TítuloProbabilismo explícito en la corrosión de armaduras en las estructuras de hormigón sometidas al ambiente marino de la costa gallega
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(2) 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:. 4.-Denominados.- DP1PF10; DP2PF10; DP3PF10; DP4PF10; DP5PF10; DP6PF10; Recubrimiento probabilista y CoV de las Variables básicas= 10%. 3.- Denominación.- dp1D30. Recubrimiento determinista y CoV de las variables básicas= 30%. 2.- Denominación.- dp1D. Recubrimiento determinista y CoV de las variables básicas = 0,6%. 1.-Denominados.- DP1; DP2; DP3; DP4; DP5; DP6 Recubrimiento semiprobabilista y CoV de las variables básicas =0,6%. Resumen de los cálculos probabilistas para conocer la variabilidad de las variables básicas utilizadas en el anejo 9º de EHE-08 y los valores determinados en esas condiciones ya estudiados. También determinar el recubrimiento probabilista con probabilidad de fallo entre 11% y 13%, aceptando variabilidad de las variables básicas del 10%. Los estudios se efectúan sobre los ambientes (IIIa-500 y IIIc-IV), un hormigón de relación a/c= 0,4 , Contenido de cemento 350 kg/m3, tiempo 50 años y para cada tipo de cemento (CEM I, CEM II/A-V y CEM III), Se recogen los recubrimientos deterministas y semiprobabilistas obtenidos en los apartados de cálculo determinista y en estas condiciones se estudian los siguientes casos:. El contenido del anejo es el siguiente:. Referencia del Análisis: Determinismo-Probabilismo.. Contenido del anejo 5. Probabilismo explicito en la corrosión de armaduras en las estructuras de hormigón sometidas al ambiente marino de la costa gallega..
(3) Emilio Mosquera Rey 0.82. 0.85. 0.88. 0.91. 0.95. 0.98. 1.01. 1.04. 1.07. 1.10. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 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. 54.25. 2.50. 8.25. 14.00. 0.00 1.75 -107374184.00 2.53 -151996493463552.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. Partial Safety Factors FLIM(1), DP1.pti. 48.50. 54.25. n Do cs cx x. 60.00. 60.00. 60.00. Variación de los Coef. parciales de seguridad en función del tiempo en años. 2.50. P.S.F. 1.13. 0.00. 0.08. 0.17. 0.25. 0.34. 0.42. 0.50. 0.59. 0.67. 0.76. 8.25. Reliability Index FLIM(1), DP1.pti. Variación de la Probabilidad de fallo en función del tiempo en años. 2.50. Beta. Failure Probability 0.84. -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 en años. Contenido del anejo 5. Probabilismo explicito en la corrosión de armaduras en las estructuras de hormigón sometidas al ambiente marino de la costa gallega..
(4) DP1 Rs=1.60, Rd=1.56. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. -----------------------------------------------------------------------------Job name ............ : DP1 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 21.01.2011 Time(hh:mm) ........ : 19:45 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: 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........ = 3.0000E-03 ( 0.300000000000000E-02) Coefficient of Variation.. = 6.0000E-03 ( 0.600000000000000E-02) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 3.0000E-03 ( 0.300000000000000E-02) ------------------------Variable: Do ; No. on X-vector = 2 Comment : Coef. Difusión inicial Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 8.900 ( 0.890000000000000E+01) Standard deviation........ = 5.3400E-02 ( 0.534000000000000E-01) Coefficient of Variation.. = 6.0000E-03 ( 0.600000000000000E-02) Distr.Param.no.1 : m = 8.900 ( 0.890000000000000E+01) Distr.Param.no.2 : sigma = 5.3400E-02 ( 0.534000000000000E-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........ = 5.5000E-03 ( 0.550000000000000E-02) Coefficient of Variation.. = 5.9783E-03 ( 0.597826086956522E-02) Distr.Param.no.1 : m = 0.9200 ( 0.920000000000000E+00) Distr.Param.no.2 : sigma = 5.5000E-03 ( 0.550000000000000E-02) ------------------------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........ = 3.6000E-03 ( 0.360000000000000E-02) Coefficient of Variation.. = 6.0000E-03 ( 0.600000000000000E-02) Distr.Param.no.1 : m = 0.6000 ( 0.600000000000000E+00) Distr.Param.no.2 : sigma = 3.6000E-03 ( 0.360000000000000E-02) ------------------------Variable: x ; No. on X-vector = 5 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 1.600 ( 0.160000000000000E+01) Standard deviation........ = 9.6000E-03 ( 0.960000000000000E-02) Coefficient of Variation.. = 6.0000E-03 ( 0.600000000000000E-02) Distr.Param.no.1 : m = 1.600 ( 0.160000000000000E+01) Distr.Param.no.2 : sigma = 9.6000E-03 ( 0.960000000000000E-02) -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años -------------------------. 1 with value =. 50.00. Análisis Probabilista. E. Mosquera..
(5) DP1 Rs=1.60, Rd=1.56. (n (cs (x. ; ; ;. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. (Lower bounds on U-space variables) 1; -36.69 ) (Do ; 2; 3; -36.69 ) (cx ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (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 ; 3; 0.9200 ) (cx ; 5; 1.600 ). ---2; 8.900 4; 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) = 0.3812E-01 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.138 Corresponding approximate prob.of failure = 0.1276 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.2192E-10 and Vector u-* (beta-point) : (n ; 1; -0.5256 ) (Do ; 2; 0.1621 ) (cs ; 3; 0.6619 ) (cx ; 4; -0.6697 ) (x ; 5; -0.3251 ) Normalized U-space gradient (alfa-U) with norm = 0.8816 : (n ; 1; 0.4619 ) (Do ; 2; -0.1424 ) (cs ; 3; -0.5817 ) (cx ; 4; 0.5885 ) (x ; 5; 0.2857 ) Normalized Representative alfa-values with norm = 1.000 : (n ; 1; 0.4619 ) (Do ; 2; -0.1424 ) (cs ; 3; -0.5817 ) (cx ; 4; 0.5885 ) (x ; 5; 0.2857 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (n ; 1; 0.4984 ) (Do ; 2; 8.909 ) (cs ; 3; 0.9236 ) (cx ; 4; 0.5976 ) (x ; 5; 1.597 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (n ; 1; 135.7 ) (Do ; 2; -2.351 ) (cs ; 3; -93.24 ) (cx ; 4; 144.1 ) (x ; 5; 26.24 ) -----------------------------------------------------------------------------Constant Parameters (PVEC): (t ; 1; 50.00 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 3 Calls of state-function : 19 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -165.144 -1278.497 1686.962. 732.020. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.140 Corresponding prob. of failure = 0.12708. ----- 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)=. 1.00 1.00 1.00 1.00. C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 0.08 0.10 0.12 0.09. (%) (%) (%) (%). Análisis Probabilista. E. Mosquera..
(6) DP1 Rs=1.60, Rd=1.56. Importance Importance Importance Importance Importance. sampling: sampling: sampling: sampling: sampling:. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. Sample Sample Sample Sample Sample. no. no. no. no. no.. 50 60 70 80 90. E(Sim)= E(Sim)= E(Sim)= E(Sim)= E(Sim)=. 1.00 1.00 1.00 1.00 1.00. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 0.09 0.09 0.10 0.09 0.09. (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.140 Corresponding prob. of failure = 0.12721 Correction factor by simulation = 1.001 Coefficient of Variation in % = 0.080 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (n : 1) 0.498420 0.500000 0.997 (Do : 2) 8.90867 8.90000 1.001 (cs : 3) 0.923648 0.920000 1.004 (cx : 4) 0.597584 0.600000 0.996 (x : 5) 1.59687 1.60000 0.998 ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 2.500 5.000 7.500 10.00 12.50 15.00 17.50 20.00 22.50 25.00 27.50 30.00 32.50 35.00 37.50 40.00 42.50 45.00 47.50 50.00 52.50 55.00 57.50 60.00. 49.47 35.95 28.69 23.83 20.24 17.42 15.11 13.16 11.49 10.02 8.725 7.562 6.511 5.552 4.673 3.862 3.110 2.409 1.754 1.140 0.5612 0.1509E-01 -0.5010 -0.9911. 0.0 2.50-283 3.25-181 8.67-126 2.36E-91 3.30E-68 7.77E-52 7.69E-40 7.89E-31 6.16E-24 1.35E-18 2.00E-14 3.76E-11 1.41E-08 1.49E-06 5.63E-05 9.36E-04 7.99E-03 3.97E-02 0.13 0.29 0.49 0.69 0.84. -8.160 -3.707 -2.308 -1.643 -1.261 -1.014 -0.8435 -0.7188 -0.6241 -0.5499 -0.4903 -0.4415 -0.4010 -0.3667 -0.3374 -0.3121 -0.2901 -0.2707 -0.2536 -0.2383 -0.2247 -0.2124 -0.2013 -0.1912. -0.4123 -0.5155 -0.6035 -0.6896 -0.7786 -0.8736 -0.9773 -1.093 -1.223 -1.372 -1.546 -1.752 -2.002 -2.312 -2.708 -3.234 -3.967 -5.060 -6.873 -10.47 -21.09 -829.0 -22.98 -11.54. Representative Alphas of Variables FLIM(1), DP1.pti. n 0.46 Do -0.14 cs -0.58 cx 0.59 x 0.29 Sum of a²1.00. Análisis Probabilista. E. Mosquera..
(7) DP1 Rs=1.60, Rd=1.56. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. Reliability Index FLIM(1), DP1.pti. Beta 49.47 44.42 39.38 34.33 29.29 24.24 19.19 14.15 9.10 4.06 -0.99. 2.50. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. 60.00. Failure Probability FLIM(1), DP1.pti. Failure Probability 0.84 0.76 0.67 0.59 0.50 0.42 0.34 0.25 0.17 0.08 0.00 2.50. 8.25. 14.00. 1.07. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. 60.00. Partial Safety Factors FLIM(1), DP1.pti. P.S.F. 1.13 1.10. 19.75. 0.00 1.75 -107374184.00 2.53 -151996493463552.00. n Do cs cx x. 1.04 1.01 0.98 0.95 0.91 0.88 0.85 0.82. 2.50. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. Análisis Probabilista. 60.00. E. Mosquera..
(8) DP1PF10 Rp=2.25, Rd=1.56. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. -----------------------------------------------------------------------------Job name ............ : DP1PF10 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 22.01.2011 Time(hh:mm) ........ : 20:17 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: n ; No. on Comment : factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 1. : Normal (2) : Mean & Std.Dev. (0) = 0.5000 ( 0.500000000000000E+00) = 5.0000E-02 ( 0.500000000000000E-01) = 0.1000 ( 0.100000000000000E+00) = 0.5000 ( 0.500000000000000E+00) = 5.0000E-02 ( 0.500000000000000E-01). Variable: Do ; No. on X-vector = 2 Comment : Coef. Difusión inicial Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) 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 = 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........ = 9.2000E-02 ( 0.920000000000000E-01) Coefficient of Variation.. = 0.1000 ( 0.100000000000000E+00) Distr.Param.no.1 : m = 0.9200 ( 0.920000000000000E+00) Distr.Param.no.2 : sigma = 9.2000E-02 ( 0.920000000000000E-01) ------------------------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 Comment : recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma. X-vector = 5 cm. : Normal (2) : Mean & Std.Dev. (0) = 2.250 ( 0.225000000000000E+01) = 2.2500E-02 ( 0.225000000000000E-01) = 1.0000E-02 ( 0.100000000000000E-01) = 2.250 ( 0.225000000000000E+01) = 2.2500E-02 ( 0.225000000000000E-01). Análisis Probabilista. E. Mosquera..
(9) DP1PF10 Rp=2.25, Rd=1.56. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años -------------------------. (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. ) ). (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 ; 3; 0.9200 ) (cx ; 5; 2.250 ). ---2; 8.900 4; 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) = 0.6881 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.195 Corresponding approximate prob.of failure = 0.1159 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.1005E-07 and Vector u-* (beta-point) : (n ; 1; -0.6964 ) (Do ; 2; 0.2105 ) (cs ; 3; 0.6237 ) (cx ; 4; -0.7135 ) (x ; 5; -4.3008E-02) Normalized U-space gradient (alfa-U) with norm = 0.9089 : (n ; 1; 0.5825 ) (Do ; 2; -0.1761 ) (cs ; 3; -0.5217 ) (cx ; 4; 0.5968 ) (x ; 5; 3.5975E-02) Normalized Representative alfa-values with norm = 1.000 : (n ; 1; 0.5825 ) (Do ; 2; -0.1761 ) (cs ; 3; -0.5217 ) (cx ; 4; 0.5968 ) (x ; 5; 3.5975E-02) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (n ; 1; 0.4652 ) (Do ; 2; 9.087 ) (cs ; 3; 0.9774 ) (cx ; 4; 0.5572 ) (x ; 5; 2.249 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (n ; 1; 10.59 ) (Do ; 2; -0.1798 ) (cs ; 3; -5.154 ) (cx ; 4; 9.041 ) (x ; 5; 1.453 ) -----------------------------------------------------------------------------Constant Parameters (PVEC): (t ; 1; 50.00 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 5 Calls of state-function : 31 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -10.730 -64.045 2788.974. 80.223. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.240 Corresponding prob. of failure = 0.10757. Análisis Probabilista. E. Mosquera..
(10) DP1PF10 Rp=2.25, Rd=1.56. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 30 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 50 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 70 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 90 E(Sim)=. 0.993 0.996 0.987 0.990 0.999 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.=. 1.50 1.61 1.95 1.51 1.40 1.35 1.47 1.36 1.29. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.230 Corresponding prob. of failure = 0.10926 Correction factor by simulation = 1.016 Coefficient of Variation in % = 1.192 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (n : 1) 0.463897 0.500000 0.928 (Do : 2) 9.09426 8.90000 1.022 (cs : 3) 0.979494 0.920000 1.065 (cx : 4) 0.555614 0.600000 0.926 (x : 5) 2.24900 2.25000 1.000 ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 2.500 5.476 2.18E-08 -0.8147 -0.3731 5.000 4.187 1.41E-05 -0.3408 -0.4091 7.500 3.534 2.05E-04 -0.2044 -0.4368 10.00 3.111 9.33E-04 -0.1424 -0.4615 12.50 2.803 2.53E-03 -0.1076 -0.4846 15.00 2.565 5.16E-03 -0.8565E-01 -0.5066 17.50 2.371 8.86E-03 -0.7066E-01 -0.5280 20.00 2.210 1.36E-02 -0.5981E-01 -0.5489 22.50 2.071 1.92E-02 -0.5166E-01 -0.5697 25.00 1.951 2.55E-02 -0.4532E-01 -0.5903 27.50 1.845 3.25E-02 -0.4027E-01 -0.6109 30.00 1.750 4.01E-02 -0.3615E-01 -0.6315 32.50 1.664 4.80E-02 -0.3274E-01 -0.6522 35.00 1.586 5.63E-02 -0.2987E-01 -0.6731 37.50 1.515 6.49E-02 -0.2743E-01 -0.6942 40.00 1.450 7.36E-02 -0.2533E-01 -0.7156 42.50 1.389 8.24E-02 -0.2350E-01 -0.7373 45.00 1.333 9.13E-02 -0.2190E-01 -0.7592 47.50 1.280 0.10 -0.2049E-01 -0.7816 50.00 1.230 0.11 -0.1923E-01 -0.8044 52.50 1.184 0.12 -0.1811E-01 -0.8277 55.00 1.140 0.13 -0.1710E-01 -0.8514 57.50 1.099 0.14 -0.1619E-01 -0.8757 60.00 1.060 0.14 -0.1537E-01 -0.9006. Representative Alphas of Variables FLIM(1), DP1PF10.pti. n 0.58 Do -0.18 cs -0.52 cx 0.60 x 0.04 Sum of a²1.00. Análisis Probabilista. E. Mosquera..
(11) DP1PF10 Rp=2.25, Rd=1.56. 5.48. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. Reliability Index FLIM(1), DP1PF10.pt i. Beta. 5.03 4.59 4.15 3.71 3.27 2.83 2.38 1.94 1.50 1.06 2.50. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. 60.00. Failure Probability FLIM(1), DP1PF10.pt i. Failure Probability 0.14 0.13 0.12 0.10 0.09 0.07 0.06 0.04 0.03 0.01 0.00 2.50. 8.25. 1.08. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. 60.00. Partial Safety Factors FLIM(1), DP1PF10.pti. P.S.F. 1.20 1.14. 14.00. 0.00 1.75 -107374184.00 2.53 -151996493463552.00. n Do cs cx x. 1.02 0.97 0.91 0.85 0.79 0.73 0.67 0.62 2.50. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. Análisis Probabilista. 60.00. E. Mosquera..
(12) dp1D Rd=1.56. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. -----------------------------------------------------------------------------Job name ............ : dp1D Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 29.01.2011 Time(hh:mm) ........ : 23:09 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: 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........ = 3.0000E-03 ( 0.300000000000000E-02) Coefficient of Variation.. = 6.0000E-03 ( 0.600000000000000E-02) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 3.0000E-03 ( 0.300000000000000E-02) ------------------------Variable: Do ; No. on X-vector = 2 Comment : Coef. Difusión inicial Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 8.900 ( 0.890000000000000E+01) Standard deviation........ = 5.3400E-02 ( 0.534000000000000E-01) Coefficient of Variation.. = 6.0000E-03 ( 0.600000000000000E-02) Distr.Param.no.1 : m = 8.900 ( 0.890000000000000E+01) Distr.Param.no.2 : sigma = 5.3400E-02 ( 0.534000000000000E-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........ = 5.5000E-03 ( 0.550000000000000E-02) Coefficient of Variation.. = 5.9783E-03 ( 0.597826086956522E-02) Distr.Param.no.1 : m = 0.9200 ( 0.920000000000000E+00) Distr.Param.no.2 : sigma = 5.5000E-03 ( 0.550000000000000E-02) ------------------------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........ = 3.6000E-03 ( 0.360000000000000E-02) Coefficient of Variation.. = 6.0000E-03 ( 0.600000000000000E-02) Distr.Param.no.1 : m = 0.6000 ( 0.600000000000000E+00) Distr.Param.no.2 : sigma = 3.6000E-03 ( 0.360000000000000E-02) ------------------------Variable: x ; No. on X-vector = 5 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 1.560 ( 0.156000000000000E+01) Standard deviation........ = 9.6000E-03 ( 0.960000000000000E-02) Coefficient of Variation.. = 6.1538E-03 ( 0.615384615384615E-02) Distr.Param.no.1 : m = 1.560 ( 0.156000000000000E+01) Distr.Param.no.2 : sigma = 9.6000E-03 ( 0.960000000000000E-02) -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años -------------------------. 1 with value =. 50.00. Análisis Probabilista. E. Mosquera..
(13) dp1D Rd=1.56. (n (cs (x. ; ; ;. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. (Lower bounds on U-space variables) 1; -36.69 ) (Do ; 2; 3; -36.69 ) (cx ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (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 ; 3; 0.9200 ) (cx ; 5; 1.560 ). ---2; 8.900 4; 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) = 0.1883E-02 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = -0.056 Corresponding approximate prob.of failure = 0.5225 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= -0.7341E-04 and Vector u-* (beta-point) : (n ; 1; 2.5629E-02) (Do ; 2; -7.9107E-03) (cs ; 3; -3.3099E-02) (cx ; 4; 3.3213E-02) (x ; 5; 1.6216E-02) Normalized U-space gradient (alfa-U) with norm = 17.73 : (n ; 1; 0.4542 ) (Do ; 2; -0.1402 ) (cs ; 3; -0.5870 ) (cx ; 4; 0.5889 ) (x ; 5; 0.2876 ) Normalized Representative alfa-values with norm = 1.000 : (n ; 1; 0.4544 ) (Do ; 2; -0.1403 ) (cs ; 3; -0.5869 ) (cx ; 4; 0.5889 ) (x ; 5; 0.2875 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (n ; 1; 0.5001 ) (Do ; 2; 8.900 ) (cs ; 3; 0.9198 ) (cx ; 4; 0.6001 ) (x ; 5; 1.560 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (n ; 1; 2684. ) (Do ; 2; -46.54 ) (cs ; 3; -1892. ) (cx ; 4; 2900. ) (x ; 5; 531.0 ) -----------------------------------------------------------------------------Constant Parameters (PVEC): (t ; 1; 50.00 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 2 Calls of state-function : 14 -----------------------------------------------------------------------------***************************************************** 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 : -717.015 -1711.726 1297.467. 165.187. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = -0.054 Corresponding prob. of failure = 0.52152. ----- Importance Sampling scheme based on SORM results -----. Análisis Probabilista. E. Mosquera..
(14) dp1D Rd=1.56. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= 0.999 C.o.V.= 0.09 (%) Importance sampling: Sample no. 20 E(Sim)= 0.999 C.o.V.= 0.08 (%) Importance sampling: Sample no. 30 E(Sim)= 1.00 C.o.V.= 0.07 (%) Importance sampling: Sample no. 40 E(Sim)= 1.00 C.o.V.= 0.06 (%) Importance sampling: Sample no. 50 E(Sim)= 1.00 C.o.V.= 0.05 (%) Importance sampling: Sample no. 60 E(Sim)= 1.00 C.o.V.= 0.06 (%) Importance sampling: Sample no. 70 E(Sim)= 1.00 C.o.V.= 0.05 (%) Importance sampling: Sample no. 80 E(Sim)= 1.00 C.o.V.= 0.05 (%) Importance sampling: Sample no. 90 E(Sim)= 1.00 C.o.V.= 0.04 (%) Note: FORM-beta was < 0: E(Sim) & C.o.V. above are for complementary event ! -------------------- Results of importance sampling -------------------Corrected reliability index = -0.054 Corresponding prob. of failure = 0.52146 Correction factor by simulation = 1.000 Coefficient of Variation in % = 0.045 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (n : 1) 0.500074 0.500000 1.000 (Do : 2) 8.89960 8.90000 1.000 (cs : 3) 0.919826 0.920000 1.000 (cx : 4) 0.600114 0.600000 1.000 (x : 5) 1.56015 1.56000 1.000 ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 2.500 47.30 0.0 -7.984 -0.4220 5.000 34.07 1.35-254 -3.630 -0.5328 7.500 26.95 3.57-160 -2.262 -0.6295 10.00 22.19 2.38-109 -1.611 -0.7258 12.50 18.67 4.73E-78 -1.236 -0.8274 15.00 15.90 3.26E-57 -0.9943 -0.9380 17.50 13.64 1.26E-42 -0.8269 -1.061 20.00 11.73 4.63E-32 -0.7047 -1.202 22.50 10.09 3.16E-24 -0.6118 -1.365 25.00 8.654 2.53E-18 -0.5391 -1.558 27.50 7.381 7.89E-14 -0.4807 -1.791 30.00 6.241 2.18E-10 -0.4329 -2.081 32.50 5.210 9.44E-08 -0.3931 -2.453 35.00 4.271 9.74E-06 -0.3595 -2.947 37.50 3.409 3.26E-04 -0.3307 -3.640 40.00 2.614 4.48E-03 -0.3059 -4.685 42.50 1.876 3.03E-02 -0.2843 -6.446 45.00 1.190 0.12 -0.2654 -10.05 47.50 0.5478 0.29 -0.2486 -21.62 50.00 -0.5383E-01 0.52 -0.2336 -210.7 52.50 -0.6206 0.73 -0.2202 -18.54 55.00 -1.156 0.88 -0.2082 -9.881 57.50 -1.662 0.95 -0.1973 -6.811 60.00 -2.143 0.98 -0.1873 -5.238. Representative Alphas of Variables FLIM(1), dp1D.pti. n 0.45 Do -0.14 cs -0.59 cx 0.59 x 0.29 Sum of a²1.00. Análisis Probabilista. E. Mosquera..
(15) dp1D Rd=1.56. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. Reliability Index FLIM(1), dp1D.pti. Beta 47.30. 42.36 37.41 32.47 27.52 22.58 17.63 12.69 7.75 2.80 -2.14. 2.50. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. 60.00. 48.50. 54.25. 60.00. Failure Probability FLIM(1), dp1D.pti. Failure Probability 0.98. 0.89 0.79 0.69 0.59 0.49 0.39 0.30 0.20 0.10 0.00. 2.50. 8.25. 14.00. P.S.F. 1.12 0.00 1.75 1.09 -107374184.00 2.53 1.07 -151996493463552.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. Partial Safety Factors FLIM(1), dp1D.pti n Do cs cx x. 1.04 1.01 0.98 0.95 0.92 0.89 0.86 0.83. 2.50. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. 60.00. Análisis Probabilista. E. Mosquera..
(16) dp1D30 Rd=1.56. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. -----------------------------------------------------------------------------Job name ............ : dp1D30 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 29.01.2011 Time(hh:mm) ........ : 23:13 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: 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........ = 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 = 2 Comment : Coef. Difusión inicial Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 8.900 ( 0.890000000000000E+01) Standard deviation........ = 2.690 ( 0.269000000000000E+01) Coefficient of Variation.. = 0.3022 ( 0.302247191011236E+00) Distr.Param.no.1 : m = 8.900 ( 0.890000000000000E+01) Distr.Param.no.2 : sigma = 2.690 ( 0.269000000000000E+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........ = 0.2760 ( 0.276000000000000E+00) Coefficient of Variation.. = 0.3000 ( 0.300000000000000E+00) Distr.Param.no.1 : m = 0.9200 ( 0.920000000000000E+00) Distr.Param.no.2 : sigma = 0.2760 ( 0.276000000000000E+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........ = 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) ------------------------Variable: x ; No. on X-vector = 5 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 1.560 ( 0.156000000000000E+01) Standard deviation........ = 0.4680 ( 0.468000000000000E+00) Coefficient of Variation.. = 0.3000 ( 0.300000000000000E+00) Distr.Param.no.1 : m = 1.560 ( 0.156000000000000E+01) Distr.Param.no.2 : sigma = 0.4680 ( 0.468000000000000E+00) -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años -------------------------. (n. ;. 1 with value =. (Lower bounds on U-space variables) 1; -36.69 ) (Do ; 2;. 50.00. -36.69. ). Análisis Probabilista. E. Mosquera..
(17) dp1D30 Rd=1.56. (cs (x. ; ;. 3; 5;. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. -36.69 -36.69. ) ). (cx. ;. -36.69. ). (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 ; 3; 0.9200 ) (cx ; 5; 1.560 ). 4;. ---2; 8.900 4; 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) = 0.1883E-02 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 0.000 Corresponding approximate prob.of failure = 0.5000 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= -0.1513E-03 and Vector u-* (beta-point) : (n ; 1; 5.1342E-04) (Do ; 2; -1.5965E-04) (cs ; 3; -6.6504E-04) (cx ; 4; 6.6504E-04) (x ; 5; 3.1655E-04) Normalized U-space gradient (alfa-U) with norm = 886.0 : (n ; 1; 0.4549 ) (Do ; 2; -0.1415 ) (cs ; 3; -0.5892 ) (cx ; 4; 0.5892 ) (x ; 5; 0.2805 ) Normalized Representative alfa-values with norm = Infinity : (n ; 1; 0.000 ) (Do ; 2; 0.000 ) (cs ; 3; 0.000 ) (cx ; 4; 0.000 ) (x ; 5; 0.000 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (n ; 1; 0.5001 ) (Do ; 2; 8.900 ) (cs ; 3; 0.9198 ) (cx ; 4; 0.6001 ) (x ; 5; 1.560 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (n ; 1; 2687. ) (Do ; 2; -46.59 ) (cs ; 3; -1892. ) (cx ; 4; 2900. ) (x ; 5; 531.0 ) -----------------------------------------------------------------------------Constant Parameters (PVEC): (t ; 1; 50.00 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 1 Calls of state-function : 7 -----------------------------------------------------------------------------***************************************************** 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 : -3.377 -25.980 35.631. 15.022. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 0.099 Corresponding prob. of failure = 0.46037. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1. Análisis Probabilista. E. Mosquera..
(18) dp1D30 Rd=1.56. Importance Importance Importance Importance Importance Importance Importance Importance Importance. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. sampling: sampling: sampling: sampling: sampling: sampling: sampling: sampling: sampling:. Sample Sample Sample Sample Sample Sample Sample Sample Sample. no. no. no. no. no. no. no. no. no.. 10 20 30 40 50 60 70 80 90. E(Sim)= E(Sim)= E(Sim)= E(Sim)= E(Sim)= E(Sim)= E(Sim)= E(Sim)= E(Sim)=. 1.01 1.00 0.984 0.987 0.990 1.01 1.03 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.=. 2.24 2.36 2.79 2.16 2.11 2.04 2.41 2.24 2.12. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 0.081 Corresponding prob. of failure = 0.46772 Correction factor by simulation = 1.016 Coefficient of Variation in % = 1.950 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (n : 1) 0.493211 0.500000 0.986 (Do : 2) 8.93786 8.90000 1.004 (cs : 3) 0.936180 0.920000 1.018 (cx : 4) 0.589448 0.600000 0.982 (x : 5) 1.54694 1.56000 0.992 ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 2.500 0.9821 0.16 -0.1617 -0.4249 5.000 0.7274 0.23 -0.7319E-01 -0.5350 7.500 0.5914 0.28 -0.4551E-01 -0.6313 10.00 0.5009 0.31 -0.3238E-01 -0.7277 12.50 0.4341 0.33 -0.2482E-01 -0.8290 15.00 0.3817 0.35 -0.1996E-01 -0.9395 17.50 0.3388 0.37 -0.1659E-01 -1.063 20.00 0.3028 0.38 -0.1413E-01 -1.203 22.50 0.2719 0.39 -0.1227E-01 -1.366 25.00 0.2448 0.40 -0.1080E-01 -1.559 27.50 0.2208 0.41 -0.9632E-02 -1.792 30.00 0.1994 0.42 -0.8669E-02 -2.080 32.50 0.1800 0.43 -0.7871E-02 -2.452 35.00 0.1623 0.44 -0.7197E-02 -2.946 37.50 0.1461 0.44 -0.6622E-02 -3.639 40.00 0.1312 0.45 -0.6125E-02 -4.683 42.50 0.1173 0.45 -0.5692E-02 -6.442 45.00 0.1044 0.46 -0.5311E-02 -10.04 47.50 0.9237E-01 0.46 -0.4975E-02 -21.58 50.00 0.1359 0.45 -0.4675E-02 -207.3 52.50 0.1255 0.45 -0.4407E-02 -18.57 55.00 0.1156 0.45 -0.4165E-02 -9.887 57.50 0.1063 0.46 -0.3947E-02 -6.813 60.00 0.9741E-01 0.46 -0.3748E-02 -5.239. Representative Alphas of Variables FLIM(1), dp1D30.pti. n 0.00 Do 0.00 cs 0.00 cx 0.00 x 0.00 Sum of a²0.00. Análisis Probabilista. E. Mosquera..
(19) dp1D30 Rd=1.56. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM I‐ a/c=0.40 – t=50 años. Reliability Index FLIM(1), dp1D30.pti. Beta 0.98. 0.89 0.80 0.72 0.63 0.54 0.45 0.36 0.27 0.18 0.09. 2.50. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. 60.00. Failure Probability FLIM(1), dp1D30.pti. Failure Probability 0.46. 0.43 0.40 0.37 0.34 0.31 0.28 0.25 0.22 0.19 0.16. 2.50. 8.25. 14.00. P.S.F. 1.13 0.00 1.75 1.10 -107374184.00 2.53 1.07 -151996493463552.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. 60.00. Partial Safety Factors FLIM(1), dp1D30.pti n Do cs cx x. 1.04 1.01 0.98 0.95 0.91 0.88 0.85 0.82. 2.50. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. 60.00. Análisis Probabilista. E. Mosquera..
(20) Ambiente IIIa‐CEM I‐Cc=350 kg/m3‐ a/c=0.4‐t=50 años 60 DP1‐Rs=1.6 cm.‐CoV=0.6%. 50. DP1PF10‐Rp=2.25cm.‐CoV=10% dp1‐Rd=1.56 cm.‐CoV=0.6%. Indice de fiabilidad. 40. dp1D30‐Rd=1.56 cm.‐CoV=30% 30 20 10 0 0. 10. 20. 30. 40. 50. 60. ‐10 Tíempo en años. Ambiente IIIa‐CEM I‐Cc=350 kg/m3‐ a/c=0.4‐t=50 años 1,00E+00 9,00E‐01 DP1‐Rs=1.6 cm.‐CoV=0.6%. Probabilidad de fallo. 8,00E‐01. DP1PF10‐Rp=2.25 cm.‐CoV=10%. 7,00E‐01. dp1‐Rd=1.56 cm.‐CoV=0.6%. 6,00E‐01. dp1D30‐Rd=1.56 cm.‐CoV=30%. 5,00E‐01 4,00E‐01 3,00E‐01 2,00E‐01 1,00E‐01 0,00E+00 0. 10. 20. 30 Tíempo en años. 40. 50. 60.
(21) DP2 Rs=1.29, Rd=1.24. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM II/A‐V‐ a/c=0.40 – t=50 años. -----------------------------------------------------------------------------Job name ............ : DP2 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 21.01.2011 Time(hh:mm) ........ : 19:53 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: 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........ = 3.0000E-03 ( 0.300000000000000E-02) Coefficient of Variation.. = 6.0000E-03 ( 0.600000000000000E-02) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 3.0000E-03 ( 0.300000000000000E-02) ------------------------Variable: Do ; No. on X-vector = 2 Comment : Coef. Difusión inicial Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 5.800 ( 0.580000000000000E+01) Standard deviation........ = 3.4800E-02 ( 0.348000000000000E-01) Coefficient of Variation.. = 6.0000E-03 ( 0.600000000000000E-02) Distr.Param.no.1 : m = 5.800 ( 0.580000000000000E+01) Distr.Param.no.2 : sigma = 3.4800E-02 ( 0.348000000000000E-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........ = 5.5000E-03 ( 0.550000000000000E-02) Coefficient of Variation.. = 5.9783E-03 ( 0.597826086956522E-02) Distr.Param.no.1 : m = 0.9200 ( 0.920000000000000E+00) Distr.Param.no.2 : sigma = 5.5000E-03 ( 0.550000000000000E-02) ------------------------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........ = 3.6000E-03 ( 0.360000000000000E-02) Coefficient of Variation.. = 6.0000E-03 ( 0.600000000000000E-02) Distr.Param.no.1 : m = 0.6000 ( 0.600000000000000E+00) Distr.Param.no.2 : sigma = 3.6000E-03 ( 0.360000000000000E-02) ------------------------Variable: x ; No. on X-vector = 5 Comment : recubrimiento en cm. Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 1.290 ( 0.129000000000000E+01) Standard deviation........ = 7.7400E-03 ( 0.774000000000000E-02) Coefficient of Variation.. = 6.0000E-03 ( 0.600000000000000E-02) Distr.Param.no.1 : m = 1.290 ( 0.129000000000000E+01) Distr.Param.no.2 : sigma = 7.7400E-03 ( 0.774000000000000E-02) -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años -------------------------. 1 with value =. 50.00. Análisis Probabilista. E. Mosquera..
(22) DP2 Rs=1.29, Rd=1.24. (n (cs (x. ; ; ;. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM II/A‐V‐ a/c=0.40 – t=50 años. (Lower bounds on U-space variables) 1; -36.69 ) (Do ; 2; 3; -36.69 ) (cx ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (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 ; 3; 0.9200 ) (cx ; 5; 1.290 ). ---2; 5.800 4; 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) = 0.2914E-01 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.078 Corresponding approximate prob.of failure = 0.1406 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.1655E-10 and Vector u-* (beta-point) : (n ; 1; -0.4975 ) (Do ; 2; 0.1534 ) (cs ; 3; 0.6273 ) (cx ; 4; -0.6344 ) (x ; 5; -0.3077 ) Normalized U-space gradient (alfa-U) with norm = 0.9306 : (n ; 1; 0.4616 ) (Do ; 2; -0.1423 ) (cs ; 3; -0.5820 ) (cx ; 4; 0.5886 ) (x ; 5; 0.2855 ) Normalized Representative alfa-values with norm = 1.000 : (n ; 1; 0.4616 ) (Do ; 2; -0.1423 ) (cs ; 3; -0.5820 ) (cx ; 4; 0.5886 ) (x ; 5; 0.2855 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (n ; 1; 0.4985 ) (Do ; 2; 5.805 ) (cs ; 3; 0.9235 ) (cx ; 4; 0.5977 ) (x ; 5; 1.288 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (n ; 1; 143.2 ) (Do ; 2; -3.806 ) (cs ; 3; -98.48 ) (cx ; 4; 152.1 ) (x ; 5; 34.32 ) -----------------------------------------------------------------------------Constant Parameters (PVEC): (t ; 1; 50.00 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 3 Calls of state-function : 19 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -165.172 -1279.299 1688.050. 732.655. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.080 Corresponding prob. of failure = 0.14002. ----- 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)=. 1.00 1.00 1.00 1.00 1.00. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 0.08 0.09 0.11 0.09 0.09. (%) (%) (%) (%) (%). Análisis Probabilista. E. Mosquera..
(23) DP2 Rs=1.29, Rd=1.24. Importance Importance Importance Importance. sampling: sampling: sampling: sampling:. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM II/A‐V‐ a/c=0.40 – t=50 años. Sample Sample Sample Sample. no. no. no. no.. 60 70 80 90. E(Sim)= E(Sim)= E(Sim)= E(Sim)=. 1.00 1.00 1.00 1.00. C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 0.09 0.09 0.09 0.08. (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.080 Corresponding prob. of failure = 0.14016 Correction factor by simulation = 1.001 Coefficient of Variation in % = 0.078 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (n : 1) 0.498504 0.500000 0.997 (Do : 2) 5.80535 5.80000 1.001 (cs : 3) 0.923458 0.920000 1.004 (cx : 4) 0.597711 0.600000 0.996 (x : 5) 1.28761 1.29000 0.998 ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 2.500 5.000 7.500 10.00 12.50 15.00 17.50 20.00 22.50 25.00 27.50 30.00 32.50 35.00 37.50 40.00 42.50 45.00 47.50 50.00 52.50 55.00 57.50 60.00. 49.38 35.87 28.60 23.75 20.16 17.34 15.03 13.09 11.42 9.955 8.659 7.497 6.446 5.488 4.610 3.799 3.048 2.348 1.694 1.080 0.5016 -0.4320E-01 -0.5594 -1.049. 0.0 5.46-282 3.35-180 5.57-125 1.09E-90 1.19E-67 2.30E-51 1.94E-39 1.75E-30 1.22E-23 2.42E-18 3.30E-14 5.77E-11 2.03E-08 2.02E-06 7.25E-05 1.15E-03 9.44E-03 4.52E-02 0.14 0.31 0.52 0.71 0.85. -8.157 -3.705 -2.307 -1.642 -1.260 -1.014 -0.8429 -0.7183 -0.6236 -0.5494 -0.4899 -0.4412 -0.4006 -0.3664 -0.3371 -0.3118 -0.2898 -0.2705 -0.2534 -0.2381 -0.2245 -0.2122 -0.2011 -0.1910. -0.4129 -0.5164 -0.6048 -0.6914 -0.7810 -0.8767 -0.9812 -1.098 -1.229 -1.380 -1.556 -1.766 -2.020 -2.337 -2.743 -3.284 -4.044 -5.188 -7.113 -11.05 -23.58 -259.4 -20.57 -10.89. Representative Alphas of Variables FLIM(1), DP2.pti. n 0.46 Do -0.14 cs -0.58 cx 0.59 x 0.29 Sum of a²1.00. Análisis Probabilista. E. Mosquera..
(24) DP2 Rs=1.29, Rd=1.24. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM II/A‐V‐ a/c=0.40 – t=50 años. Reliability Index FLIM(1), DP2.pti. Beta 49.38 44.34 39.30 34.25 29.21 24.17 19.12 14.08 9.04 3.99 -1.05 2.50. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. 60.00. Failure Probability FLIM(1), DP2.pti. Failure Probability 0.85 0.77 0.68 0.60 0.51 0.43 0.34 0.26 0.17 0.09 0.00 2.50. 8.25. 14.00. 1.07. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. 60.00. Partial Safety Factors FLIM(1), DP2.pti. P.S.F. 1.13 1.10. 19.75. 0.00 1.75 0.00 2.36 -151996493463552.00. n Do cs cx x. 1.04 1.01 0.98 0.95 0.92 0.88 0.85 0.82 2.50. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. Análisis Probabilista. 60.00. E. Mosquera..
(25) DP2PF10 Rp=1.90, Rd=1.24. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM II/A‐V‐ a/c=0.40 – t=50 años. -----------------------------------------------------------------------------Job name ............ : DP2PF10 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 22.01.2011 Time(hh:mm) ........ : 20:22 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: n ; No. on Comment : factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 1. : Normal (2) : Mean & Std.Dev. (0) = 0.5000 ( 0.500000000000000E+00) = 5.0000E-02 ( 0.500000000000000E-01) = 0.1000 ( 0.100000000000000E+00) = 0.5000 ( 0.500000000000000E+00) = 5.0000E-02 ( 0.500000000000000E-01). Variable: Do ; No. on X-vector = 2 Comment : Coef. Difusión inicial Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 5.800 ( 0.580000000000000E+01) Standard deviation........ = 0.5800 ( 0.580000000000000E+00) Coefficient of Variation.. = 0.1000 ( 0.100000000000000E+00) Distr.Param.no.1 : m = 5.800 ( 0.580000000000000E+01) Distr.Param.no.2 : sigma = 0.5800 ( 0.580000000000000E+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........ = 9.2000E-02 ( 0.920000000000000E-01) Coefficient of Variation.. = 0.1000 ( 0.100000000000000E+00) Distr.Param.no.1 : m = 0.9200 ( 0.920000000000000E+00) Distr.Param.no.2 : sigma = 9.2000E-02 ( 0.920000000000000E-01) ------------------------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 Comment : recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma. X-vector = 5 cm. : Normal (2) : Mean & Std.Dev. (0) = 1.900 ( 0.190000000000000E+01) = 0.1900 ( 0.190000000000000E+00) = 0.1000 ( 0.100000000000000E+00) = 1.900 ( 0.190000000000000E+01) = 0.1900 ( 0.190000000000000E+00). Análisis Probabilista. E. Mosquera..
(26) DP2PF10 Rp=1.90, Rd=1.24. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM II/A‐V‐ a/c=0.40 – t=50 años. -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años -------------------------. (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. ) ). (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 ; 3; 0.9200 ) (cx ; 5; 1.900 ). ---2; 5.800 4; 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) = 0.6391 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.275 Corresponding approximate prob.of failure = 0.1012 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.1029E-07 and Vector u-* (beta-point) : (n ; 1; -0.6952 ) (Do ; 2; 0.2101 ) (cs ; 3; 0.6229 ) (cx ; 4; -0.7124 ) (x ; 5; -0.4493 ) Normalized U-space gradient (alfa-U) with norm = 0.8434 : (n ; 1; 0.5454 ) (Do ; 2; -0.1649 ) (cs ; 3; -0.4887 ) (cx ; 4; 0.5589 ) (x ; 5; 0.3525 ) Normalized Representative alfa-values with norm = 1.000 : (n ; 1; 0.5454 ) (Do ; 2; -0.1649 ) (cs ; 3; -0.4887 ) (cx ; 4; 0.5589 ) (x ; 5; 0.3525 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (n ; 1; 0.4652 ) (Do ; 2; 5.922 ) (cs ; 3; 0.9773 ) (cx ; 4; 0.5573 ) (x ; 5; 1.815 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (n ; 1; 9.199 ) (Do ; 2; -0.2397 ) (cs ; 3; -4.479 ) (cx ; 4; 7.856 ) (x ; 5; 1.565 ) -----------------------------------------------------------------------------Constant Parameters (PVEC): (t ; 1; 50.00 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 5 Calls of state-function : 31 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -10.098 -67.687 87.178. 34.959. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.307 Corresponding prob. of failure = 9.56228E-02. Análisis Probabilista. E. Mosquera..
(27) DP2PF10 Rp=1.90, Rd=1.24. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM II/A‐V‐ a/c=0.40 – t=50 años. ----- 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 1.00 0.989 0.991 0.997 1.01 1.02 1.02 1.01. 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.=. 1.46 1.64 2.00 1.55 1.53 1.47 1.72 1.59 1.51. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.299 Corresponding prob. of failure = 9.69505E-02 Correction factor by simulation = 1.014 Coefficient of Variation in % = 1.395 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (n : 1) 0.464363 0.500000 0.929 (Do : 2) 5.92496 5.80000 1.022 (cs : 3) 0.978754 0.920000 1.064 (cx : 4) 0.556175 0.600000 0.927 (x : 5) 1.81247 1.90000 0.954 ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 2.500 4.690 1.37E-06 -0.5230 -0.2791 5.000 3.795 7.38E-05 -0.2534 -0.3344 7.500 3.295 4.93E-04 -0.1620 -0.3699 10.00 2.953 1.57E-03 -0.1171 -0.3982 12.50 2.698 3.49E-03 -0.9077E-01 -0.4227 15.00 2.495 6.29E-03 -0.7359E-01 -0.4451 17.50 2.328 9.95E-03 -0.6157E-01 -0.4661 20.00 2.187 1.44E-02 -0.5272E-01 -0.4861 22.50 2.065 1.95E-02 -0.4596E-01 -0.5054 25.00 1.958 2.51E-02 -0.4064E-01 -0.5242 27.50 1.862 3.13E-02 -0.3636E-01 -0.5427 30.00 1.777 3.78E-02 -0.3283E-01 -0.5609 32.50 1.699 4.47E-02 -0.2989E-01 -0.5791 35.00 1.628 5.18E-02 -0.2740E-01 -0.5971 37.50 1.563 5.91E-02 -0.2527E-01 -0.6151 40.00 1.502 6.65E-02 -0.2342E-01 -0.6331 42.50 1.446 7.40E-02 -0.2180E-01 -0.6512 45.00 1.394 8.16E-02 -0.2038E-01 -0.6694 47.50 1.345 8.93E-02 -0.1913E-01 -0.6877 50.00 1.299 9.70E-02 -0.1800E-01 -0.7062 52.50 1.256 0.10 -0.1700E-01 -0.7249 55.00 1.215 0.11 -0.1609E-01 -0.7438 57.50 1.176 0.12 -0.1526E-01 -0.7630 60.00 1.139 0.13 -0.1452E-01 -0.7824. Representative Alphas of Variables FLIM(1), DP2PF10.pti. n 0.55 Do -0.16 cs -0.49 cx 0.56 x 0.35 Sum of a²1.00. Análisis Probabilista. E. Mosquera..
(28) DP2PF10 Rp=1.90, Rd=1.24. 4.69. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM II/A‐V‐ a/c=0.40 – t=50 años. Reliability Index FLIM(1), DP2PF10.pt i. Beta. 4.33 3.98 3.62 3.27 2.91 2.56 2.20 1.85 1.49 1.14. 2.50. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. 60.00. Failure Probability FLIM(1), DP2PF10.pt i. Failure Probability 0.13 0.11 0.10 0.09 0.08 0.06 0.05 0.04 0.03 0.01 0.00 2.50. 8.25. 1.07. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. 60.00. Partial Safety Factors FLIM(1), DP2PF10.pti. P.S.F. 1.16 1.12. 14.00. 0.00 1.75 0.00 2.36 -151996493463552.00. n Do cs cx x. 1.03 0.98 0.93 0.89 0.84 0.80 0.75 0.71. 2.50. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. Análisis Probabilista. 60.00. E. Mosquera..
(29) Ambiente IIIa-CEM II/A-V-Cc=350 kg/m3- a/c=0.4-t=50 años 60 50. DP2-Rs=1,29 cm.-CoV=0.6%. Indice de fiabilidad. 40. DP2PF10-Rp=1.90cm.-CoV=10%. 30 20 10 0 0. 10. 20. 30. -10. 40. 50. 60. Tíempo en años. Ambiente IIIa-CEM II/A-V-Cc=350 kg/m3- a/c=0.4-t=50 años 6,00E-01. 5,00E-01 Probabilidad de fallo. DP2-Rs=1.29 cm.-CoV=0.6% 4,00E-01 DP2PF10-Rp=1,90 cm.-CoV=10% 3,00E-01. 2,00E-01. 1,00E-01. 0,00E+00 0. 10. 20. 30 Tíempo en años. 40. 50. 60.
(30) DP3 Rs=0.63, Rd=0.62. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM III‐ a/c=0.40 – t=50 años. -----------------------------------------------------------------------------Job name ............ : DP3 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 21.01.2011 Time(hh:mm) ........ : 19:57 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: n ; No. on Comment : factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 1. : Normal (2) : Mean & Std.Dev. (0) = 0.5000 ( 0.500000000000000E+00) = 3.0000E-03 ( 0.300000000000000E-02) = 6.0000E-03 ( 0.600000000000000E-02) = 0.5000 ( 0.500000000000000E+00) = 3.0000E-03 ( 0.300000000000000E-02). Variable: Do ; No. on X-vector = 2 Comment : Coef. Difusión inicial Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 1.400 ( 0.140000000000000E+01) Standard deviation........ = 8.4000E-03 ( 0.840000000000000E-02) Coefficient of Variation.. = 6.0000E-03 ( 0.600000000000000E-02) Distr.Param.no.1 : m = 1.400 ( 0.140000000000000E+01) Distr.Param.no.2 : sigma = 8.4000E-03 ( 0.840000000000000E-02) ------------------------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........ = 5.5000E-03 ( 0.550000000000000E-02) Coefficient of Variation.. = 5.9783E-03 ( 0.597826086956522E-02) Distr.Param.no.1 : m = 0.9200 ( 0.920000000000000E+00) Distr.Param.no.2 : sigma = 5.5000E-03 ( 0.550000000000000E-02) ------------------------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........ = 3.6000E-03 ( 0.360000000000000E-02) Coefficient of Variation.. = 6.0000E-03 ( 0.600000000000000E-02) Distr.Param.no.1 : m = 0.6000 ( 0.600000000000000E+00) Distr.Param.no.2 : sigma = 3.6000E-03 ( 0.360000000000000E-02) ------------------------Variable: x ; No. on Comment : recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma. X-vector = 5 cm. : Normal (2) : Mean & Std.Dev. (0) = 0.6350 ( 0.635000000000000E+00) = 3.8100E-03 ( 0.381000000000000E-02) = 6.0000E-03 ( 0.600000000000000E-02) = 0.6350 ( 0.635000000000000E+00) = 3.8100E-03 ( 0.381000000000000E-02). Análisis Probabilista. E. Mosquera..
(31) DP3 Rs=0.63, Rd=0.62. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM III‐ a/c=0.40 – t=50 años. -------------------------- Constant (deterministic) Parameters -Parameter :t ; No. on PVEC= Comment : tiempo en años -------------------------. (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. ) ). (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 ; 3; 0.9200 ) (cx ; 5; 0.6350 ). ---2; 1.400 4; 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) = 0.1553E-01 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.169 Corresponding approximate prob.of failure = 0.1212 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.2507E-10 and Vector u-* (beta-point) : (n ; 1; -0.5402 ) (Do ; 2; 0.1666 ) (cs ; 3; 0.6799 ) (cx ; 4; -0.6879 ) (x ; 5; -0.3341 ) Normalized U-space gradient (alfa-U) with norm = 0.8582 : (n ; 1; 0.4621 ) (Do ; 2; -0.1425 ) (cs ; 3; -0.5816 ) (cx ; 4; 0.5885 ) (x ; 5; 0.2858 ) Normalized Representative alfa-values with norm = 1.000 : (n ; 1; 0.4621 ) (Do ; 2; -0.1425 ) (cs ; 3; -0.5816 ) (cx ; 4; 0.5885 ) (x ; 5; 0.2858 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (n ; 1; 0.4984 ) (Do ; 2; 1.401 ) (cs ; 3; 0.9237 ) (cx ; 4; 0.5975 ) (x ; 5; 0.6337 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (n ; 1; 132.2 ) (Do ; 2; -14.56 ) (cs ; 3; -90.74 ) (cx ; 4; 140.3 ) (x ; 5; 64.38 ) -----------------------------------------------------------------------------Constant Parameters (PVEC): (t ; 1; 50.00 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 3 Calls of state-function : 19 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -165.129 -1278.082 1686.398. 731.691. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.171 Corresponding prob. of failure = 0.12071. Análisis Probabilista. E. Mosquera..
(32) DP3 Rs=0.63, Rd=0.62. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM III‐ a/c=0.40 – t=50 años. ----- 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)=. 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00. 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.=. 0.08 0.10 0.12 0.09 0.09 0.09 0.10 0.09 0.09. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.171 Corresponding prob. of failure = 0.12083 Correction factor by simulation = 1.001 Coefficient of Variation in % = 0.081 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (n : 1) 0.498376 0.500000 0.997 (Do : 2) 1.40140 1.40000 1.001 (cs : 3) 0.923747 0.920000 1.004 (cx : 4) 0.597518 0.600000 0.996 (x : 5) 0.633724 0.635000 0.998 ---------- Parameter study for Parameter: t ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 2.500 5.000 7.500 10.00 12.50 15.00 17.50 20.00 22.50 25.00 27.50 30.00 32.50 35.00 37.50 40.00 42.50 45.00 47.50 50.00 52.50 55.00 57.50 60.00. 49.52 36.00 28.73 23.87 20.28 17.45 15.14 13.20 11.52 10.06 8.760 7.596 6.544 5.585 4.706 3.894 3.142 2.441 1.786 1.171 0.5921 0.4573E-01 -0.4706 -0.9609. 0.0 5.03-284 9.66-182 3.29-126 1.07E-91 1.69E-68 4.42E-52 4.75E-40 5.22E-31 4.32E-24 9.91E-19 1.54E-14 3.00E-11 1.17E-08 1.27E-06 4.93E-05 8.40E-04 7.32E-03 3.71E-02 0.12 0.28 0.48 0.68 0.83. -8.162 -3.708 -2.309 -1.644 -1.261 -1.015 -0.8439 -0.7191 -0.6243 -0.5501 -0.4905 -0.4417 -0.4011 -0.3668 -0.3375 -0.3122 -0.2902 -0.2708 -0.2537 -0.2385 -0.2248 -0.2125 -0.2014 -0.1912. -0.4120 -0.5150 -0.6028 -0.6887 -0.7774 -0.8721 -0.9753 -1.090 -1.219 -1.368 -1.540 -1.745 -1.993 -2.299 -2.691 -3.209 -3.928 -4.997 -6.755 -10.20 -19.99 -261.3 -24.47 -11.91. Representative Alphas of Variables FLIM(1), DP3.pti. n 0.46 Do -0.14 cs -0.58 cx 0.59 x 0.29 Sum of a²1.00. Análisis Probabilista. E. Mosquera..
(33) DP3 Rs=0.63, Rd=0.62. 49.52. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM III‐ a/c=0.40 – t=50 años. Reliability Index FLIM(1), DP3.pti. Beta. 44.47 39.43 34.38 29.33 24.28 19.23 14.18 9.14 4.09 -0.96 2.50. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. 60.00. Failure Probability FLIM(1), DP3.pti. Failure Probability 0.83 0.75 0.67 0.58 0.50 0.42 0.33 0.25 0.17 0.08 0.00 2.50. 8.25. 14.00. 1.07. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. 60.00. Partial Safety Factors FLIM(1), DP3.pti. P.S.F. 1.13 1.10. 19.75. 0.00 1.75 272008302207532160000000.00 1.92 -151996493463552.00. n Do cs cx x. 1.04 1.01 0.98 0.95 0.91 0.88 0.85 0.82. 2.50. 8.25. 14.00. 19.75. 25.50. 31.25 t. 37.00. 42.75. 48.50. 54.25. Análisis Probabilista. 60.00. E. Mosquera..
(34) DP3PF10 Rp=0.93, Rd=0.62. Ambiente IIIa ‐Cc=350 Kg/m3‐CEM III‐ a/c=0.40 – t=50 años. -----------------------------------------------------------------------------Job name ............ : DP3PF10 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 22.01.2011 Time(hh:mm) ........ : 20:30 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: n ; No. on Comment : factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 1. : Normal (2) : Mean & Std.Dev. (0) = 0.5000 ( 0.500000000000000E+00) = 5.0000E-02 ( 0.500000000000000E-01) = 0.1000 ( 0.100000000000000E+00) = 0.5000 ( 0.500000000000000E+00) = 5.0000E-02 ( 0.500000000000000E-01). Variable: Do ; No. on X-vector = 2 Comment : Coef. Difusión inicial Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 1.400 ( 0.140000000000000E+01) Standard deviation........ = 0.1400 ( 0.140000000000000E+00) Coefficient of Variation.. = 0.1000 ( 0.100000000000000E+00) Distr.Param.no.1 : m = 1.400 ( 0.140000000000000E+01) Distr.Param.no.2 : sigma = 0.1400 ( 0.140000000000000E+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........ = 9.2000E-02 ( 0.920000000000000E-01) Coefficient of Variation.. = 0.1000 ( 0.100000000000000E+00) Distr.Param.no.1 : m = 0.9200 ( 0.920000000000000E+00) Distr.Param.no.2 : sigma = 9.2000E-02 ( 0.920000000000000E-01) ------------------------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 Comment : recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma. X-vector = 5 cm. : Normal (2) : Mean & Std.Dev. (0) = 0.9300 ( 0.930000000000000E+00) = 9.3000E-02 ( 0.930000000000000E-01) = 0.1000 ( 0.100000000000000E+00) = 0.9300 ( 0.930000000000000E+00) = 9.3000E-02 ( 0.930000000000000E-01). Análisis Probabilista. E. Mosquera..
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