.4966 ) (cx ; 5; 0.5093 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 2.180 ) (n ; 2; 0.4927 ) (Do ; 3; 8.940 ) (cs ; 4; 1.087 ) (cx ; 5; 0.5923 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 6.544 ) (n ; 2; 46.22 ) (Do ; 3; -0.7978 ) (cs ; 4; -18.52 ) (cx ; 5; 33.98 ) -----------------------------------------------------------------------------Constant Parameters (PVEC): (t ; 1; 50.00 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 3 Calls of state-function : 19 -----------------------------------------------------------------------------***************************************************** 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 : -6.545 -41.486 59.007. 23.558. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 0.221 Corresponding prob. of failure = 0.41244. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 100 E(Sim)= Importance sampling: Sample no. 120 E(Sim)= Importance sampling: Sample no. 140 E(Sim)= Importance sampling: Sample no. 160 E(Sim)= Importance sampling: Sample no. 180 E(Sim)=. 0.973 0.983 1.01 1.01 0.997 0.992 0.992 0.992 0.990. 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.=. 2.32 1.85 1.56 1.73 1.53 1.35 1.22 1.13 1.04. (%) (%) (%) (%) (%) (%) (%) (%) (%). Análisis Probabilista. E. Mosquera..

(14) Estudio Cof. Variación(15%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. -------------------- Results of importance sampling -------------------Corrected reliability index = 0.232 Corresponding prob. of failure = 0.40837 Correction factor by simulation = 0.990 Coefficient of Variation in % = 0.975 200(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 2.17374 2.20000 0.988 (n : 2) 0.490420 0.500000 0.981 (Do : 3) 8.95239 8.90000 1.006 (cs : 4) 1.09069 1.07300 1.016 (cx : 5) 0.589859 0.600000 0.983 ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 3.932 4.22E-05 -1.579 -0.2012 3.500 2.214 1.34E-02 -0.2584 -0.4130 6.500 1.679 4.66E-02 -0.1303 -0.5144 9.500 1.373 8.49E-02 -0.8448E-01 -0.6020 12.50 1.161 0.12 -0.6151E-01 -0.6881 15.50 1.001 0.16 -0.4788E-01 -0.7772 18.50 0.8744 0.19 -0.3893E-01 -0.8725 21.50 0.7697 0.22 -0.3264E-01 -0.9764 24.50 0.6809 0.25 -0.2799E-01 -1.092 27.50 0.6041 0.27 -0.2443E-01 -1.222 30.50 0.5367 0.30 -0.2162E-01 -1.372 33.50 0.4766 0.32 -0.1935E-01 -1.546 36.50 0.4227 0.34 -0.1749E-01 -1.752 39.50 0.3737 0.35 -0.1593E-01 -2.003 42.50 0.3289 0.37 -0.1461E-01 -2.313 45.50 0.2878 0.39 -0.1347E-01 -2.709 48.50 0.2497 0.40 -0.1249E-01 -3.233 51.50 0.2144 0.42 -0.1164E-01 -3.963 54.50 0.1814 0.43 -0.1088E-01 -5.048 57.50 0.1505 0.44 -0.1021E-01 -6.789 60.50 0.1215 0.45 -0.9616E-02 -10.31 63.50 0.9412E-01 0.46 -0.9079E-02 -20.46 66.50 0.6826E-01 0.47 -0.8598E-02 -0.6920+293 69.50 0.4558E-01 0.48 -0.8158E-02 -24.16 72.50 0.2241E-01 0.49 -0.7759E-02 -11.92. Representative Alphas of Variables FLIM(1), cv15.pti. x 0.36 n 0.58 Do -0.18 cs -0.50 cx 0.51 Sum of a² 1.00. Análisis Probabilista. E. Mosquera..

(15) Estudio Cof. Variación(15%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. Reliability Index FLIM(1), cv15.pti. Beta 3.93. 3.54 3.15 2.76 2.37 1.98 1.59 1.20 0.80 0.41 0.02. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. 58.10. 65.30. 72.50. 58.10. 65.30. 72.50. Failure Probability FLIM(1), cv15.pti. Failure Probability 0.49. 0.44 0.39 0.34 0.29 0.25 0.20 0.15 0.10 0.05 0.00. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. Partial Safety Factors FLIM(1), cv15.pti. P.S.F. 1.16 -0.00 2.02 1.10 0.00 1.75 1.03 -107374184.00. x n Do cs cx. 0.97 0.90 0.84 0.78 0.71 0.65 0.58 0.52. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. 58.10. 65.30. 72.50. Análisis Probabilista. E. Mosquera..

(16) Estudio Cof. Variación(30%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. Job name ............ : cv30 -----------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: FLIM(1)=x-(2*(1-sqrt(cx/cs))*sqrt(3*0.315*Do*(0.0767/t)^n*t)) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************ Variable: x ; No. on X-vector = 1 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 2.200 ( 0.220000000000000E+01) Standard deviation........ = 0.6600 ( 0.660000000000000E+00) Coefficient of Variation.. = 0.3000 ( 0.300000000000000E+00) Distr.Param.no.1 : m = 2.200 ( 0.220000000000000E+01) Distr.Param.no.2 : sigma = 0.6600 ( 0.660000000000000E+00) ------------------------Variable: n ; No. on X-vector = 2 Comment : factor de edad Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.1500 ( 0.150000000000000E+00) Coefficient of Variation.. = 0.3000 ( 0.300000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.1500 ( 0.150000000000000E+00) ------------------------Variable: Do ; No. on X-vector = 3 Comment : Coef. Difusión inicial en cm2/s Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 8.900 ( 0.890000000000000E+01) Standard deviation........ = 2.670 ( 0.267000000000000E+01) Coefficient of Variation.. = 0.3000 ( 0.300000000000000E+00) Distr.Param.no.1 : m = 8.900 ( 0.890000000000000E+01) Distr.Param.no.2 : sigma = 2.670 ( 0.267000000000000E+01) ------------------------Variable: cs ; No. on X-vector = 4 Comment : contenido superficial (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 1.073 ( 0.107300000000000E+01) Standard deviation........ = 0.3220 ( 0.322000000000000E+00) Coefficient of Variation.. = 0.3001 ( 0.300093196644921E+00) Distr.Param.no.1 : m = 1.073 ( 0.107300000000000E+01) Distr.Param.no.2 : sigma = 0.3220 ( 0.322000000000000E+00) ------------------------Variable: cx ; No. on X-vector = 5 Comment : contenido critico (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.6000 ( 0.600000000000000E+00) Standard deviation........ = 0.1800 ( 0.180000000000000E+00) Coefficient of Variation.. = 0.3000 ( 0.300000000000000E+00) Distr.Param.no.1 : m = 0.6000 ( 0.600000000000000E+00) Distr.Param.no.2 : sigma = 0.1800 ( 0.180000000000000E+00) -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años -------------------------. (x (Do (cx. (x (Do (cx. ; ; ;. 1 with value =. (Lower bounds on U-space variables) 1; -30.00 ) (n ; 2; 3; -30.00 ) (cs ; 4; 5; -30.00 ). ----- U-start as given by user ; 1; 0.000 ) (n ; 3; 0.000 ) (cs ; 5; 0.000 ) ---- X-start computed from U-start. ; ;. 50.00. -30.00 -30.00. ) ). -----2; 0.000 4; 0.000. ) ). -----. Análisis Probabilista. E. Mosquera..

(17) Estudio Cof. Variación(30%). (x (Do (cx. ; ; ;. 1; 3; 5;. 2.200 8.900 0.6000. ) ) ). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. (n (cs. ; ;. 2; 4;. 0.5000 1.073. ) ). (Upper bounds on U-space variables) (x ; 1; 30.00 ) (n ; 2; 30.00 ) (Do ; 3; 30.00 ) (cs ; 4; 30.00 ) (cx ; 5; 30.00 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 200 1 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) = 0.1528 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 0.085 Corresponding approximate prob.of failure = 0.4663 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.8968E-08 and Vector u-* (beta-point) : (x ; 1; -3.0389E-02) (n ; 2; -4.8780E-02) (Do ; 3; 1.4988E-02) (cs ; 4; 4.1964E-02) (cx ; 5; -4.3034E-02) Normalized U-space gradient (alfa-U) with norm = 12.01 : (x ; 1; 0.3596 ) (n ; 2; 0.5773 ) (Do ; 3; -0.1774 ) (cs ; 4; -0.4966 ) (cx ; 5; 0.5093 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.3596 ) (n ; 2; 0.5773 ) (Do ; 3; -0.1774 ) (cs ; 4; -0.4966 ) (cx ; 5; 0.5093 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 2.180 ) (n ; 2; 0.4927 ) (Do ; 3; 8.940 ) (cs ; 4; 1.087 ) (cx ; 5; 0.5923 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 6.544 ) (n ; 2; 46.22 ) (Do ; 3; -0.7978 ) (cs ; 4; -18.52 ) (cx ; 5; 33.98 ) -----------------------------------------------------------------------------Constant Parameters (PVEC): (t ; 1; 50.00 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 3 Calls of state-function : 19 -----------------------------------------------------------------------------***************************************************** 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 : -3.305 -20.905 29.841. 11.813. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 0.178 Corresponding prob. of failure = 0.42928. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 100 E(Sim)= Importance sampling: Sample no. 120 E(Sim)= Importance sampling: Sample no. 140 E(Sim)= Importance sampling: Sample no. 160 E(Sim)= Importance sampling: Sample no. 180 E(Sim)=. 0.948 0.965 1.02 1.02 0.991 0.981 0.981 0.979 0.973. 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.=. 4.17 3.36 2.80 3.25 2.88 2.55 2.31 2.13 1.97. (%) (%) (%) (%) (%) (%) (%) (%) (%). Análisis Probabilista. E. Mosquera..

(18) Estudio Cof. Variación(30%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. -------------------- Results of importance sampling -------------------Corrected reliability index = 0.206 Corresponding prob. of failure = 0.41835 Correction factor by simulation = 0.975 Coefficient of Variation in % = 1.831 200(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 2.15770 2.20000 0.981 (n : 2) 0.484568 0.500000 0.969 (Do : 3) 8.98440 8.90000 1.009 (cs : 4) 1.10150 1.07300 1.027 (cx : 5) 0.583663 0.600000 0.973 ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 1.975 2.41E-02 -0.7895 -0.2012 3.500 1.141 0.13 -0.1292 -0.4130 6.500 0.8853 0.19 -0.6513E-01 -0.5143 9.500 0.7440 0.23 -0.4224E-01 -0.6020 12.50 0.6438 0.26 -0.3076E-01 -0.6881 15.50 0.5684 0.28 -0.2395E-01 -0.7774 18.50 0.5085 0.31 -0.1947E-01 -0.8725 21.50 0.4591 0.32 -0.1632E-01 -0.9764 24.50 0.4172 0.34 -0.1400E-01 -1.092 27.50 0.3811 0.35 -0.1221E-01 -1.222 30.50 0.3494 0.36 -0.1081E-01 -1.372 33.50 0.3211 0.37 -0.9675E-02 -1.546 36.50 0.2957 0.38 -0.8743E-02 -1.752 39.50 0.2727 0.39 -0.7964E-02 -2.003 42.50 0.2517 0.40 -0.7304E-02 -2.313 45.50 0.2324 0.41 -0.6737E-02 -2.709 48.50 0.2146 0.42 -0.6247E-02 -3.233 51.50 0.1980 0.42 -0.5818E-02 -3.963 54.50 0.1825 0.43 -0.5442E-02 -4.998 57.50 0.1680 0.43 -0.5107E-02 -6.789 60.50 0.1545 0.44 -0.4808E-02 -10.31 63.50 0.1417 0.44 -0.4540E-02 -20.46 66.50 0.1295 0.45 -0.4299E-02 -0.6920+293 69.50 0.1254 0.45 -0.4079E-02 -24.16 72.50 0.1148 0.45 -0.3879E-02 -11.92. Representative Alphas of Variables FLIM(1), cv30.pti. x 0.36 n 0.58 Do -0.18 cs -0.50 cx 0.51 Sum of a² 1.00. Análisis Probabilista. E. Mosquera..

(19) Estudio Cof. Variación(30%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. Reliability Index FLIM(1), cv30.pti. Beta 1.97. 1.79 1.60 1.42 1.23 1.04 0.86 0.67 0.49 0.30 0.11. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. 58.10. 65.30. 72.50. 58.10. 65.30. 72.50. Failure Probability FLIM(1), cv30.pti. Failure Probability 0.45. 0.41 0.37 0.33 0.28 0.24 0.20 0.15 0.11 0.07 0.02. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. Partial Safety Factors FLIM(1), cv30.pti. P.S.F. 1.16 -0.00 2.02 1.10 0.00 1.75 1.03 -107374184.00. x n Do cs cx. 0.97 0.90 0.84 0.78 0.71 0.65 0.58 0.52. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. 58.10. 65.30. 72.50. Análisis Probabilista. E. Mosquera..

(20) Estudio Cof. Variación(70%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. Job name ............ : cv70 -----------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: FLIM(1)=x-(2*(1-sqrt(cx/cs))*sqrt(3*0.315*Do*(0.0767/t)^n*t)) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************ Variable: x ; No. on X-vector = 1 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 2.200 ( 0.220000000000000E+01) Standard deviation........ = 1.540 ( 0.154000000000000E+01) Coefficient of Variation.. = 0.7000 ( 0.700000000000000E+00) Distr.Param.no.1 : m = 2.200 ( 0.220000000000000E+01) Distr.Param.no.2 : sigma = 1.540 ( 0.154000000000000E+01) ------------------------Variable: n ; No. on X-vector = 2 Comment : factor de edad Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.3500 ( 0.350000000000000E+00) Coefficient of Variation.. = 0.7000 ( 0.700000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.3500 ( 0.350000000000000E+00) ------------------------Variable: Do ; No. on X-vector = 3 Comment : Coef. Difusión inicial en cm2/s Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 8.900 ( 0.890000000000000E+01) Standard deviation........ = 6.230 ( 0.623000000000000E+01) Coefficient of Variation.. = 0.7000 ( 0.700000000000000E+00) Distr.Param.no.1 : m = 8.900 ( 0.890000000000000E+01) Distr.Param.no.2 : sigma = 6.230 ( 0.623000000000000E+01) ------------------------Variable: cs ; No. on X-vector = 4 Comment : contenido superficial (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 1.073 ( 0.107300000000000E+01) Standard deviation........ = 0.7510 ( 0.751000000000000E+00) Coefficient of Variation.. = 0.6999 ( 0.699906803355079E+00) Distr.Param.no.1 : m = 1.073 ( 0.107300000000000E+01) Distr.Param.no.2 : sigma = 0.7510 ( 0.751000000000000E+00) ------------------------Variable: cx ; No. on X-vector = 5 Comment : contenido critico (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.6000 ( 0.600000000000000E+00) Standard deviation........ = 0.4200 ( 0.420000000000000E+00) Coefficient of Variation.. = 0.7000 ( 0.700000000000000E+00) Distr.Param.no.1 : m = 0.6000 ( 0.600000000000000E+00) Distr.Param.no.2 : sigma = 0.4200 ( 0.420000000000000E+00) -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años -------------------------. (x (Do (cx. (x (Do (cx. ; ; ;. 1 with value =. (Lower bounds on U-space variables) 1; -30.00 ) (n ; 2; 3; -30.00 ) (cs ; 4; 5; -30.00 ). ----- U-start as given by user ; 1; 0.000 ) (n ; 3; 0.000 ) (cs ; 5; 0.000 ) ---- X-start computed from U-start. ; ;. 50.00. -30.00 -30.00. ) ). -----2; 0.000 4; 0.000. ) ). -----. Análisis Probabilista. E. Mosquera..

(21) Estudio Cof. Variación(70%). (x (Do (cx. ; ; ;. 1; 3; 5;. 2.200 8.900 0.6000. ) ) ). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. (n (cs. ; ;. 2; 4;. 0.5000 1.073. ) ). (Upper bounds on U-space variables) (x ; 1; 30.00 ) (n ; 2; 30.00 ) (Do ; 3; 30.00 ) (cs ; 4; 30.00 ) (cx ; 5; 30.00 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 0 1 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) = 0.1528 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 0.037 Corresponding approximate prob.of failure = 0.4854 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.1195E-04 and Vector u-* (beta-point) : (x ; 1; -1.3031E-02) (n ; 2; -2.0929E-02) (Do ; 3; 6.4312E-03) (cs ; 4; 1.7960E-02) (cx ; 5; -1.8440E-02) Normalized U-space gradient (alfa-U) with norm = 28.01 : (x ; 1; 0.3598 ) (n ; 2; 0.5779 ) (Do ; 3; -0.1776 ) (cs ; 4; -0.4959 ) (cx ; 5; 0.5091 ) Normalized Representative alfa-values with norm = 0.9861 : (x ; 1; 0.3598 ) (n ; 2; 0.5779 ) (Do ; 3; -0.1776 ) (cs ; 4; -0.4959 ) (cx ; 5; 0.5091 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 2.180 ) (n ; 2; 0.4927 ) (Do ; 3; 8.940 ) (cs ; 4; 1.086 ) (cx ; 5; 0.5923 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 6.544 ) (n ; 2; 46.24 ) (Do ; 3; -0.7983 ) (cs ; 4; -18.49 ) (cx ; 5; 33.95 ) -----------------------------------------------------------------------------Constant Parameters (PVEC): (t ; 1; 50.00 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 2 Calls of state-function : 13 -----------------------------------------------------------------------------***************************************************** 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 . Tvedts formula used instead of Hohenbichlers formula. 2nd-order improvement might be inaccurate ! ----- Second-Order Improvement : ----radii of curvature in U-space : -1.452 -9.146 13.163. 5.104. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 0.248 Corresponding prob. of failure = 0.40196 -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 2.06244 2.20000 0.937 (n : 2) 0.449785 0.500000 0.900 (Do : 3) 9.17466 8.90000 1.031 (cs : 4) 1.16546 1.07300 1.086 (cx : 5) 0.546907 0.600000 0.912. Análisis Probabilista. E. Mosquera..

(22) Estudio Cof. Variación(70%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 0.8555 0.20 -0.3384 -0.2012 3.500 0.5424 0.29 -0.5536E-01 -0.4129 6.500 0.4593 0.32 -0.2791E-01 -0.5143 9.500 0.4130 0.34 -0.1811E-01 -0.6023 12.50 0.3814 0.35 -0.1319E-01 -0.6883 15.50 0.3579 0.36 -0.1026E-01 -0.7773 18.50 0.3393 0.37 -0.8344E-02 -0.8725 21.50 0.3241 0.37 -0.6995E-02 -0.9764 24.50 0.3109 0.38 -0.5995E-02 -1.092 27.50 0.3000 0.38 -0.5233E-02 -1.222 30.50 0.2904 0.39 -0.4632E-02 -1.372 33.50 0.2819 0.39 -0.4147E-02 -1.546 36.50 0.2743 0.39 -0.3747E-02 -1.752 39.50 0.2674 0.39 -0.3413E-02 -2.003 42.50 0.2611 0.40 -0.3130E-02 -2.313 45.50 0.2553 0.40 -0.2888E-02 -2.709 48.50 0.2510 0.40 -0.2679E-02 -3.185 51.50 0.2457 0.40 -0.2494E-02 -3.914 54.50 0.2409 0.40 -0.2332E-02 -4.998 57.50 0.2364 0.41 -0.2189E-02 -6.789 60.50 0.2322 0.41 -0.2061E-02 -10.31 63.50 0.2284 0.41 -0.1946E-02 -20.46 66.50 0.2243 0.41 -0.1843E-02 -0.6920+293 69.50 0.2214 0.41 -0.1748E-02 -24.16 72.50 0.2183 0.41 -0.1663E-02 -11.92. Representative Alphas of Variables FLIM(1), cv70.pti. x 0.36 n 0.58 Do -0.18 cs -0.50 cx 0.51 Sum of a² 1.00. Análisis Probabilista. E. Mosquera..

(23) Estudio Cof. Variación(70%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=2.2 cm. Reliability Index FLIM(1), cv70.pti. Beta 0.86. 0.79 0.73 0.66 0.60 0.54 0.47 0.41 0.35 0.28 0.22. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. 58.10. 65.30. 72.50. Failure Probability FLIM(1), cv70.pti. Failure Probability 0.41. 0.39 0.37 0.35 0.33 0.30 0.28 0.26 0.24 0.22 0.20. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. 58.10. 65.30. 72.50. Partial Safety Factors FLIM(1), cv70.pti. P.S.F. 1.16 -0.00 2.02 1.10 0.00 1.75 1.03 -107374184.00. x n Do cs cx. 0.97 0.90 0.84 0.77 0.71 0.64 0.58 0.51. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. 58.10. 65.30. 72.50. Análisis Probabilista. E. Mosquera..

(24) Estudio Cof. Variación(5%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=4 cm. -----------------------------------------------------------------------------Job name ............ : cv5r4 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 07.01.2011 Time(hh:mm) ........ : 10:20 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: FLIM(1)=x-(2*(1-sqrt(cx/cs))*sqrt(3*0.315*Do*(0.0767/t)^n*t)) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************ Variable: x ; No. on X-vector = 1 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 4.000 ( 0.400000000000000E+01) Standard deviation........ = 0.2000 ( 0.200000000000000E+00) Coefficient of Variation.. = 5.0000E-02 ( 0.500000000000000E-01) Distr.Param.no.1 : m = 4.000 ( 0.400000000000000E+01) Distr.Param.no.2 : sigma = 0.2000 ( 0.200000000000000E+00) ------------------------Variable: n ; No. on X-vector = 2 Comment : factor de edad Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 2.5000E-02 ( 0.250000000000000E-01) Coefficient of Variation.. = 5.0000E-02 ( 0.500000000000000E-01) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 2.5000E-02 ( 0.250000000000000E-01) ------------------------Variable: Do ; No. on X-vector = 3 Comment : Coef. Difusión inicial en cm2/s Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 8.900 ( 0.890000000000000E+01) Standard deviation........ = 0.4450 ( 0.445000000000000E+00) Coefficient of Variation.. = 5.0000E-02 ( 0.500000000000000E-01) Distr.Param.no.1 : m = 8.900 ( 0.890000000000000E+01) Distr.Param.no.2 : sigma = 0.4450 ( 0.445000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 4 Comment : contenido superficial (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 1.073 ( 0.107300000000000E+01) Standard deviation........ = 5.3600E-02 ( 0.536000000000000E-01) Coefficient of Variation.. = 4.9953E-02 ( 0.499534016775396E-01) Distr.Param.no.1 : m = 1.073 ( 0.107300000000000E+01) Distr.Param.no.2 : sigma = 5.3600E-02 ( 0.536000000000000E-01) ------------------------Variable: cx ; No. on X-vector = 5 Comment : contenido critico (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.6000 ( 0.600000000000000E+00) Standard deviation........ = 3.0000E-02 ( 0.300000000000000E-01) Coefficient of Variation.. = 5.0000E-02 ( 0.500000000000000E-01) Distr.Param.no.1 : m = 0.6000 ( 0.600000000000000E+00) Distr.Param.no.2 : sigma = 3.0000E-02 ( 0.300000000000000E-01) -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años -------------------------. 1 with value =. 50.00. (Lower bounds on U-space variables). Análisis Probabilista. E. Mosquera..

(25) Estudio Cof. Variación(5%). (x (Do (cx. ; ; ;. 1; 3; 5;. -30.00 -30.00 -30.00. ) ) ). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=4 cm. (n (cs. ; ;. 2; 4;. -30.00 -30.00. ) ). -----2; 0.000 4; 0.000. ) ). (x (Do (cx. ----- U-start as given by user ; 1; 0.000 ) (n ; 3; 0.000 ) (cs ; 5; 0.000 ). (x (Do (cx. ---- X-start computed from U-start ----; 1; 4.000 ) (n ; 2; 0.5000 ; 3; 8.900 ) (cs ; 4; 1.073 ; 5; 0.6000 ). ; ;. ) ). (Upper bounds on U-space variables) (x ; 1; 30.00 ) (n ; 2; 30.00 ) (Do ; 3; 30.00 ) (cs ; 4; 30.00 ) (cx ; 5; 30.00 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 200 1 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) = 1.953 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 5.060 Corresponding approximate prob.of failure = 2.1006E-07 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.9286E-09 and Vector u-* (beta-point) : (x ; 1; -2.266 ) (n ; 2; -3.254 ) (Do ; 3; 0.9585 ) (cs ; 4; 1.880 ) (cx ; 5; -2.330 ) Normalized U-space gradient (alfa-U) with norm = 0.2287 : (x ; 1; 0.4477 ) (n ; 2; 0.6432 ) (Do ; 3; -0.1894 ) (cs ; 4; -0.3715 ) (cx ; 5; 0.4604 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.4477 ) (n ; 2; 0.6432 ) (Do ; 3; -0.1894 ) (cs ; 4; -0.3715 ) (cx ; 5; 0.4604 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 3.547 ) (n ; 2; 0.4186 ) (Do ; 3; 9.327 ) (cs ; 4; 1.174 ) (cx ; 5; 0.5301 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.5121 ) (n ; 2; 5.885 ) (Do ; 3; -9.7372E-02) (cs ; 4; -1.585 ) (cx ; 5; 3.510 ) -----------------------------------------------------------------------------Constant Parameters (PVEC): (t ; 1; 50.00 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 7 Calls of state-function : 43 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -23.922 -120.082 156.588. 53.728. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 5.070 Corresponding prob. of failure = 1.99400E-07. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 100 E(Sim)= Importance sampling: Sample no. 120 E(Sim)=. 0.950 0.971 1.02 1.03 1.00 0.991. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 4.09 3.23 2.76 3.20 2.79 2.47. (%) (%) (%) (%) (%) (%). Análisis Probabilista. E. Mosquera..

(26) Estudio Cof. Variación(5%). Importance sampling: Sample no. 140 Importance sampling: Sample no. 160 Importance sampling: Sample no. 180. Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=4 cm. E(Sim)= E(Sim)= E(Sim)=. 0.992 0.991 0.987. C.o.V.= C.o.V.= C.o.V.=. 2.22 (%) 2.04 (%) 1.88 (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 5.073 Corresponding prob. of failure = 1.96494E-07 Correction factor by simulation = 0.985 Coefficient of Variation in % = 1.746 200(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 3.54601 4.00000 0.887 (n : 2) 0.418483 0.500000 0.837 (Do : 3) 9.32737 8.90000 1.048 (cs : 4) 1.17396 1.07300 1.094 (cx : 5) 0.529974 0.600000 0.883 ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 15.77 2.49E-56 -2.672 -0.8471E-01 3.500 11.99 2.19E-33 -0.7297 -0.2131 6.500 10.34 2.33E-25 -0.4193 -0.2636 9.500 9.306 6.75E-21 -0.2874 -0.2936 12.50 8.562 5.63E-18 -0.2158 -0.3153 15.50 7.987 6.99E-16 -0.1714 -0.3329 18.50 7.521 2.73E-14 -0.1413 -0.3480 21.50 7.132 4.98E-13 -0.1197 -0.3614 24.50 6.799 5.30E-12 -0.1035 -0.3736 27.50 6.508 3.82E-11 -0.9097E-01 -0.3850 30.50 6.252 2.04E-10 -0.8097E-01 -0.3957 33.50 6.022 8.66E-10 -0.7283E-01 -0.4059 36.50 5.814 3.06E-09 -0.6608E-01 -0.4157 39.50 5.625 9.31E-09 -0.6041E-01 -0.4251 42.50 5.451 2.50E-08 -0.5558E-01 -0.4342 45.50 5.291 6.08E-08 -0.5141E-01 -0.4431 48.50 5.143 1.35E-07 -0.4780E-01 -0.4518 51.50 5.005 2.80E-07 -0.4462E-01 -0.4604 54.50 4.875 5.44E-07 -0.4182E-01 -0.4687 57.50 4.754 9.99E-07 -0.3933E-01 -0.4770 60.50 4.640 1.75E-06 -0.3709E-01 -0.4851 63.50 4.532 2.93E-06 -0.3509E-01 -0.4932 66.50 4.429 4.73E-06 -0.3327E-01 -0.5011 69.50 4.332 7.39E-06 -0.3163E-01 -0.5090 72.50 4.240 1.12E-05 -0.3012E-01 -0.5169. Representative Alphas of Variables FLIM(1), cv5r4.pti. x 0.45 n 0.64 Do -0.19 cs -0.37 cx 0.46 Sum of a²1.00. Análisis Probabilista. E. Mosquera..

(27) Estudio Cof. Variación(5%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=4 cm. Reliability Index FLIM(1), cv5r4.pti. Beta 15.77. 14.62 13.47 12.31 11.16 10.01 8.85 7.70 6.55 5.39 4.24. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. 58.10. 65.30. 72.50. 58.10. 65.30. 72.50. Failure Probability FLIM(1), cv5r4.pti. Failure Probability 0.00. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. Partial Safety Factors FLIM(1), cv5r4.pti. P.S.F. 1.16 0.00 2.25 1.07 0.00 1.75 0.98 -107374184.00. x n Do cs cx. 0.89 0.80 0.71 0.62 0.53 0.44 0.35 0.26. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. 58.10. 65.30. 72.50. Análisis Probabilista. E. Mosquera..

(28) Estudio Cof. Variación(10%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=4 cm. -----------------------------------------------------------------------------Job name ............ : cv10r4 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 07.01.2011 Time(hh:mm) ........ : 10:37 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: FLIM(1)=x-(2*(1-sqrt(cx/cs))*sqrt(3*0.315*Do*(0.0767/t)^n*t)) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************ Variable: x ; No. on X-vector = 1 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 4.000 ( 0.400000000000000E+01) Standard deviation........ = 0.4000 ( 0.400000000000000E+00) Coefficient of Variation.. = 0.1000 ( 0.100000000000000E+00) Distr.Param.no.1 : m = 4.000 ( 0.400000000000000E+01) Distr.Param.no.2 : sigma = 0.4000 ( 0.400000000000000E+00) ------------------------Variable: n ; No. on X-vector = 2 Comment : factor de edad Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 5.0000E-02 ( 0.500000000000000E-01) Coefficient of Variation.. = 0.1000 ( 0.100000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 5.0000E-02 ( 0.500000000000000E-01) ------------------------Variable: Do ; No. on X-vector = 3 Comment : Coef. Difusión inicial en cm2/s Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 8.900 ( 0.890000000000000E+01) Standard deviation........ = 0.8900 ( 0.890000000000000E+00) Coefficient of Variation.. = 0.1000 ( 0.100000000000000E+00) Distr.Param.no.1 : m = 8.900 ( 0.890000000000000E+01) Distr.Param.no.2 : sigma = 0.8900 ( 0.890000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 4 Comment : contenido superficial (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 1.073 ( 0.107300000000000E+01) Standard deviation........ = 0.1070 ( 0.107000000000000E+00) Coefficient of Variation.. = 9.9720E-02 ( 0.997204100652377E-01) Distr.Param.no.1 : m = 1.073 ( 0.107300000000000E+01) Distr.Param.no.2 : sigma = 0.1070 ( 0.107000000000000E+00) ------------------------Variable: cx ; No. on X-vector = 5 Comment : contenido critico (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.6000 ( 0.600000000000000E+00) Standard deviation........ = 6.0000E-02 ( 0.600000000000000E-01) Coefficient of Variation.. = 0.1000 ( 0.100000000000000E+00) Distr.Param.no.1 : m = 0.6000 ( 0.600000000000000E+00) Distr.Param.no.2 : sigma = 6.0000E-02 ( 0.600000000000000E-01) -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años -------------------------. 1 with value =. 50.00. (Lower bounds on U-space variables). Análisis Probabilista. E. Mosquera..

(29) Estudio Cof. Variación(10%). (x (Do (cx. ; ; ;. 1; 3; 5;. -30.00 -30.00 -30.00. ) ) ). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=4 cm. (n (cs. ; ;. 2; 4;. -30.00 -30.00. ) ). -----2; 0.000 4; 0.000. ) ). (x (Do (cx. ----- U-start as given by user ; 1; 0.000 ) (n ; 3; 0.000 ) (cs ; 5; 0.000 ). (x (Do (cx. ---- X-start computed from U-start ----; 1; 4.000 ) (n ; 2; 0.5000 ; 3; 8.900 ) (cs ; 4; 1.073 ; 5; 0.6000 ). ; ;. ) ). (Upper bounds on U-space variables) (x ; 1; 30.00 ) (n ; 2; 30.00 ) (Do ; 3; 30.00 ) (cs ; 4; 30.00 ) (cx ; 5; 30.00 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 200 1 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) = 1.953 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 2.531 Corresponding approximate prob.of failure = 5.6932E-03 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.2032E-07 and Vector u-* (beta-point) : (x ; 1; -1.133 ) (n ; 2; -1.628 ) (Do ; 3; 0.4795 ) (cs ; 4; 0.9388 ) (cx ; 5; -1.166 ) Normalized U-space gradient (alfa-U) with norm = 0.4574 : (x ; 1; 0.4478 ) (n ; 2; 0.6433 ) (Do ; 3; -0.1895 ) (cs ; 4; -0.3710 ) (cx ; 5; 0.4606 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.4478 ) (n ; 2; 0.6433 ) (Do ; 3; -0.1895 ) (cs ; 4; -0.3710 ) (cx ; 5; 0.4606 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 3.547 ) (n ; 2; 0.4186 ) (Do ; 3; 9.327 ) (cs ; 4; 1.173 ) (cx ; 5; 0.5301 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.5121 ) (n ; 2; 5.884 ) (Do ; 3; -9.7369E-02) (cs ; 4; -1.586 ) (cx ; 5; 3.511 ) -----------------------------------------------------------------------------Constant Parameters (PVEC): (t ; 1; 50.00 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 6 Calls of state-function : 37 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -12.014 -60.192 78.467. 26.887. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 2.550 Corresponding prob. of failure = 5.38825E-03. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 100 E(Sim)= Importance sampling: Sample no. 120 E(Sim)=. 0.946 0.968 1.02 1.03 1.00 0.989. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 4.35 3.47 2.97 3.46 3.01 2.67. (%) (%) (%) (%) (%) (%). Análisis Probabilista. E. Mosquera..

(30) Estudio Cof. Variación(10%). Importance sampling: Sample no. 140 Importance sampling: Sample no. 160 Importance sampling: Sample no. 180. Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=4 cm. E(Sim)= E(Sim)= E(Sim)=. 0.990 0.989 0.984. C.o.V.= C.o.V.= C.o.V.=. 2.40 (%) 2.21 (%) 2.03 (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 2.556 Corresponding prob. of failure = 5.29418E-03 Correction factor by simulation = 0.983 Coefficient of Variation in % = 1.890 200(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 3.54324 4.00000 0.886 (n : 2) 0.417988 0.500000 0.836 (Do : 3) 9.32996 8.90000 1.048 (cs : 4) 1.17422 1.07300 1.094 (cx : 5) 0.529535 0.600000 0.883 ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 7.890 1.53E-15 -1.336 -0.8469E-01 3.500 5.994 1.03E-09 -0.3648 -0.2131 6.500 5.176 1.14E-07 -0.2097 -0.2636 9.500 4.660 1.58E-06 -0.1437 -0.2935 12.50 4.290 8.94E-06 -0.1079 -0.3153 15.50 4.005 3.10E-05 -0.8570E-01 -0.3329 18.50 3.773 8.05E-05 -0.7066E-01 -0.3479 21.50 3.580 1.72E-04 -0.5987E-01 -0.3613 24.50 3.414 3.20E-04 -0.5177E-01 -0.3735 27.50 3.270 5.38E-04 -0.4549E-01 -0.3849 30.50 3.142 8.39E-04 -0.4049E-01 -0.3956 33.50 3.028 1.23E-03 -0.3642E-01 -0.4058 36.50 2.925 1.72E-03 -0.3305E-01 -0.4156 39.50 2.831 2.32E-03 -0.3021E-01 -0.4250 42.50 2.744 3.03E-03 -0.2779E-01 -0.4342 45.50 2.665 3.85E-03 -0.2571E-01 -0.4431 48.50 2.591 4.79E-03 -0.2390E-01 -0.4518 51.50 2.522 5.83E-03 -0.2232E-01 -0.4603 54.50 2.458 6.99E-03 -0.2091E-01 -0.4687 57.50 2.398 8.25E-03 -0.1967E-01 -0.4770 60.50 2.341 9.62E-03 -0.1855E-01 -0.4851 63.50 2.287 1.11E-02 -0.1755E-01 -0.4931 66.50 2.236 1.27E-02 -0.1664E-01 -0.5011 69.50 2.188 1.43E-02 -0.1582E-01 -0.5090 72.50 2.142 1.61E-02 -0.1506E-01 -0.5168. Representative Alphas of Variables FLIM(1), cv10r4.pti. x 0.45 n 0.64 Do -0.19 cs -0.37 cx 0.46 Sum of a²1.00. Análisis Probabilista. E. Mosquera..

(31) Estudio Cof. Variación(10%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=4 cm. Reliability Index FLIM(1), cv10r4.pti. Beta 7.89. 7.32 6.74 6.17 5.59 5.02 4.44 3.87 3.29 2.72 2.14. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. 58.10. 65.30. 72.50. 58.10. 65.30. 72.50. Failure Probability FLIM(1), cv10r4.pti. Failure Probability 0.02. 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.00 0.00. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. Partial Safety Factors FLIM(1), cv10r4.pti. P.S.F. 1.16 0.00 2.25 1.07 0.00 1.75 0.98 -107374184.00. x n Do cs cx. 0.89 0.80 0.71 0.62 0.53 0.44 0.35 0.26. 0.50. 7.70. 14.90. 22.10. 29.30. 36.50 t. 43.70. 50.90. 58.10. 65.30. 72.50. Análisis Probabilista. E. Mosquera..

(32) Estudio Cof. Variación(15%). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=4 cm. -----------------------------------------------------------------------------Job name ............ : cv15r4 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 07.01.2011 Time(hh:mm) ........ : 10:39 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ---------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: FLIM(1)=x-(2*(1-sqrt(cx/cs))*sqrt(3*0.315*Do*(0.0767/t)^n*t)) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************ Variable: x ; No. on X-vector = 1 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 4.000 ( 0.400000000000000E+01) Standard deviation........ = 0.6000 ( 0.600000000000000E+00) Coefficient of Variation.. = 0.1500 ( 0.150000000000000E+00) Distr.Param.no.1 : m = 4.000 ( 0.400000000000000E+01) Distr.Param.no.2 : sigma = 0.6000 ( 0.600000000000000E+00) ------------------------Variable: n ; No. on X-vector = 2 Comment : factor de edad Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 7.5000E-02 ( 0.750000000000000E-01) Coefficient of Variation.. = 0.1500 ( 0.150000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 7.5000E-02 ( 0.750000000000000E-01) ------------------------Variable: Do ; No. on X-vector = 3 Comment : Coef. Difusión inicial en cm2/s Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 8.900 ( 0.890000000000000E+01) Standard deviation........ = 1.335 ( 0.133500000000000E+01) Coefficient of Variation.. = 0.1500 ( 0.150000000000000E+00) Distr.Param.no.1 : m = 8.900 ( 0.890000000000000E+01) Distr.Param.no.2 : sigma = 1.335 ( 0.133500000000000E+01) ------------------------Variable: cs ; No. on X-vector = 4 Comment : contenido superficial (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 1.073 ( 0.107300000000000E+01) Standard deviation........ = 0.1610 ( 0.161000000000000E+00) Coefficient of Variation.. = 0.1500 ( 0.150046598322460E+00) Distr.Param.no.1 : m = 1.073 ( 0.107300000000000E+01) Distr.Param.no.2 : sigma = 0.1610 ( 0.161000000000000E+00) ------------------------Variable: cx ; No. on X-vector = 5 Comment : contenido critico (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Dist.Parameters (1) Mean value................ = 0.6000 ( 0.600000000000000E+00) Standard deviation........ = 9.0000E-02 ( 0.900000000000000E-01) Coefficient of Variation.. = 0.1500 ( 0.150000000000000E+00) Distr.Param.no.1 : m = 0.6000 ( 0.600000000000000E+00) Distr.Param.no.2 : sigma = 9.0000E-02 ( 0.900000000000000E-01) -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años -------------------------. 1 with value =. 50.00. (Lower bounds on U-space variables). Análisis Probabilista. E. Mosquera..

(33) Estudio Cof. Variación(15%). (x (Do (cx. ; ; ;. 1; 3; 5;. -30.00 -30.00 -30.00. ) ) ). Ambiente IIIa, Cc=300 Kg/m3,CEM I, 50 años‐ a/c=0,4, Recubr.=4 cm. (n (cs. ; ;. 2; 4;. -30.00 -30.00. ) ). -----2; 0.000 4; 0.000. ) ). (x (Do (cx. ----- U-start as given by user ; 1; 0.000 ) (n ; 3; 0.000 ) (cs ; 5; 0.000 ). (x (Do (cx. ---- X-start computed from U-start ----; 1; 4.000 ) (n ; 2; 0.5000 ; 3; 8.900 ) (cs ; 4; 1.073 ; 5; 0.6000 ). ; ;. ) ). (Upper bounds on U-space variables) (x ; 1; 30.00 ) (n ; 2; 30.00 ) (Do ; 3; 30.00 ) (cs ; 4; 30.00 ) (cx ; 5; 30.00 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 200 1 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) = 1.953 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.686 Corresponding approximate prob.of failure = 4.5864E-02 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.2082E-07 and Vector u-* (beta-point) : (x ; 1; -0.7550 ) (n ; 2; -1.085 ) (Do ; 3; 0.3194 ) (cs ; 4; 0.6269 ) (cx ; 5; -0.7761 ) Normalized U-space gradient (alfa-U) with norm = 0.6863 : (x ; 1; 0.4477 ) (n ; 2; 0.6431 ) (Do ; 3; -0.1894 ) (cs ; 4; -0.3718 ) (cx ; 5; 0.4602 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.4477 ) (n ; 2; 0.6431 ) (Do ; 3; -0.1894 ) (cs ; 4; -0.3718 ) (cx ; 5; 0.4602 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 3.547 ) (n ; 2; 0.4187 ) (Do ; 3; 9.326 ) (cs ; 4; 1.174 ) (cx ; 5; 0.5301 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.5121 ) (n ; 2; 5.885 ) (Do ; 3; -9.7380E-02) (cs ; 4; -1.585 ) (cx ; 5; 3.509 ) -----------------------------------------------------------------------------Constant Parameters (PVEC): (t ; 1; 50.00 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 6 Calls of state-function : 37 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -8.014 -40.236 52.340. 17.950. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.714 Corresponding prob. of failure = 4.32326E-02. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 100 E(Sim)= Importance sampling: Sample no. 120 E(Sim)=. 0.940 0.964 1.02 1.03 0.999 0.986. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 4.73 3.80 3.26 3.81 3.33 2.95. (%) (%) (%) (%) (%) (%). Análisis Probabilista. E. Mosquera..

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