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 Ambientes IIIa-500 y IIIc. Las variables básicas analizadas son: Coeficiente de difusión; Concentración superficial de cloruros; Concentración crítica de cloruros y factor de edad del coeficiente de difusión.. Influencias de cada variable y su variabilidad en la probabilidad de fallo.. Anejo nº 7.-. Probabilismo explicito en la corrosión de armaduras en las estructuras de hormigón sometidas al ambiente marino de la costa gallega.. Emilio Mosquera Rey.

(2) Emilio Mosquera Rey. 6.- Denominados.- Hormigón malo HM10; Hormigón malo. 5.- Denominados.- Hormigón bueno HB10; Hormigón bueno. 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:. HM30.. HB30.. 4.- Denominados.- Factor de edad, 10º-1,-2,-3,-4,-5; 11º1,-2,-3,-4,-5; respecto de la variable, y los denominados.- 10º-1,-2,-3,-4; 11º-1,-2,-3,-4; respecto de la variabilidad.. 3.- Denominados.- Concentración crítica, 8º-1,-2,-3,-4,-5; 9º-1,-2,-3,-4,-5; respecto de la variable, y los denominados.- 8º-1,-2,-3,-4; 9º-1,-2,-3,-4; respecto de la variabilidad.. 2.- Denominados.-Concentración superficial, 6º-1,-2,-3; 7º-1,-2,-3, respecto de la variable, y los denominados.- 6º-1,-2,-3,-4; 7º-1,2,-3,-4. respecto de la variabilidad.. 1.-Denominados.-Coeficiente de difusión, 1º-1,-2,-3,-4; 2º1,-2,-3,-4; 3º-1,-2,-3,-4; 4º-1,-2,-3,-4; 5º-1,-2,-3,-4; 5ºb-1,-2,-3,-4, respecto de la variable, y los denominados.- 1º-1,-2,-3,-4; 2º-1,-2,-3,-4; 3º1,-2,-3,-4; 4º-1,-2,-3,-4; 5º-1,-2,-3,-4; 5ºb-1,-2,-3,-4, respecto de la variabilidad.. Los estudios se efectúan sobre los ambientes IIIa-500, y IIIc, y variables básicas: Coef. de Difusión; Concentración superficial de cloruros; Concentración crítica de cloruros y Factor de edad Y en estas condiciones se estudian los siguientes conjuntos de casos:. Resumen de los cálculos probabilistas para conocer la influencia de cada variable básica y la significación de su variabilidad sobre la probabilidad de fallo. También se ha estudiado, al objeto de tener un entorno de valores respecto del recubrimiento, el diseño subjetivo de dos tipos de hormigones con distintas prestaciones respecto de la corrosión, genéricamente los llamo hormigón bueno, hormigón malo.. El contenido del anejo es el siguiente:. Referencia del Análisis: Influencia de cada variable y su variabilidad. Contenido del anejo 7. Probabilismo explicito en la corrosión de armaduras en las estructuras de hormigón sometidas al ambiente marino de la costa gallega..

(3) Emilio Mosquera Rey. 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. 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. 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. 60.00. n 0.46 Do -0. 14 cs -0. 58 cx 0.59 x 0.29 S um of a²1.00. Variación del Índice de fiabilidad en función del tiempo o del recubrimiento. Cosenos directores de la significación de cada variable básica en el análisis efectuado.. Representative Alphas of Variables FLIM(1), DP1.pti. Los gráficos que se muestran, de los análisis realizados son:.

(4) Comparación del índice de fiabilidad-Recubrimiento. Hormigón bueno-Hormigón malo. Resúmenes de los índices de fiabilidad y probabilidad de fallo, respecto la variabilidad. Resúmenes de los índices de fiabilidad y probabilidad de fallo, respecto la variable. Comparación Probabilidad de fallo-Recubrimiento. Hormigón bueno-Hormigón malo. Emilio Mosquera Rey.

(5) Resumen 1º Difusión. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm.. VALORES ESTOCÁSTICOS DE LAS VARIABLES. 1º Análisis- Variación de la relación a/c (Difusión) a 50 años Condiciones del análisis : Ambiente IIIa-500 – CEM I – Contenido de Cemento= 350 kg/m3 Variable. Media. CoV. Desviación Típica. Tipo de distribución. Recubrimiento (cm). 3. 18%. 0.54. Normal. 8.9/10/15.8/19.7. -. 2.84. Normal. Conc. Superficial (% en peso cemento). 0,92. 18%. 0,16. Normal. Conc. Crítica (% en peso cemento). 0,60. 10%. 0.06. Normal. Factor de edad (n). 0.5. 10%. 0.05. Normal. Difusión inicial (D0) (10. -12. 2. m /s). 1º CV- Coef. de Variación de la relación a/c (Difusión) a 50 años Ambiente IIIa-500 – CEM I – Contenido de Cemento= 350 kg/m3- a/c=0.45 Variable. Media. CoV. Desviación Típica. Tipo de distribución. Recubrimiento (cm). 3. 18%. 0.54. Normal. 10. 5-10-20-30%. 0.5-1-2-3. Normal. Conc. Superficial (% en peso cemento). 0,92. 18%. 0,16. Normal. Conc. Crítica (% en peso cemento). 0,60. 10%. 0.06. Normal. Factor de edad (n). 0.5. 10%. 0.05. Normal. Difusión inicial (D0) (10. -12. 2. m /s). Análisis Probabilista. E. Mosquera..

(6) Resumen 1º Difusión. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm.. Respecto de la Variable Difusión ó relación a/c 1º Significación de Variables-Índice de Fiabilidad y Probabilidad de fallo.. Coeficiente de difusión D0=8.9*10-12m2/s. Corrected reliability index = 1.578 Corresponding prob. of failure = 5.72778E-02. Coeficiente de difusión D0=10*10-12m2/s. Corrected reliability index = 1.442 Corresponding prob. of failure = 7.45951E-02. Coeficiente de difusión D0=15.8*10-12m2/s. Corrected reliability index = 0.879 Corresponding prob. of failure = 0.18958. Coeficiente de difusión D0=19.7*10-12m2/s. Corrected reliability index = 0.609 Corresponding prob. of failure = 0.27141. Análisis Probabilista. E. Mosquera..

(7) Resumen 1º Difusión. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm.. 2º Índices de Fiabilidad y Probabilidadaes de fallo. Análisis Probabilista. E. Mosquera..

(8) Resumen 1º Difusión. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm.. Respecto del Coeficiente de Variación de la variable. 1º Significación de Variables-Índice de Fiabilidad y Probabilidad de fallo. Coeficiente de Variación 5%. Corrected reliability index = 1.498 Corresponding prob. of failure = 6.71237E-02. Coeficiente de Variación 10%. Corrected reliability index = 1.493 Corresponding prob. of failure = 6.76641E-02. Coeficiente de Variación 20%. Corrected reliability index = 1.475 Corresponding prob. of failure = 7.01053E-02. Coeficiente de Variación 30%. Corrected reliability index = 1.444 Corresponding prob. of failure = 7.43192E-02. Análisis Probabilista. E. Mosquera..

(9) Resumen 1º Difusión. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm.. 2º Índices de Fiabilidad y Probabilidadaes de fallo. Análisis Probabilista. E. Mosquera..

(10) Coeficiente de Difusión. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm‐ a/c=0.40. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Job name ............ : 1º ‐1 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 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: n ; No. on X‐vector = 1 Comment : factor de edad Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) 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 = 2 Comment : Coef. Difusión inicial en cm2/s Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 8.900 ( 0.890000000000000E+01) Standard deviation........ = 2.840 ( 0.284000000000000E+01) Coefficient of Variation.. = 0.3191 ( 0.319101123595506E+00) Distr.Param.no.1 : m = 8.900 ( 0.890000000000000E+01) Distr.Param.no.2 : sigma = 2.840 ( 0.284000000000000E+01) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Variable: cs ; No. on X‐vector = 3 Comment : contenido superficial (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.9200 ( 0.920000000000000E+00) Standard deviation........ = 0.1680 ( 0.168000000000000E+00) Coefficient of Variation.. = 0.1826 ( 0.182608695652174E+00) Distr.Param.no.1 : m = 0.9200 ( 0.920000000000000E+00) Distr.Param.no.2 : sigma = 0.1680 ( 0.168000000000000E+00) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Variable: cx ; No. on X‐vector = 4 Comment : contenido critico (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) 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) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Variable: x ; No. on X‐vector = 5 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 3.000 ( 0.300000000000000E+01) Standard deviation........ = 0.5000 ( 0.500000000000000E+00) Coefficient of Variation.. = 0.1667 ( 0.166666666666667E+00) Distr.Param.no.1 : m = 3.000 ( 0.300000000000000E+01) Distr.Param.no.2 : sigma = 0.5000 ( 0.500000000000000E+00) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐ Constant (deterministic) Parameters ‐‐ Parameter :t ; No. on PVEC= 1 with value = 50.00 Comment : tiempo en años ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (n (cs (x. (Lower bounds on U‐space variables) ; 1; ‐36.69 ) (Do ; 2; ‐36.69 ) ; 3; ‐36.69 ) (cx ; 4; ‐36.69 ) ; 5; ‐36.69 ). Análisis Probabilista. E. Mosquera..

(11) Coeficiente de Difusión. (n (cs (x. ‐‐‐‐‐ Default U‐start = Origin (U=0) ‐‐‐‐ ; 1; 0.000 ) (Do ; 2; 0.000 ) ; 3; 0.000 ) (cx ; 4; 0.000 ) ; 5; 0.000 ). (n (cs (x. ‐‐‐ X‐start: Median values from U=0 ‐‐‐‐ ; 1; 0.5000 ) (Do ; 2; 8.900 ) ; 3; 0.9200 ) (cx ; 4; 0.6000 ) ; 5; 3.000 ). Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm‐ a/c=0.40. (Upper bounds on U‐space variables) (n ; 1; 36.69 ) (Do ; 2; 36.69 ) (cs ; 3; 36.69 ) (cx ; 4; 36.69 ) (x ; 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) = 1.438 ********************************** RESULTS: ********************************** First‐Order reliability index : (FORMBE) = 1.510 Corresponding approximate prob.of failure = 6.5559E‐02 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Scaled State‐Function value at x‐*(u‐*)= 0.1058E‐07 and Vector u‐* (beta‐point) : (n ; 1; ‐0.6366 ) (Do ; 2; 0.5354 ) (cs ; 3; 0.8422 ) (cx ; 4; ‐0.5639 ) (x ; 5; ‐0.7483 ) Normalized U‐space gradient (alfa‐U) with norm = 0.7015 : (n ; 1; 0.4217 ) (Do ; 2; ‐0.3547 ) (cs ; 3; ‐0.5579 ) (cx ; 4; 0.3735 ) (x ; 5; 0.4956 ) Normalized Representative alfa‐values with norm = 1.000 : (n ; 1; 0.4217 ) (Do ; 2; ‐0.3547 ) (cs ; 3; ‐0.5579 ) (cx ; 4; 0.3735 ) (x ; 5; 0.4956 ) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Solution in Basic‐ (X‐) space (x‐*): (n ; 1; 0.4682 ) (Do ; 2; 10.42 ) (cs ; 3; 1.061 ) (cx ; 4; 0.5662 ) (x ; 5; 2.626 ) Gradient in Basic‐ (X‐) space (scaled by 1/SCAL, see above): (n ; 1; 5.916 ) (Do ; 2; ‐8.7603E‐02) (cs ; 3; ‐2.329 ) (cx ; 4; 4.367 ) (x ; 5; 0.6954 ) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 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 : ‐5.697 ‐17.622 95.165 19.088 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Results of Second‐Order improvement‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Second‐Order reliability index = 1.578 Corresponding prob. of failure = 5.72653E‐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)=. 1.02 1.00 1.02 1.01 1.00 1.00 1.02. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 3.04 (%) 2.82 (%) 4.16 (%) 3.33 (%) 2.81 (%) 2.65 (%) 3.02 (%). Análisis Probabilista. E. Mosquera..

(12) Coeficiente de Difusión. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm‐ a/c=0.40. Importance sampling: Sample no. 80 E(Sim)= 1.01 Importance sampling: Sample no. 90 E(Sim)= 1.02. C.o.V.= 2.67 (%) C.o.V.= 2.46 (%). ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Results of importance sampling ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Corrected reliability index = 1.578 Corresponding prob. of failure = 5.72778E‐02 Correction factor by simulation = 1.000 Coefficient of Variation in % = 2.420 100(=NSIMUL) samples generated; 0 samples failed. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Partial Safety Factors: Equival. x‐* / Characteristic Value Basic Variable, Equival. x‐* , Charact. Value, Part.Safety Fact. (n : 1) 0.466728 0.500000 0.933 (Do : 2) 10.4896 8.90000 1.179 (cs : 3) 1.06791 0.920000 1.161 (cx : 4) 0.564630 0.600000 0.941 (x : 5) 2.60891 3.00000 0.870 ‐‐‐‐‐‐‐‐‐‐ Parameter study for Parameter: t ‐‐‐‐‐‐‐‐‐‐ Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 3.000 5.500 8.000 10.50 13.00 15.50 18.00 20.50 23.00 25.50 28.00 30.50 33.00 35.50 38.00 40.50 43.00 45.50 48.00 50.50 53.00. 4.595 3.603 3.178 2.904 2.702 2.543 2.412 2.302 2.207 2.123 2.048 1.981 1.920 1.866 1.815 1.767 1.723 1.681 1.642 1.606 1.571 1.539. 2.16E‐06 1.57E‐04 7.41E‐04 1.84E‐03 3.45E‐03 5.50E‐03 7.93E‐03 1.07E‐02 1.37E‐02 1.69E‐02 2.03E‐02 2.38E‐02 2.74E‐02 3.10E‐02 3.48E‐02 3.86E‐02 4.25E‐02 4.64E‐02 5.03E‐02 5.42E‐02 5.81E‐02 6.19E‐02. ‐0.8649 ‐0.9460E‐01 ‐0.2262 ‐0.1899 ‐0.1335 ‐0.2336 ‐0.9407E‐01 ‐0.2628 ‐0.7219E‐01 ‐0.2851 ‐0.5830E‐01 ‐0.3036 ‐0.4872E‐01 ‐0.3195 ‐0.4172E‐01 ‐0.3337 ‐0.3640E‐01 ‐0.3465 ‐0.3223E‐01 ‐0.3585 ‐0.2887E‐01 ‐0.3697 ‐0.2611E‐01 ‐0.3802 ‐0.2381E‐01 ‐0.3903 ‐0.2186E‐01 ‐0.3999 ‐0.2019E‐01 ‐0.4092 ‐0.1874E‐01 ‐0.4182 ‐0.1747E‐01 ‐0.4270 ‐0.1636E‐01 ‐0.4355 ‐0.1537E‐01 ‐0.4439 ‐0.1448E‐01 ‐0.4521 ‐0.1369E‐01 ‐0.4601 ‐0.1297E‐01 ‐0.4680. Representative Alphas of Variables FLIM(1), 1º -1.pti. n 0.42 Do -0.35 cs -0.56 cx 0.37 x 0.50 Sum of a² 1.00. Análisis Probabilista. E. Mosquera..

(13) Coeficiente de Difusión. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm‐ a/c=0.40. Reliability Index FLIM(1), 1º -1.pti. Beta 4.60. 4.29 3.98 3.68 3.37 3.07 2.76 2.46 2.15 1.84 1.54. 0.50. 5.75. 11.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. 42.50. 47.75. 53.00. Failure Probability FLIM(1), 1º -1.pti. Failure Probability 0.50. 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00. 0.50. 5.75. 11.00. P.S.F. 1.34 0.00 1.75 1.24 -107374184.00 2.53 1.13 -151996493463552.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. 42.50. 47.75. 53.00. Partial Safety Factors FLIM(1), 1º -1.pti n Do cs cx x. 1.03 0.93 0.82 0.72 0.61 0.51 0.41 0.30. 0.50. 5.75. 11.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. 42.50. 47.75. Análisis Probabilista. 53.00. E. Mosquera..

(14) Coeficiente de Difusión. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ Recubrimiento=3 cm.‐ a/c=0.45. Job name ............ : 1º‐2 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 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: n ; No. on X‐vector = 1 Comment : factor de edad Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) 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 = 2 Comment : Coef. Difusión inicial en cm2/s Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 10.00 ( 0.100000000000000E+02) Standard deviation........ = 2.840 ( 0.284000000000000E+01) Coefficient of Variation.. = 0.2840 ( 0.284000000000000E+00) Distr.Param.no.1 : m = 10.00 ( 0.100000000000000E+02) Distr.Param.no.2 : sigma = 2.840 ( 0.284000000000000E+01) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Variable: cs ; No. on X‐vector = 3 Comment : contenido superficial (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.9200 ( 0.920000000000000E+00) Standard deviation........ = 0.1680 ( 0.168000000000000E+00) Coefficient of Variation.. = 0.1826 ( 0.182608695652174E+00) Distr.Param.no.1 : m = 0.9200 ( 0.920000000000000E+00) Distr.Param.no.2 : sigma = 0.1680 ( 0.168000000000000E+00) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Variable: cx ; No. on X‐vector = 4 Comment : contenido critico (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) 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) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Variable: x ; No. on X‐vector = 5 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 3.000 ( 0.300000000000000E+01) Standard deviation........ = 0.5000 ( 0.500000000000000E+00) Coefficient of Variation.. = 0.1667 ( 0.166666666666667E+00) Distr.Param.no.1 : m = 3.000 ( 0.300000000000000E+01) Distr.Param.no.2 : sigma = 0.5000 ( 0.500000000000000E+00) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐ Constant (deterministic) Parameters ‐‐ Parameter :t ; No. on PVEC= 1 with value = 50.00 Comment : tiempo en años ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (n (cs (x. (Lower bounds on U‐space variables) ; 1; ‐36.69 ) (Do ; 2; ‐36.69 ) ; 3; ‐36.69 ) (cx ; 4; ‐36.69 ) ; 5; ‐36.69 ) ‐‐‐‐‐ Default U‐start = Origin (U=0) ‐‐‐‐. Análisis Probabilista. E. Mosquera..

(15) Coeficiente de Difusión (n (cs (x (n (cs (x. ; 1; 0.000 ) ; 3; 0.000 ) ; 5; 0.000 ). (Do (cx. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ Recubrimiento=3 cm.‐ a/c=0.45. ; 2; 0.000 ) ; 4; 0.000 ). ‐‐‐ X‐start: Median values from U=0 ‐‐‐‐ ; 1; 0.5000 ) (Do ; 2; 10.00 ) ; 3; 0.9200 ) (cx ; 4; 0.6000 ) ; 5; 3.000 ). (Upper bounds on U‐space variables) (n ; 1; 36.69 ) (Do ; 2; 36.69 ) (cs ; 3; 36.69 ) (cx ; 4; 36.69 ) (x ; 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) = 1.344 ********************************** RESULTS: ********************************** First‐Order reliability index : (FORMBE) = 1.378 Corresponding approximate prob.of failure = 8.4161E‐02 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Scaled State‐Function value at x‐*(u‐*)= 0.4551E‐07 and Vector u‐* (beta‐point) : (n ; 1; ‐0.5811 ) (Do ; 2; 0.4515 ) (cs ; 3; 0.7924 ) (cx ; 4; ‐0.5242 ) (x ; 5; ‐0.6734 ) Normalized U‐space gradient (alfa‐U) with norm = 0.7608 : (n ; 1; 0.4218 ) (Do ; 2; ‐0.3278 ) (cs ; 3; ‐0.5752 ) (cx ; 4; 0.3805 ) (x ; 5; 0.4888 ) Normalized Representative alfa‐values with norm = 1.000 : (n ; 1; 0.4218 ) (Do ; 2; ‐0.3278 ) (cs ; 3; ‐0.5752 ) (cx ; 4; 0.3805 ) (x ; 5; 0.4888 ) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Solution in Basic‐ (X‐) space (x‐*): (n ; 1; 0.4709 ) (Do ; 2; 11.28 ) (cs ; 3; 1.053 ) (cx ; 4; 0.5685 ) (x ; 5; 2.663 ) Gradient in Basic‐ (X‐) space (scaled by 1/SCAL, see above): (n ; 1; 6.419 ) (Do ; 2; ‐8.7806E‐02) (cs ; 3; ‐2.605 ) (cx ; 4; 4.825 ) (x ; 5; 0.7438 ) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 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 : ‐5.872 ‐19.224 94.844 19.461 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Results of Second‐Order improvement‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Second‐Order reliability index = 1.443 Corresponding prob. of failure = 7.44750E‐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)=. 1.02 1.00 1.02 1.01 1.00 1.00 1.02 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.=. 2.79 (%) 2.69 (%) 3.84 (%) 3.07 (%) 2.59 (%) 2.45 (%) 2.85 (%) 2.52 (%) 2.33 (%). Análisis Probabilista. E. Mosquera..

(16) Coeficiente de Difusión. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ Recubrimiento=3 cm.‐ a/c=0.45. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Results of importance sampling ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Corrected reliability index = 1.442 Corresponding prob. of failure = 7.45951E‐02 Correction factor by simulation = 1.002 Coefficient of Variation in % = 2.292 100(=NSIMUL) samples generated; 0 samples failed. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Partial Safety Factors: Equival. x‐* / Characteristic Value Basic Variable, Equival. x‐* , Charact. Value, Part.Safety Fact. (n : 1) 0.469559 0.500000 0.939 (Do : 2) 11.3435 10.0000 1.134 (cs : 3) 1.05946 0.920000 1.152 (cx : 4) 0.567046 0.600000 0.945 (x : 5) 2.64724 3.00000 0.882 ‐‐‐‐‐‐‐‐‐‐ Parameter study for Parameter: t ‐‐‐‐‐‐‐‐‐‐ Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 4.517 3.15E‐06 ‐0.9029 ‐0.1005 3.000 3.489 2.43E‐04 ‐0.2320 ‐0.2012 5.500 3.055 1.13E‐03 ‐0.1359 ‐0.2474 8.000 2.775 2.76E‐03 ‐0.9533E‐01 ‐0.2786 10.50 2.571 5.07E‐03 ‐0.7293E‐01 ‐0.3028 13.00 2.410 7.97E‐03 ‐0.5876E‐01 ‐0.3229 15.50 2.279 1.13E‐02 ‐0.4901E‐01 ‐0.3404 18.00 2.168 1.51E‐02 ‐0.4191E‐01 ‐0.3561 20.50 2.072 1.91E‐02 ‐0.3652E‐01 ‐0.3705 23.00 1.988 2.34E‐02 ‐0.3230E‐01 ‐0.3839 25.50 1.913 2.79E‐02 ‐0.2890E‐01 ‐0.3966 28.00 1.846 3.25E‐02 ‐0.2612E‐01 ‐0.4086 30.50 1.786 3.70E‐02 ‐0.2380E‐01 ‐0.4201 33.00 1.730 4.18E‐02 ‐0.2183E‐01 ‐0.4313 35.50 1.679 4.66E‐02 ‐0.2015E‐01 ‐0.4420 38.00 1.631 5.14E‐02 ‐0.1869E‐01 ‐0.4525 40.50 1.587 5.63E‐02 ‐0.1742E‐01 ‐0.4627 43.00 1.545 6.11E‐02 ‐0.1630E‐01 ‐0.4728 45.50 1.507 6.60E‐02 ‐0.1531E‐01 ‐0.4826 48.00 1.470 7.08E‐02 ‐0.1442E‐01 ‐0.4923 50.50 1.436 7.55E‐02 ‐0.1362E‐01 ‐0.5019 53.00 1.403 8.03E‐02 ‐0.1290E‐01 ‐0.5113. Representative Alphas of Variables FLIM(1), 1º-2.pti. n 0.42 Do -0.33 cs -0.58 cx 0.38 x 0.49 Sum of a² 1.00. Análisis Probabilista. E. Mosquera..

(17) Coeficiente de Difusión. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ Recubrimiento=3 cm.‐ a/c=0.45. Reliability Index FLIM(1), 1º-2.pti. Beta 4.52. 4.21 3.89 3.58 3.27 2.96 2.65 2.34 2.03 1.71 1.40. 0.50. 5.75. 11.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. 42.50. 47.75. 53.00. 42.50. 47.75. 53.00. Failure Probability FLIM(1), 1º-2.pti. Failure Probability 0.50. 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00. 0.50. 5.75. 11.00. P.S.F. 1.28 0.00 1.75 1.19 0.00 2.56 1.09 -151996493463552.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. Partial Safety Factors FLIM(1), 1º-2.pti n Do cs cx x. 0.99 0.90 0.80 0.70 0.61 0.51 0.41 0.32. 0.50. 5.75. 11.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. 42.50. 47.75. Análisis Probabilista. 53.00. E. Mosquera..

(18) Coeficiente de Difusión. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐Recubrimiento=3 cm.‐ a/c=0.50. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Job name ............ : 1º‐3 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 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: n ; No. on X‐vector = 1 Comment : factor de edad Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) 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 = 2 Comment : Coef. Difusión inicial en cm2/s Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 15.80 ( 0.158000000000000E+02) Standard deviation........ = 2.840 ( 0.284000000000000E+01) Coefficient of Variation.. = 0.1797 ( 0.179746835443038E+00) Distr.Param.no.1 : m = 15.80 ( 0.158000000000000E+02) Distr.Param.no.2 : sigma = 2.840 ( 0.284000000000000E+01) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Variable: cs ; No. on X‐vector = 3 Comment : contenido superficial (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.9200 ( 0.920000000000000E+00) Standard deviation........ = 0.1680 ( 0.168000000000000E+00) Coefficient of Variation.. = 0.1826 ( 0.182608695652174E+00) Distr.Param.no.1 : m = 0.9200 ( 0.920000000000000E+00) Distr.Param.no.2 : sigma = 0.1680 ( 0.168000000000000E+00) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Variable: cx ; No. on X‐vector = 4 Comment : contenido critico (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) 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) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Variable: x ; No. on X‐vector = 5 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 3.000 ( 0.300000000000000E+01) Standard deviation........ = 0.5000 ( 0.500000000000000E+00) Coefficient of Variation.. = 0.1667 ( 0.166666666666667E+00) Distr.Param.no.1 : m = 3.000 ( 0.300000000000000E+01) Distr.Param.no.2 : sigma = 0.5000 ( 0.500000000000000E+00) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐ Constant (deterministic) Parameters ‐‐ Parameter :t ; No. on PVEC= 1 with value = 50.00 Comment : tiempo en años ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (n (cs (x (n. (Lower bounds on U‐space variables) ; 1; ‐36.69 ) (Do ; 2; ‐36.69 ) ; 3; ‐36.69 ) (cx ; 4; ‐36.69 ) ; 5; ‐36.69 ) ‐‐‐‐‐ Default U‐start = Origin (U=0) ‐‐‐‐ ; 1; 0.000 ) (Do ; 2; 0.000 ). Análisis Probabilista. E. Mosquera..

(19) Coeficiente de Difusión (cs (x (n (cs (x. ; 3; 0.000 ) ; 5; 0.000 ). (cx. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐Recubrimiento=3 cm.‐ a/c=0.50. ; 4; 0.000 ). ‐‐‐ X‐start: Median values from U=0 ‐‐‐‐ ; 1; 0.5000 ) (Do ; 2; 15.80 ) ; 3; 0.9200 ) (cx ; 4; 0.6000 ) ; 5; 3.000 ). (Upper bounds on U‐space variables) (n ; 1; 36.69 ) (Do ; 2; 36.69 ) (cs ; 3; 36.69 ) (cx ; 4; 36.69 ) (x ; 5; 36.69 ) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E‐03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 0.9190 ********************************** RESULTS: ********************************** First‐Order reliability index : (FORMBE) = 0.829 Corresponding approximate prob.of failure = 0.2035 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Scaled State‐Function value at x‐*(u‐*)= 0.4427E‐08 and Vector u‐* (beta‐point) : (n ; 1; ‐0.3370 ) (Do ; 2; 0.1811 ) (cs ; 3; 0.5399 ) (cx ; 4; ‐0.3361 ) (x ; 5; ‐0.3695 ) Normalized U‐space gradient (alfa‐U) with norm = 1.221 : (n ; 1; 0.4065 ) (Do ; 2; ‐0.2184 ) (cs ; 3; ‐0.6512 ) (cx ; 4; 0.4054 ) (x ; 5; 0.4457 ) Normalized Representative alfa‐values with norm = 1.000 : (n ; 1; 0.4065 ) (Do ; 2; ‐0.2184 ) (cs ; 3; ‐0.6512 ) (cx ; 4; 0.4054 ) (x ; 5; 0.4457 ) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Solution in Basic‐ (X‐) space (x‐*): (n ; 1; 0.4832 ) (Do ; 2; 16.31 ) (cs ; 3; 1.011 ) (cx ; 4; 0.5798 ) (x ; 5; 2.815 ) Gradient in Basic‐ (X‐) space (scaled by 1/SCAL, see above): (n ; 1; 9.926 ) (Do ; 2; ‐9.3890E‐02) (cs ; 3; ‐4.733 ) (cx ; 4; 8.249 ) (x ; 5; 1.088 ) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Constant Parameters (PVEC): (t ; 1; 50.00 ) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Statistics after beta‐point search Gradient evaluations : 5 Calls of state‐function : 31 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ ***************************************************** Report of an error by traceback facility (*YERR*) : Error in module :YSOMHO Warning from 2nd‐order improvement: Absolute value of 1st‐order beta(FORMBE) < 1 . 2nd‐order improvement by Hohenbichlers formula might be inaccurate because it is based on asymptotic theory ! ‐‐‐‐‐ Second‐Order Improvement : ‐‐‐‐‐ radii of curvature in U‐space : ‐6.542 ‐33.291 96.676 21.827 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Results of Second‐Order improvement‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Second‐Order reliability index = 0.883 Corresponding prob. of failure = 0.18853 ‐‐‐‐‐ Importance Sampling scheme based on SORM results ‐‐‐‐‐ Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= 1.02 Importance sampling: Sample no. 20 E(Sim)= 1.00 Importance sampling: Sample no. 30 E(Sim)= 1.00. C.o.V.= 1.85 (%) C.o.V.= 2.13 (%) C.o.V.= 2.66 (%). Análisis Probabilista. E. Mosquera..

(20) Coeficiente de Difusión. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐Recubrimiento=3 cm.‐ a/c=0.50. Importance sampling: Sample no. Importance sampling: Sample no. Importance sampling: Sample no. Importance sampling: Sample no. Importance sampling: Sample no. Importance sampling: Sample no.. 40 50 60 70 80 90. E(Sim)= E(Sim)= E(Sim)= E(Sim)= E(Sim)= E(Sim)=. 1.00 1.00 1.01 1.02 1.01 1.02. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 2.13 (%) 1.84 (%) 1.75 (%) 2.17 (%) 1.92 (%) 1.79 (%). ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Results of importance sampling ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Corrected reliability index = 0.879 Corresponding prob. of failure = 0.18958 Correction factor by simulation = 1.006 Coefficient of Variation in % = 1.797 100(=NSIMUL) samples generated; 0 samples failed. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Partial Safety Factors: Equival. x‐* / Characteristic Value Basic Variable, Equival. x‐* , Charact. Value, Part.Safety Fact. (n : 1) 0.482047 0.500000 0.964 (Do : 2) 16.3479 15.8000 1.035 (cs : 3) 1.01664 0.920000 1.105 (cx : 4) 0.578514 0.600000 0.964 (x : 5) 2.80317 3.00000 0.934 ‐‐‐‐‐‐‐‐‐‐ Parameter study for Parameter: t ‐‐‐‐‐‐‐‐‐‐ Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 3.000 5.500 8.000 10.50 13.00 15.50 18.00 20.50 23.00 25.50 28.00 30.50 33.00 35.50 38.00 40.50 43.00 45.50 48.00 50.50 53.00. 4.145 2.964 2.495 2.203 1.992 1.829 1.698 1.587 1.491 1.408 1.334 1.269 1.209 1.155 1.105 1.059 1.017 0.9774 0.9404 0.9057 0.8731 0.8423. 1.70E‐05 ‐1.078 ‐0.1307 1.52E‐03 ‐0.2545 ‐0.2599 6.29E‐03 ‐0.1436 ‐0.3204 1.38E‐02 ‐0.9855E‐01 ‐0.3634 2.32E‐02 ‐0.7424E‐01 ‐0.3985 3.37E‐02 ‐0.5912E‐01 ‐0.4291 4.48E‐02 ‐0.4886E‐01 ‐0.4571 5.63E‐02 ‐0.4147E‐01 ‐0.4833 6.80E‐02 ‐0.3590E‐01 ‐0.5083 7.96E‐02 ‐0.3157E‐01 ‐0.5324 9.10E‐02 ‐0.2811E‐01 ‐0.5559 0.10 ‐0.2529E‐01 ‐0.5791 0.11 ‐0.2295E‐01 ‐0.6020 0.12 ‐0.2097E‐01 ‐0.6248 0.13 ‐0.1929E‐01 ‐0.6475 0.14 ‐0.1783E‐01 ‐0.6702 0.15 ‐0.1657E‐01 ‐0.6931 0.16 ‐0.1546E‐01 ‐0.7162 0.17 ‐0.1448E‐01 ‐0.7395 0.18 ‐0.1360E‐01 ‐0.7631 0.19 ‐0.1282E‐01 ‐0.7870 0.20 ‐0.1212E‐01 ‐0.8114. Representative Alphas of Variables FLIM(1), 1º-3.pti. n 0.41 Do -0.22 cs -0.65 cx 0.41 x 0.45 Sum of a² 1.00. Análisis Probabilista. E. Mosquera..

(21) Coeficiente de Difusión. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐Recubrimiento=3 cm.‐ a/c=0.50. Reliability Index FLIM(1), 1º-3.pti. Beta 4.14. 3.81 3.48 3.15 2.82 2.49 2.16 1.83 1.50 1.17 0.84. 0.50. 5.75. 11.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. 42.50. 47.75. 53.00. Failure Probability FLIM(1), 1º-3.pti. Failure Probability 0.50. 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00. 0.50. 5.75. 11.00. P.S.F. 1.25 0.00 1.75 1.16 -0.00 2.74 1.08 -151996493463552.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. 42.50. 47.75. 53.00. Partial Safety Factors FLIM(1), 1º-3.pti n Do cs cx x. 0.99 0.90 0.82 0.73 0.64 0.56 0.47 0.38. 0.50. 5.75. 11.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. 42.50. 47.75. 53.00. Análisis Probabilista. E. Mosquera..

(22) Coeficiente de Difusión. Ambiente IIIa ‐Cc=350 ‐Kg/m3‐CEM I‐Recubrimiento=3 cm.‐ a/c=0.55. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Job name ............ : 1º‐4 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 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: n ; No. on X‐vector = 1 Comment : factor de edad Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) 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 = 2 Comment : Coef. Difusión inicial en cm2/s Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 19.70 ( 0.197000000000000E+02) Standard deviation........ = 2.840 ( 0.284000000000000E+01) Coefficient of Variation.. = 0.1442 ( 0.144162436548223E+00) Distr.Param.no.1 : m = 19.70 ( 0.197000000000000E+02) Distr.Param.no.2 : sigma = 2.840 ( 0.284000000000000E+01) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Variable: cs ; No. on X‐vector = 3 Comment : contenido superficial (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.9200 ( 0.920000000000000E+00) Standard deviation........ = 0.1680 ( 0.168000000000000E+00) Coefficient of Variation.. = 0.1826 ( 0.182608695652174E+00) Distr.Param.no.1 : m = 0.9200 ( 0.920000000000000E+00) Distr.Param.no.2 : sigma = 0.1680 ( 0.168000000000000E+00) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Variable: cx ; No. on X‐vector = 4 Comment : contenido critico (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) 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) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Variable: x ; No. on X‐vector = 5 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 3.000 ( 0.300000000000000E+01) Standard deviation........ = 0.5000 ( 0.500000000000000E+00) Coefficient of Variation.. = 0.1667 ( 0.166666666666667E+00) Distr.Param.no.1 : m = 3.000 ( 0.300000000000000E+01) Distr.Param.no.2 : sigma = 0.5000 ( 0.500000000000000E+00) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐ Constant (deterministic) Parameters ‐‐ Parameter :t ; No. on PVEC= 1 with value = 50.00 Comment : tiempo en años ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (n (cs (x (n. (Lower bounds on U‐space variables) ; 1; ‐36.69 ) (Do ; 2; ‐36.69 ) ; 3; ‐36.69 ) (cx ; 4; ‐36.69 ) ; 5; ‐36.69 ) ‐‐‐‐‐ Default U‐start = Origin (U=0) ‐‐‐‐ ; 1; 0.000 ) (Do ; 2; 0.000 ). Análisis Probabilista. E. Mosquera..

(23) Coeficiente de Difusión (cs (x (n (cs (x. ; 3; 0.000 ) ; 5; 0.000 ). (cx. Ambiente IIIa ‐Cc=350 ‐Kg/m3‐CEM I‐Recubrimiento=3 cm.‐ a/c=0.55. ; 4; 0.000 ). ‐‐‐ X‐start: Median values from U=0 ‐‐‐‐ ; 1; 0.5000 ) (Do ; 2; 19.70 ) ; 3; 0.9200 ) (cx ; 4; 0.6000 ) ; 5; 3.000 ). (Upper bounds on U‐space variables) (n ; 1; 36.69 ) (Do ; 2; 36.69 ) (cs ; 3; 36.69 ) (cx ; 4; 36.69 ) (x ; 5; 36.69 ) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E‐03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 0.6763 ********************************** RESULTS: ********************************** First‐Order reliability index : (FORMBE) = 0.564 Corresponding approximate prob.of failure = 0.2864 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Scaled State‐Function value at x‐*(u‐*)= 0.1359E‐07 and Vector u‐* (beta‐point) : (n ; 1; ‐0.2191 ) (Do ; 2; 9.6179E‐02) (cs ; 3; 0.3887 ) (cx ; 4; ‐0.2334 ) (x ; 5; ‐0.2346 ) Normalized U‐space gradient (alfa‐U) with norm = 1.777 : (n ; 1; 0.3887 ) (Do ; 2; ‐0.1706 ) (cs ; 3; ‐0.6894 ) (cx ; 4; 0.4140 ) (x ; 5; 0.4162 ) Normalized Representative alfa‐values with norm = 1.000 : (n ; 1; 0.3887 ) (Do ; 2; ‐0.1706 ) (cs ; 3; ‐0.6894 ) (cx ; 4; 0.4140 ) (x ; 5; 0.4162 ) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Solution in Basic‐ (X‐) space (x‐*): (n ; 1; 0.4890 ) (Do ; 2; 19.97 ) (cs ; 3; 0.9853 ) (cx ; 4; 0.5860 ) (x ; 5; 2.883 ) Gradient in Basic‐ (X‐) space (scaled by 1/SCAL, see above): (n ; 1; 13.81 ) (Do ; 2; ‐0.1067 ) (cs ; 3; ‐7.290 ) (cx ; 4; 12.26 ) (x ; 5; 1.479 ) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Constant Parameters (PVEC): (t ; 1; 50.00 ) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 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 : ‐6.895 ‐48.584 99.920 23.593 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Results of Second‐Order improvement‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Second‐Order reliability index = 0.613 Corresponding prob. of failure = 0.26983 ‐‐‐‐‐ Importance Sampling scheme based on SORM results ‐‐‐‐‐ Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= 1.02 C.o.V.= 1.47 (%) Importance sampling: Sample no. 20 E(Sim)= 0.999 C.o.V.= 1.83 (%) Importance sampling: Sample no. 30 E(Sim)= 1.00 C.o.V.= 2.18 (%). Análisis Probabilista. E. Mosquera..

(24) Coeficiente de Difusión Importance sampling: Sample no. Importance sampling: Sample no. Importance sampling: Sample no. Importance sampling: Sample no. Importance sampling: Sample no. Importance sampling: Sample no.. Ambiente IIIa ‐Cc=350 ‐Kg/m3‐CEM I‐Recubrimiento=3 cm.‐ a/c=0.55 40 50 60 70 80 90. E(Sim)= E(Sim)= E(Sim)= E(Sim)= E(Sim)= E(Sim)=. 0.999 1.00 1.01 1.02 1.01 1.02. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 1.74 (%) 1.55 (%) 1.47 (%) 1.85 (%) 1.64 (%) 1.54 (%). ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Results of importance sampling ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Corrected reliability index = 0.609 Corresponding prob. of failure = 0.27141 Correction factor by simulation = 1.006 Coefficient of Variation in % = 1.555 100(=NSIMUL) samples generated; 0 samples failed. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Partial Safety Factors: Equival. x‐* / Characteristic Value Basic Variable, Equival. x‐* , Charact. Value, Part.Safety Fact. (n : 1) 0.488080 0.500000 0.976 (Do : 2) 19.9971 19.7000 1.015 (cs : 3) 0.991033 0.920000 1.077 (cx : 4) 0.584765 0.600000 0.975 (x : 5) 2.87238 3.00000 0.957 ‐‐‐‐‐‐‐‐‐‐ Parameter study for Parameter: t ‐‐‐‐‐‐‐‐‐‐ Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 3.000 5.500 8.000 10.50 13.00 15.50 18.00 20.50 23.00 25.50 28.00 30.50 33.00 35.50 38.00 40.50 43.00 45.50 48.00 50.50 53.00. 3.927 2.671 2.192 1.897 1.688 1.527 1.397 1.288 1.195 1.115 1.044 0.9801 0.9229 0.8709 0.8234 0.7796 0.7391 0.7015 0.6664 0.6334 0.6025 0.5734. 4.30E‐05 ‐1.175 ‐0.1504 3.78E‐03 ‐0.2632 ‐0.2983 1.42E‐02 ‐0.1453 ‐0.3693 2.89E‐02 ‐0.9840E‐01 ‐0.4218 4.57E‐02 ‐0.7345E‐01 ‐0.4663 6.34E‐02 ‐0.5810E‐01 ‐0.5066 8.13E‐02 ‐0.4776E‐01 ‐0.5445 9.89E‐02 ‐0.4035E‐01 ‐0.5811 0.12 ‐0.3480E‐01 ‐0.6170 0.13 ‐0.3050E‐01 ‐0.6527 0.15 ‐0.2708E‐01 ‐0.6884 0.16 ‐0.2429E‐01 ‐0.7244 0.18 ‐0.2199E‐01 ‐0.7610 0.19 ‐0.2005E‐01 ‐0.7984 0.21 ‐0.1840E‐01 ‐0.8368 0.22 ‐0.1698E‐01 ‐0.8762 0.23 ‐0.1575E‐01 ‐0.9170 0.24 ‐0.1467E‐01 ‐0.9593 0.25 ‐0.1372E‐01 ‐1.003 0.26 ‐0.1287E‐01 ‐1.049 0.27 ‐0.1211E‐01 ‐1.097 0.28 ‐0.1143E‐01 ‐1.147. Representative Alphas of Variables FLIM(1), 1º-4.pti. n 0.39 Do -0.17 cs -0.69 cx 0.41 x 0.42 Sum of a² 1.00. Análisis Probabilista. E. Mosquera..

(25) Coeficiente de Difusión. Ambiente IIIa ‐Cc=350 ‐Kg/m3‐CEM I‐Recubrimiento=3 cm.‐ a/c=0.55. Reliability Index FLIM(1), 1º-4.pti. Beta 3.93. 3.59 3.26 2.92 2.59 2.25 1.91 1.58 1.24 0.91 0.57. 0.50. 5.75. 11.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. 42.50. 47.75. 53.00. 42.50. 47.75. 53.00. Failure Probability FLIM(1), 1º-4.pti. Failure Probability 0.50. 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00. 0.50. 5.75. 11.00. P.S.F. 1.25 0.00 1.75 1.17 0.00 2.81 1.09 -151996493463552.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. Partial Safety Factors FLIM(1), 1º-4.pti n Do cs cx x. 1.01 0.92 0.84 0.76 0.67 0.59 0.51 0.43. 0.50. 5.75. 11.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. 42.50. 47.75. Análisis Probabilista. 53.00. E. Mosquera..

(26) Coeficiente de DifusiónCV‐5%. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm‐ a/c=0.45. Job name ............ : 1ºcv-1 -----------------------------------------------------------------------------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: n ; No. on X-vector = 1 Comment : factor de edad Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) 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 = 2 Comment : Coef. Difusión inicial en cm2/s Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 10.00 ( 0.100000000000000E+02) Standard deviation........ = 0.5000 ( 0.500000000000000E+00) Coefficient of Variation.. = 5.0000E-02 ( 0.500000000000000E-01) Distr.Param.no.1 : m = 10.00 ( 0.100000000000000E+02) Distr.Param.no.2 : sigma = 0.5000 ( 0.500000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 3 Comment : contenido superficial (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.9200 ( 0.920000000000000E+00) Standard deviation........ = 0.1650 ( 0.165000000000000E+00) Coefficient of Variation.. = 0.1793 ( 0.179347826086957E+00) Distr.Param.no.1 : m = 0.9200 ( 0.920000000000000E+00) Distr.Param.no.2 : sigma = 0.1650 ( 0.165000000000000E+00) ------------------------Variable: cx ; No. on X-vector = 4 Comment : contenido critico (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) 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) ------------------------Variable: x ; No. on X-vector = 5 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 3.000 ( 0.300000000000000E+01) Standard deviation........ = 0.5000 ( 0.500000000000000E+00) Coefficient of Variation.. = 0.1667 ( 0.166666666666667E+00) Distr.Param.no.1 : m = 3.000 ( 0.300000000000000E+01) Distr.Param.no.2 : sigma = 0.5000 ( 0.500000000000000E+00) -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años ------------------------(n (cs (x (n (cs (x. ; ; ;. 1 with value =. (Lower bounds on U-space variables) 1; -36.69 ) (Do ; 2; 3; -36.69 ) (cx ; 4; 5; -36.69 ). 50.00. -36.69 -36.69. ) ). ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (Do ; 2; 0.000 ; 3; 0.000 ) (cx ; 4; 0.000 ; 5; 0.000 ). ) ). --- X-start: Median values from U=0. ----. Análisis Probabilista. E. Mosquera..

(27) Coeficiente de DifusiónCV‐5% (n (cs (x. ; ; ;. 1; 3; 5;. 0.5000 0.9200 3.000. ) ) ). Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm‐ a/c=0.45 (Do (cx. ; ;. 2; 4;. 10.00 0.6000. ) ). (Upper bounds on U-space variables) (n ; 1; 36.69 ) (Do ; 2; 36.69 ) (cs ; 3; 36.69 ) (cx ; 4; 36.69 ) (x ; 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) = 1.344 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.475 Corresponding approximate prob.of failure = 7.0156E-02 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.9370E-08 and Vector u-* (beta-point) : (n ; 1; -0.6681 ) (Do ; 2; 0.1026 ) (cs ; 3; 0.8619 ) (cx ; 4; -0.5897 ) (x ; 5; -0.7919 ) Normalized U-space gradient (alfa-U) with norm = 0.6926 : (n ; 1; 0.4531 ) (Do ; 2; -6.9564E-02) (cs ; 3; -0.5845 ) (cx ; 4; 0.3999 ) (x ; 5; 0.5370 ) Normalized Representative alfa-values with norm = 1.000 : (n ; 1; 0.4531 ) (Do ; 2; -6.9564E-02) (cs ; 3; -0.5845 ) (cx ; 4; 0.3999 ) (x ; 5; 0.5370 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (n ; 1; 0.4666 ) (Do ; 2; 10.05 ) (cs ; 3; 1.062 ) (cx ; 4; 0.5646 ) (x ; 5; 2.604 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (n ; 1; 6.276 ) (Do ; 2; -9.6357E-02) (cs ; 3; -2.453 ) (cx ; 4; 4.616 ) (x ; 5; 0.7438 ) -----------------------------------------------------------------------------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 : -7.295 -296.893 89.238. 18.868. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.503 Corresponding prob. of failure = 6.63717E-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)=. 1.01 0.975 0.986 0.988 0.995 1.01 1.02 1.02 1.03. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 2.57 2.95 3.84 3.11 2.90 2.71 3.14 2.78 2.62. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.498 Corresponding prob. of failure = 6.71237E-02 Correction factor by simulation = 1.011 Coefficient of Variation in % = 2.597 100(=NSIMUL) samples generated; 0 samples failed.. Análisis Probabilista. E. Mosquera..

(28) Coeficiente de DifusiónCV‐5%. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm‐ a/c=0.45. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (n : 1) 0.465943 0.500000 0.932 (Do : 2) 10.0523 10.0000 1.005 (cs : 3) 1.06498 0.920000 1.158 (cx : 4) 0.563931 0.600000 0.940 (x : 5) 2.59635 3.00000 0.865 ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 4.608 2.03E-06 -0.8177 -0.8896E-01 3.000 3.646 1.33E-04 -0.2231 -0.1840 5.500 3.215 6.52E-04 -0.1360 -0.2332 8.000 2.929 1.70E-03 -0.9770E-01 -0.2677 10.50 2.715 3.31E-03 -0.7590E-01 -0.2946 13.00 2.546 5.45E-03 -0.6179E-01 -0.3170 15.50 2.405 8.08E-03 -0.5192E-01 -0.3363 18.00 2.286 1.11E-02 -0.4464E-01 -0.3536 20.50 2.183 1.45E-02 -0.3905E-01 -0.3693 23.00 2.092 1.82E-02 -0.3464E-01 -0.3838 25.50 2.011 2.21E-02 -0.3108E-01 -0.3974 28.00 1.938 2.63E-02 -0.2813E-01 -0.4102 30.50 1.872 3.06E-02 -0.2567E-01 -0.4225 33.00 1.811 3.50E-02 -0.2357E-01 -0.4342 35.50 1.756 3.96E-02 -0.2177E-01 -0.4455 38.00 1.704 4.42E-02 -0.2021E-01 -0.4565 40.50 1.655 4.90E-02 -0.1885E-01 -0.4672 43.00 1.610 5.37E-02 -0.1764E-01 -0.4776 45.50 1.567 5.85E-02 -0.1657E-01 -0.4879 48.00 1.528 6.33E-02 -0.1561E-01 -0.4979 50.50 1.490 6.81E-02 -0.1475E-01 -0.5078 53.00 1.455 7.29E-02 -0.1398E-01 -0.5175. Representative Alphas of Variables FLIM(1), 1ºcv-1.pti. n 0.45 Do -0.07 cs -0.58 cx 0.40 x 0.54 Sum of a² 1.00. Análisis Probabilista. E. Mosquera..

(29) Coeficiente de DifusiónCV‐5%. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm‐ a/c=0.45. Reliability Index FLIM(1), 1ºcv-1.pti. Beta 4.61. 4.29 3.98 3.66 3.35 3.03 2.72 2.40 2.09 1.77 1.45. 0.50. 5.75. 11.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. 42.50. 47.75. 53.00. 42.50. 47.75. 53.00. Failure Probability FLIM(1), 1ºcv-1.pti. Failure Probability 0.08. 0.07 0.06 0.06 0.05 0.04 0.03 0.02 0.02 0.01 0.00. 0.50. 5.75. 11.00. P.S.F. 1.25 0.00 1.75 1.15 0.00 2.56 1.06 -151996493463552.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. Partial Safety Factors FLIM(1), 1ºcv-1.pti n Do cs cx x. 0.96 0.86 0.76 0.67 0.57 0.47 0.38 0.28. 0.50. 5.75. 11.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. 42.50. 47.75. Análisis Probabilista. 53.00. E. Mosquera..

(30) Coeficiente de DifusiónCV‐10%. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm‐ a/c=0.45. Job name ............ : 1ºcv-2 -----------------------------------------------------------------------------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: n ; No. on X-vector = 1 Comment : factor de edad Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) 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 = 2 Comment : Coef. Difusión inicial en cm2/s Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 10.00 ( 0.100000000000000E+02) Standard deviation........ = 1.000 ( 0.100000000000000E+01) Coefficient of Variation.. = 0.1000 ( 0.100000000000000E+00) Distr.Param.no.1 : m = 10.00 ( 0.100000000000000E+02) Distr.Param.no.2 : sigma = 1.000 ( 0.100000000000000E+01) ------------------------Variable: cs ; No. on X-vector = 3 Comment : contenido superficial (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.9200 ( 0.920000000000000E+00) Standard deviation........ = 0.1650 ( 0.165000000000000E+00) Coefficient of Variation.. = 0.1793 ( 0.179347826086957E+00) Distr.Param.no.1 : m = 0.9200 ( 0.920000000000000E+00) Distr.Param.no.2 : sigma = 0.1650 ( 0.165000000000000E+00) ------------------------Variable: cx ; No. on X-vector = 4 Comment : contenido critico (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) 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) ------------------------Variable: x ; No. on X-vector = 5 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 3.000 ( 0.300000000000000E+01) Standard deviation........ = 0.5000 ( 0.500000000000000E+00) Coefficient of Variation.. = 0.1667 ( 0.166666666666667E+00) Distr.Param.no.1 : m = 3.000 ( 0.300000000000000E+01) Distr.Param.no.2 : sigma = 0.5000 ( 0.500000000000000E+00) -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años ------------------------(n (cs (x (n (cs (x. ; ; ;. 1 with value =. (Lower bounds on U-space variables) 1; -36.69 ) (Do ; 2; 3; -36.69 ) (cx ; 4; 5; -36.69 ). 50.00. -36.69 -36.69. ) ). ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (Do ; 2; 0.000 ; 3; 0.000 ) (cx ; 4; 0.000 ; 5; 0.000 ). ) ). --- X-start: Median values from U=0. ----. Análisis Probabilista. E. Mosquera..

(31) Coeficiente de DifusiónCV‐10% (n (cs (x. ; ; ;. 1; 3; 5;. 0.5000 0.9200 3.000. ) ) ). Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm‐ a/c=0.45 (Do (cx. ; ;. 2; 4;. 10.00 0.6000. ) ). (Upper bounds on U-space variables) (n ; 1; 36.69 ) (Do ; 2; 36.69 ) (cs ; 3; 36.69 ) (cx ; 4; 36.69 ) (x ; 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) = 1.344 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.464 Corresponding approximate prob.of failure = 7.1568E-02 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.1092E-07 and Vector u-* (beta-point) : (n ; 1; -0.6578 ) (Do ; 2; 0.1991 ) (cs ; 3; 0.8531 ) (cx ; 4; -0.5824 ) (x ; 5; -0.7775 ) Normalized U-space gradient (alfa-U) with norm = 0.7004 : (n ; 1; 0.4493 ) (Do ; 2; -0.1360 ) (cs ; 3; -0.5826 ) (cx ; 4; 0.3978 ) (x ; 5; 0.5310 ) Normalized Representative alfa-values with norm = 1.000 : (n ; 1; 0.4493 ) (Do ; 2; -0.1360 ) (cs ; 3; -0.5826 ) (cx ; 4; 0.3978 ) (x ; 5; 0.5310 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (n ; 1; 0.4671 ) (Do ; 2; 10.20 ) (cs ; 3; 1.061 ) (cx ; 4; 0.5651 ) (x ; 5; 2.611 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (n ; 1; 6.293 ) (Do ; 2; -9.5223E-02) (cs ; 3; -2.473 ) (cx ; 4; 4.643 ) (x ; 5; 0.7438 ) -----------------------------------------------------------------------------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 : -7.164 -81.663 89.758. 18.751. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.498 Corresponding prob. of failure = 6.70498E-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)=. 1.01 0.981 0.992 0.992 0.997 1.01 1.02 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.=. 2.59 2.89 3.82 3.09 2.79 2.62 3.09 2.73 2.56. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.493 Corresponding prob. of failure = 6.76641E-02 Correction factor by simulation = 1.009 Coefficient of Variation in % = 2.533 100(=NSIMUL) samples generated; 0 samples failed.. Análisis Probabilista. E. Mosquera..

(32) Coeficiente de DifusiónCV‐10%. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm‐ a/c=0.45. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (n : 1) 0.466347 0.500000 0.933 (Do : 2) 10.2037 10.0000 1.020 (cs : 3) 1.06402 0.920000 1.157 (cx : 4) 0.564246 0.600000 0.940 (x : 5) 2.60223 3.00000 0.867 ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 4.599 2.12E-06 -0.8273 -0.9021E-01 3.000 3.629 1.42E-04 -0.2244 -0.1861 5.500 3.198 6.92E-04 -0.1361 -0.2349 8.000 2.912 1.79E-03 -0.9746E-01 -0.2690 10.50 2.700 3.47E-03 -0.7555E-01 -0.2955 13.00 2.531 5.68E-03 -0.6142E-01 -0.3175 15.50 2.392 8.37E-03 -0.5155E-01 -0.3366 18.00 2.274 1.15E-02 -0.4429E-01 -0.3536 20.50 2.172 1.49E-02 -0.3873E-01 -0.3691 23.00 2.082 1.87E-02 -0.3434E-01 -0.3834 25.50 2.002 2.27E-02 -0.3080E-01 -0.3969 28.00 1.930 2.68E-02 -0.2788E-01 -0.4096 30.50 1.864 3.12E-02 -0.2543E-01 -0.4218 33.00 1.804 3.56E-02 -0.2335E-01 -0.4334 35.50 1.748 4.02E-02 -0.2157E-01 -0.4447 38.00 1.697 4.49E-02 -0.2002E-01 -0.4556 40.50 1.649 4.96E-02 -0.1867E-01 -0.4662 43.00 1.604 5.43E-02 -0.1747E-01 -0.4766 45.50 1.563 5.91E-02 -0.1641E-01 -0.4868 48.00 1.523 6.38E-02 -0.1547E-01 -0.4968 50.50 1.486 6.86E-02 -0.1461E-01 -0.5066 53.00 1.451 7.34E-02 -0.1384E-01 -0.5163. Representative Alphas of Variables FLIM(1), 1ºcv-2.pti. n 0.45 Do -0.14 cs -0.58 cx 0.40 x 0.53 Sum of a² 1.00. Análisis Probabilista. E. Mosquera..

(33) Coeficiente de DifusiónCV‐10%. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm‐ a/c=0.45. Reliability Index FLIM(1), 1ºcv-2.pti. Beta 4.60. 4.28 3.97 3.65 3.34 3.03 2.71 2.40 2.08 1.77 1.45. 0.50. 5.75. 11.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. 42.50. 47.75. 53.00. 42.50. 47.75. 53.00. Failure Probability FLIM(1), 1ºcv-2.pti. Failure Probability 0.08. 0.07 0.06 0.06 0.05 0.04 0.03 0.02 0.02 0.01 0.00. 0.50. 5.75. 11.00. P.S.F. 1.25 0.00 1.75 1.15 0.00 2.56 1.06 -151996493463552.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. Partial Safety Factors FLIM(1), 1ºcv-2.pti n Do cs cx x. 0.96 0.86 0.77 0.67 0.57 0.48 0.38 0.28. 0.50. 5.75. 11.00. 16.25. 21.50. 26.75 t. 32.00. 37.25. 42.50. 47.75. Análisis Probabilista. 53.00. E. Mosquera..

(34) Coeficiente de DifusiónCV‐20%. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I Recubrimiento=3 cm‐ a/c=0.45. Job name ............ : 1ºcv-3 -----------------------------------------------------------------------------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: n ; No. on X-vector = 1 Comment : factor de edad Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) 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 = 2 Comment : Coef. Difusión inicial en cm2/s Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 10.00 ( 0.100000000000000E+02) Standard deviation........ = 2.000 ( 0.200000000000000E+01) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 10.00 ( 0.100000000000000E+02) Distr.Param.no.2 : sigma = 2.000 ( 0.200000000000000E+01) ------------------------Variable: cs ; No. on X-vector = 3 Comment : contenido superficial (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.9200 ( 0.920000000000000E+00) Standard deviation........ = 0.1650 ( 0.165000000000000E+00) Coefficient of Variation.. = 0.1793 ( 0.179347826086957E+00) Distr.Param.no.1 : m = 0.9200 ( 0.920000000000000E+00) Distr.Param.no.2 : sigma = 0.1650 ( 0.165000000000000E+00) ------------------------Variable: cx ; No. on X-vector = 4 Comment : contenido critico (%cemento) Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) 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) ------------------------Variable: x ; No. on X-vector = 5 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 3.000 ( 0.300000000000000E+01) Standard deviation........ = 0.5000 ( 0.500000000000000E+00) Coefficient of Variation.. = 0.1667 ( 0.166666666666667E+00) Distr.Param.no.1 : m = 3.000 ( 0.300000000000000E+01) Distr.Param.no.2 : sigma = 0.5000 ( 0.500000000000000E+00) -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años ------------------------(n (cs (x (n (cs (x. ; ; ;. 1 with value =. (Lower bounds on U-space variables) 1; -36.69 ) (Do ; 2; 3; -36.69 ) (cx ; 4; 5; -36.69 ). 50.00. -36.69 -36.69. ) ). ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (Do ; 2; 0.000 ; 3; 0.000 ) (cx ; 4; 0.000 ; 5; 0.000 ). ) ). --- X-start: Median values from U=0. ----. Análisis Probabilista. E. Mosquera..