Respecto de la Variable Difusión ó relación a/c
1º Significación de Variables-Índice de Fiabilidad y Probabilidad de fallo.
Coeficiente de difusión D0=5.8*10
-12m
2/s
Corrected reliability index = 1.315
Corresponding prob. of failure = 9.42847E-02
Coeficiente de difusión D0=6.9*10
-12m
2/s
Corrected reliability index = 1.053
Corresponding prob. of failure = 0.14620
Coeficiente de difusión D0=9*10
-12m
2/s
Corrected reliability index = 0.611
Corresponding prob. of failure = 0.27059
Coeficiente de difusión D0=10.9*10
-12m
2/s
Corrected reliability index = 0.267
Corresponding prob. of failure = 0.39486
Resumen 5º Difusión Ambiente IIIc ‐Cc=350 Kg/m3‐CEM II/AV‐ Recubrimiento=5.5 cm.
2º Índices de Fiabilidad y Probabilidades de fallo
Resumen 5º Difusión Ambiente IIIc ‐Cc=350 Kg/m3‐CEM II/AV‐ Recubrimiento=5.5 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 = 1.101
Corresponding prob. of failure = 0.13541
Coeficiente de Variación 10%
Corrected reliability index = 1.094
Corresponding prob. of failure = 0.13695
Coeficiente de Variación 20%
Corrected reliability index = 1.066
Corresponding prob. of failure = 0.14313
Coeficiente de Variación 30%
Corrected reliability index = 1.024
Corresponding prob. of failure = 0.15303
Resumen 5º Difusión Ambiente IIIc ‐Cc=350 Kg/m3‐CEM II/AV‐ Recubrimiento=5.5 cm.
2º Índices de Fiabilidad y Probabilidades de fallo
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.40
Job name ... : 5º -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... = 5.800 ( 0.580000000000000E+01) Standard deviation... = 1.620 ( 0.162000000000000E+01) Coefficient of Variation.. = 0.2793 ( 0.279310344827586E+00) Distr.Param.no.1 : m = 5.800 ( 0.580000000000000E+01) Distr.Param.no.2 : sigma = 1.620 ( 0.162000000000000E+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... = 3.286 ( 0.328600000000000E+01) Standard deviation... = 0.5900 ( 0.590000000000000E+00) Coefficient of Variation.. = 0.1795 ( 0.179549604382228E+00) Distr.Param.no.1 : m = 3.286 ( 0.328600000000000E+01) Distr.Param.no.2 : sigma = 0.5900 ( 0.590000000000000E+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... = 5.500 ( 0.550000000000000E+01) Standard deviation... = 1.000 ( 0.100000000000000E+01) Coefficient of Variation.. = 0.1818 ( 0.181818181818182E+00) Distr.Param.no.1 : m = 5.500 ( 0.550000000000000E+01) Distr.Param.no.2 : sigma = 1.000 ( 0.100000000000000E+01) ---
-- Constant (deterministic) Parameters --
Parameter :t ; No. on PVEC= 1 with value = 50.00
Comment : tiempo en años ---
(Lower 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 )
--- Default U-start = Origin (U=0) ----
(n ; 1; 0.000 ) (Do ; 2; 0.000 ) (cs ; 3; 0.000 ) (cx ; 4; 0.000 ) (x ; 5; 0.000 )
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.40
(n ; 1; 0.5000 ) (Do ; 2; 5.800 )(cs ; 3; 3.286 ) (cx ; 4; 0.6000 ) (x ; 5; 5.500 )
(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) = 1.747
********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.289
Corresponding approximate prob.of failure = 9.8613E-02
--- Scaled State-Function value at x-*(u-*)= -0.2567E-08
and Vector u-* (beta-point) :
(n ; 1; -0.6820 ) (Do ; 2; 0.5141 ) (cs ; 3; 0.2560 ) (cx ; 4; -0.1514 ) (x ; 5; -0.9191 )
Normalized U-space gradient (alfa-U) with norm = 0.8028 : (n ; 1; 0.5289 ) (Do ; 2; -0.3987 ) (cs ; 3; -0.1985 ) (cx ; 4; 0.1174 ) (x ; 5; 0.7128 )
Normalized Representative alfa-values with norm = 1.000 : (n ; 1; 0.5289 ) (Do ; 2; -0.3987 ) (cs ; 3; -0.1985 ) (cx ; 4; 0.1174 ) (x ; 5; 0.7128 )
--- Solution in Basic- (X-) space (x-*):
(n ; 1; 0.4659 ) (Do ; 2; 6.633 ) (cs ; 3; 3.437 ) (cx ; 4; 0.5909 ) (x ; 5; 4.581 )
Gradient in Basic- (X-) space (scaled by 1/SCAL, see above):
(n ; 1; 8.493 ) (Do ; 2; -0.1976 ) (cs ; 3; -0.2701 ) (cx ; 4; 1.571 ) (x ; 5; 0.5722 )
--- Constant Parameters (PVEC):
(t ; 1; 50.00 )
--- Statistics after beta-point search
Gradient evaluations : 4 Calls of state-function : 25
--- --- Second-Order Improvement : ---
radii of curvature in U-space :
-12.466 -18.333 169.652 15.232
--- Results of Second-Order improvement--- Second-Order reliability index = 1.315
Corresponding prob. of failure = 9.42466E-02
--- Importance Sampling scheme based on SORM results --- Initialize Rand.Numb.Gen. with set no. 1
Importance sampling: Sample no. 10 E(Sim)= 0.988 C.o.V.= 0.88 (%) Importance sampling: Sample no. 20 E(Sim)= 0.988 C.o.V.= 0.64 (%) Importance sampling: Sample no. 30 E(Sim)= 1.00 C.o.V.= 1.27 (%) Importance sampling: Sample no. 40 E(Sim)= 1.00 C.o.V.= 1.03 (%) Importance sampling: Sample no. 50 E(Sim)= 1.00 C.o.V.= 0.95 (%) Importance sampling: Sample no. 60 E(Sim)= 1.00 C.o.V.= 0.89 (%) Importance sampling: Sample no. 70 E(Sim)= 0.999 C.o.V.= 0.80 (%) Importance sampling: Sample no. 80 E(Sim)= 1.00 C.o.V.= 0.74 (%) Importance sampling: Sample no. 90 E(Sim)= 1.00 C.o.V.= 0.67 (%) --- Results of importance sampling --- Corrected reliability index = 1.315
Corresponding prob. of failure = 9.42847E-02 Correction factor by simulation = 1.000 Coefficient of Variation in % = 0.692
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.40
---Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (n : 1) 0.465222 0.500000 0.930 (Do : 2) 6.64939 5.80000 1.146 (cs : 3) 3.44002 3.28600 1.047 (cx : 4) 0.590735 0.600000 0.985 (x : 5) 4.56264 5.50000 0.830 --- Parameter study for Parameter: t ---
Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 4.247 1.08E-05 -0.6771 -0.7997E-01 3.000 3.451 2.79E-04 -0.1898 -0.1657 5.500 3.076 1.05E-03 -0.1213 -0.2179 8.000 2.815 2.44E-03 -0.9079E-01 -0.2594 10.50 2.612 4.50E-03 -0.7293E-01 -0.2948 13.00 2.446 7.22E-03 -0.6104E-01 -0.3264 15.50 2.305 1.06E-02 -0.5249E-01 -0.3553 18.00 2.183 1.45E-02 -0.4603E-01 -0.3824 20.50 2.076 1.90E-02 -0.4097E-01 -0.4080 23.00 1.979 2.39E-02 -0.3688E-01 -0.4326 25.50 1.892 2.92E-02 -0.3352E-01 -0.4563 28.00 1.813 3.49E-02 -0.3071E-01 -0.4795 30.50 1.740 4.10E-02 -0.2832E-01 -0.5023 33.00 1.672 4.72E-02 -0.2626E-01 -0.5248 35.50 1.610 5.37E-02 -0.2447E-01 -0.5470 38.00 1.551 6.04E-02 -0.2290E-01 -0.5692 40.50 1.496 6.73E-02 -0.2151E-01 -0.5913 43.00 1.445 7.43E-02 -0.2027E-01 -0.6134 45.50 1.396 8.14E-02 -0.1917E-01 -0.6357 48.00 1.350 8.85E-02 -0.1817E-01 -0.6581 50.50 1.306 9.57E-02 -0.1726E-01 -0.6807 53.00 1.265 0.10 -0.1644E-01 -0.7035
n
0.53
Do
-0.40
cs
-0.20
cx
0.12
x
0.71
Sum of a² 1.00
Representative Alphas of Variables FLIM(1), 5º -1.pti
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.40
Reliability Index FLIM(1), 5º -1.pti
0.50 5.75 11.00 16.25 21.50 26.75 32.00 37.25 42.50 47.75 53.00 1.26 1.56 1.86 2.16 2.46 2.76 3.05 3.35 3.65 3.95 4.25 Beta t
Failure Probability FLIM(1), 5º -1.pti
0.50 5.75 11.00 16.25 21.50 26.75 32.00 37.25 42.50 47.75 53.00 0.00 0.04 0.08 0.13 0.17 0.21 0.25 0.29 0.34 0.38 0.42 Failure Probability t
Partial Safety Factors FLIM(1), 5º -1.pti
0.50 5.75 11.00 16.25 21.50 26.75 32.00 37.25 42.50 47.75 53.00 0.24 0.34 0.44 0.54 0.64 0.74 0.84 0.94 1.04 1.14 1.24 P.S.F. t n 0.00 Do 1.75 cs 0.00 cx 2.36 x 3265073720837799900.00
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.45
Job name ... : 5º -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... = 6.900 ( 0.690000000000000E+01) Standard deviation... = 1.620 ( 0.162000000000000E+01) Coefficient of Variation.. = 0.2348 ( 0.234782608695652E+00) Distr.Param.no.1 : m = 6.900 ( 0.690000000000000E+01) Distr.Param.no.2 : sigma = 1.620 ( 0.162000000000000E+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... = 3.286 ( 0.328600000000000E+01) Standard deviation... = 0.5900 ( 0.590000000000000E+00) Coefficient of Variation.. = 0.1795 ( 0.179549604382228E+00) Distr.Param.no.1 : m = 3.286 ( 0.328600000000000E+01) Distr.Param.no.2 : sigma = 0.5900 ( 0.590000000000000E+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... = 5.500 ( 0.550000000000000E+01) Standard deviation... = 1.000 ( 0.100000000000000E+01) Coefficient of Variation.. = 0.1818 ( 0.181818181818182E+00) Distr.Param.no.1 : m = 5.500 ( 0.550000000000000E+01) Distr.Param.no.2 : sigma = 1.000 ( 0.100000000000000E+01) ---
-- Constant (deterministic) Parameters --
Parameter :t ; No. on PVEC= 1 with value = 50.00
Comment : tiempo en años ---
(Lower 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 )
--- Default U-start = Origin (U=0) ----
(n ; 1; 0.000 ) (Do ; 2; 0.000 ) (cs ; 3; 0.000 ) (cx ; 4; 0.000 ) (x ; 5; 0.000 )
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.45
(n ; 1; 0.5000 ) (Do ; 2; 6.900 )(cs ; 3; 3.286 ) (cx ; 4; 0.6000 ) (x ; 5; 5.500 )
(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) = 1.407
********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.030
Corresponding approximate prob.of failure = 0.1515
--- Scaled State-Function value at x-*(u-*)= -0.9648E-09
and Vector u-* (beta-point) :
(n ; 1; -0.5658 ) (Do ; 2; 0.3767 ) (cs ; 3; 0.2156 ) (cx ; 4; -0.1263 ) (x ; 5; -0.7327 )
Normalized U-space gradient (alfa-U) with norm = 0.9993 : (n ; 1; 0.5492 ) (Do ; 2; -0.3657 ) (cs ; 3; -0.2093 ) (cx ; 4; 0.1226 ) (x ; 5; 0.7112 )
Normalized Representative alfa-values with norm = 1.000 : (n ; 1; 0.5492 ) (Do ; 2; -0.3657 ) (cs ; 3; -0.2093 ) (cx ; 4; 0.1226 ) (x ; 5; 0.7112 )
--- Solution in Basic- (X-) space (x-*):
(n ; 1; 0.4717 ) (Do ; 2; 7.510 ) (cs ; 3; 3.413 ) (cx ; 4; 0.5924 ) (x ; 5; 4.767 )
Gradient in Basic- (X-) space (scaled by 1/SCAL, see above):
(n ; 1; 10.98 ) (Do ; 2; -0.2256 ) (cs ; 3; -0.3544 ) (cx ; 4; 2.042 ) (x ; 5; 0.7107 )
--- Constant Parameters (PVEC):
(t ; 1; 50.00 )
--- Statistics after beta-point search
Gradient evaluations : 4 Calls of state-function : 25
--- --- Second-Order Improvement : ---
radii of curvature in U-space :
-13.528 -18.815 163.031 15.370
--- Results of Second-Order improvement--- Second-Order reliability index = 1.053
Corresponding prob. of failure = 0.14613
--- Importance Sampling scheme based on SORM results --- Initialize Rand.Numb.Gen. with set no. 1
Importance sampling: Sample no. 10 E(Sim)= 0.990 C.o.V.= 0.74 (%) Importance sampling: Sample no. 20 E(Sim)= 0.990 C.o.V.= 0.54 (%) Importance sampling: Sample no. 30 E(Sim)= 1.00 C.o.V.= 1.06 (%) Importance sampling: Sample no. 40 E(Sim)= 0.999 C.o.V.= 0.88 (%) Importance sampling: Sample no. 50 E(Sim)= 1.00 C.o.V.= 0.82 (%) Importance sampling: Sample no. 60 E(Sim)= 1.00 C.o.V.= 0.75 (%) Importance sampling: Sample no. 70 E(Sim)= 1.00 C.o.V.= 0.69 (%) Importance sampling: Sample no. 80 E(Sim)= 1.00 C.o.V.= 0.63 (%) Importance sampling: Sample no. 90 E(Sim)= 1.00 C.o.V.= 0.57 (%) --- Results of importance sampling --- Corrected reliability index = 1.053
Corresponding prob. of failure = 0.14620 Correction factor by simulation = 1.000 Coefficient of Variation in % = 0.592
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.45
---Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (n : 1) 0.471077 0.500000 0.942 (Do : 2) 7.52389 6.90000 1.090 (cs : 3) 3.41603 3.28600 1.040 (cx : 4) 0.592252 0.600000 0.987 (x : 5) 4.75098 5.50000 0.864 --- Parameter study for Parameter: t ---
Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 4.144 1.71E-05 -0.7276 -0.8807E-01 3.000 3.290 5.01E-04 -0.2025 -0.1854 5.500 2.891 1.92E-03 -0.1287 -0.2459 8.000 2.614 4.47E-03 -0.9584E-01 -0.2947 10.50 2.401 8.18E-03 -0.7667E-01 -0.3371 13.00 2.227 1.30E-02 -0.6395E-01 -0.3756 15.50 2.079 1.88E-02 -0.5484E-01 -0.4115 18.00 1.952 2.55E-02 -0.4797E-01 -0.4457 20.50 1.840 3.29E-02 -0.4260E-01 -0.4787 23.00 1.740 4.10E-02 -0.3829E-01 -0.5110 25.50 1.649 4.96E-02 -0.3475E-01 -0.5428 28.00 1.567 5.86E-02 -0.3178E-01 -0.5744 30.50 1.491 6.80E-02 -0.2927E-01 -0.6060 33.00 1.421 7.76E-02 -0.2711E-01 -0.6378 35.50 1.357 8.74E-02 -0.2524E-01 -0.6700 38.00 1.296 9.74E-02 -0.2360E-01 -0.7026 40.50 1.240 0.11 -0.2215E-01 -0.7358 43.00 1.187 0.12 -0.2086E-01 -0.7697 45.50 1.136 0.13 -0.1971E-01 -0.8044 48.00 1.089 0.14 -0.1867E-01 -0.8400 50.50 1.044 0.15 -0.1773E-01 -0.8767 53.00 1.001 0.16 -0.1688E-01 -0.9146
n
0.55
Do
-0.37
cs
-0.21
cx
0.12
x
0.71
Sum of a² 1.00
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.45
Reliability Index FLIM(1), 5º -2.pti
0.50 5.75 11.00 16.25 21.50 26.75 32.00 37.25 42.50 47.75 53.00 1.00 1.32 1.63 1.94 2.26 2.57 2.89 3.20 3.52 3.83 4.14 Beta t
Failure Probability FLIM(1), 5º -2.pti
0.50 5.75 11.00 16.25 21.50 26.75 32.00 37.25 42.50 47.75 53.00 0.00 0.04 0.08 0.13 0.17 0.21 0.25 0.29 0.34 0.38 0.42 Failure Probability t
Partial Safety Factors FLIM(1), 5º -2.pti
0.50 5.75 11.00 16.25 21.50 26.75 32.00 37.25 42.50 47.75 53.00 0.26 0.35 0.44 0.54 0.63 0.72 0.81 0.90 0.99 1.09 1.18 P.S.F. t n 0.00 Do 1.75 cs -0.00 cx 2.43 x 3265073720837799900.00
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.50
Job name ... : 5º -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... = 9.000 ( 0.900000000000000E+01) Standard deviation... = 1.620 ( 0.162000000000000E+01) Coefficient of Variation.. = 0.1800 ( 0.180000000000000E+00) Distr.Param.no.1 : m = 9.000 ( 0.900000000000000E+01) Distr.Param.no.2 : sigma = 1.620 ( 0.162000000000000E+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... = 3.286 ( 0.328600000000000E+01) Standard deviation... = 0.5900 ( 0.590000000000000E+00) Coefficient of Variation.. = 0.1795 ( 0.179549604382228E+00) Distr.Param.no.1 : m = 3.286 ( 0.328600000000000E+01) Distr.Param.no.2 : sigma = 0.5900 ( 0.590000000000000E+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... = 5.500 ( 0.550000000000000E+01) Standard deviation... = 1.000 ( 0.100000000000000E+01) Coefficient of Variation.. = 0.1818 ( 0.181818181818182E+00) Distr.Param.no.1 : m = 5.500 ( 0.550000000000000E+01) Distr.Param.no.2 : sigma = 1.000 ( 0.100000000000000E+01) ---
-- Constant (deterministic) Parameters --
Parameter :t ; No. on PVEC= 1 with value = 50.00
Comment : tiempo en años ---
(Lower 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 )
--- Default U-start = Origin (U=0) ----
(n ; 1; 0.000 ) (Do ; 2; 0.000 ) (cs ; 3; 0.000 ) (cx ; 4; 0.000 ) (x ; 5; 0.000 )
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.50
(n ; 1; 0.5000 ) (Do ; 2; 9.000 )(cs ; 3; 3.286 ) (cx ; 4; 0.6000 ) (x ; 5; 5.500 )
(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) = 0.8256
********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 0.592
Corresponding approximate prob.of failure = 0.2768
--- Scaled State-Function value at x-*(u-*)= -0.1016E-07
and Vector u-* (beta-point) :
(n ; 1; -0.3437 ) (Do ; 2; 0.1848 ) (cs ; 3; 0.1350 ) (cx ; 4; -7.7598E-02) (x ; 5; -0.4174 )
Normalized U-space gradient (alfa-U) with norm = 1.719 : (n ; 1; 0.5803 ) (Do ; 2; -0.3120 ) (cs ; 3; -0.2279 ) (cx ; 4; 0.1310 ) (x ; 5; 0.7048 )
Normalized Representative alfa-values with norm = 1.000 : (n ; 1; 0.5803 ) (Do ; 2; -0.3120 ) (cs ; 3; -0.2279 ) (cx ; 4; 0.1310 ) (x ; 5; 0.7048 )
--- Solution in Basic- (X-) space (x-*):
(n ; 1; 0.4828 ) (Do ; 2; 9.299 ) (cs ; 3; 3.366 ) (cx ; 4; 0.5953 ) (x ; 5; 5.083 )
Gradient in Basic- (X-) space (scaled by 1/SCAL, see above):
(n ; 1; 19.95 ) (Do ; 2; -0.3310 ) (cs ; 3; -0.6639 ) (cx ; 4; 3.753 ) (x ; 5; 1.211 )
--- Constant Parameters (PVEC):
(t ; 1; 50.00 )
--- Statistics after beta-point search
Gradient evaluations : 3 Calls of state-function : 19
--- *****************************************************
Report of an error by traceback facility (*YERR*) : Error in module :YSOMHO
Warning from 2nd-order improvement:
Absolute value of 1st-order beta(FORMBE) < 1 .
2nd-order improvement by Hohenbichlers formula might be inaccurate because it is based on asymptotic theory ! --- Second-Order Improvement : ---
radii of curvature in U-space :
-13.566 -23.200 153.603 15.703
--- Results of Second-Order improvement--- Second-Order reliability index = 0.612
Corresponding prob. of failure = 0.27026
--- Importance Sampling scheme based on SORM results --- Initialize Rand.Numb.Gen. with set no. 1
Importance sampling: Sample no. 10 E(Sim)= 0.992 C.o.V.= 0.59 (%) Importance sampling: Sample no. 20 E(Sim)= 0.993 C.o.V.= 0.48 (%) Importance sampling: Sample no. 30 E(Sim)= 0.999 C.o.V.= 0.78 (%) Importance sampling: Sample no. 40 E(Sim)= 0.996 C.o.V.= 0.70 (%) Importance sampling: Sample no. 50 E(Sim)= 1.00 C.o.V.= 0.68 (%) Importance sampling: Sample no. 60 E(Sim)= 1.00 C.o.V.= 0.61 (%) Importance sampling: Sample no. 70 E(Sim)= 1.00 C.o.V.= 0.59 (%) Importance sampling: Sample no. 80 E(Sim)= 1.00 C.o.V.= 0.54 (%) Importance sampling: Sample no. 90 E(Sim)= 1.00 C.o.V.= 0.49 (%)
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.50
--- Results of importance sampling --- Corrected reliability index = 0.611
Corresponding prob. of failure = 0.27059 Correction factor by simulation = 1.001 Coefficient of Variation in % = 0.508
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) 0.482242 0.500000 0.964 (Do : 2) 9.30936 9.00000 1.034 (cs : 3) 3.36830 3.28600 1.025 (cx : 4) 0.595188 0.600000 0.992 (x : 5) 5.06863 5.50000 0.922 --- Parameter study for Parameter: t ---
Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 3.964 3.69E-05 -0.8174 -0.1034 3.000 3.008 1.31E-03 -0.2247 -0.2248 5.500 2.568 5.12E-03 -0.1412 -0.3035 8.000 2.266 1.17E-02 -0.1042 -0.3693 10.50 2.035 2.09E-02 -0.8271E-01 -0.4289 13.00 1.847 3.24E-02 -0.6855E-01 -0.4852 15.50 1.690 4.56E-02 -0.5848E-01 -0.5400 18.00 1.554 6.01E-02 -0.5093E-01 -0.5944 20.50 1.435 7.57E-02 -0.4506E-01 -0.6494 23.00 1.329 9.19E-02 -0.4037E-01 -0.7056 25.50 1.234 0.11 -0.3653E-01 -0.7635 28.00 1.147 0.13 -0.3333E-01 -0.8239 30.50 1.068 0.14 -0.3063E-01 -0.8872 33.00 0.9947 0.16 -0.2831E-01 -0.9541 35.50 0.9271 0.18 -0.2631E-01 -1.025 38.00 0.8640 0.19 -0.2456E-01 -1.101 40.50 0.8051 0.21 -0.2302E-01 -1.183 43.00 0.7498 0.23 -0.2165E-01 -1.271 45.50 0.6977 0.24 -0.2042E-01 -1.367 48.00 0.6485 0.26 -0.1933E-01 -1.472 50.50 0.6019 0.27 -0.1834E-01 -1.588 53.00 0.5576 0.29 -0.1744E-01 -1.717
n
0.58
Do
-0.31
cs
-0.23
cx
0.13
x
0.70
Sum of a² 1.00
Representative Alphas of Variables FLIM(1), 5º -3.pti
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.50
Reliability Index FLIM(1), 5º -3.pti
0.50 5.75 11.00 16.25 21.50 26.75 32.00 37.25 42.50 47.75 53.00 0.56 0.90 1.24 1.58 1.92 2.26 2.60 2.94 3.28 3.62 3.96 Beta t
Failure Probability FLIM(1), 5º -3.pti
0.50 5.75 11.00 16.25 21.50 26.75 32.00 37.25 42.50 47.75 53.00 0.00 0.04 0.08 0.13 0.17 0.21 0.25 0.29 0.34 0.38 0.42 Failure Probability t
Partial Safety Factors FLIM(1), 5º -3.pti
0.50 5.75 11.00 16.25 21.50 26.75 32.00 37.25 42.50 47.75 53.00 0.29 0.37 0.46 0.54 0.62 0.70 0.78 0.86 0.95 1.03 1.11 P.S.F. t n 0.00 Do 1.75 cs 0.00 cx 2.53 x 3265073720837799900.00
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II –Rec.=5.5 cm.‐ a/c=0.55
Job name ... : 5º -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... = 10.90 ( 0.109000000000000E+02) Standard deviation... = 1.620 ( 0.162000000000000E+01) Coefficient of Variation.. = 0.1486 ( 0.148623853211009E+00) Distr.Param.no.1 : m = 10.90 ( 0.109000000000000E+02) Distr.Param.no.2 : sigma = 1.620 ( 0.162000000000000E+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... = 3.286 ( 0.328600000000000E+01) Standard deviation... = 0.5900 ( 0.590000000000000E+00) Coefficient of Variation.. = 0.1795 ( 0.179549604382228E+00) Distr.Param.no.1 : m = 3.286 ( 0.328600000000000E+01) Distr.Param.no.2 : sigma = 0.5900 ( 0.590000000000000E+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... = 5.500 ( 0.550000000000000E+01) Standard deviation... = 1.000 ( 0.100000000000000E+01) Coefficient of Variation.. = 0.1818 ( 0.181818181818182E+00) Distr.Param.no.1 : m = 5.500 ( 0.550000000000000E+01) Distr.Param.no.2 : sigma = 1.000 ( 0.100000000000000E+01) ---
-- Constant (deterministic) Parameters --
Parameter :t ; No. on PVEC= 1 with value = 50.00
Comment : tiempo en años ---
(Lower 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 )
--- Default U-start = Origin (U=0) ----
(n ; 1; 0.000 ) (Do ; 2; 0.000 ) (cs ; 3; 0.000 ) (cx ; 4; 0.000 ) (x ; 5; 0.000 )
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II –Rec.=5.5 cm.‐ a/c=0.55
(n ; 1; 0.5000 ) (Do ; 2; 10.90 ) (cs ; 3; 3.286 ) (cx ; 4; 0.6000 ) (x ; 5; 5.500 )
(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) = 0.3558
********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 0.250
Corresponding approximate prob.of failure = 0.4013
--- Scaled State-Function value at x-*(u-*)= -0.1828E-06
and Vector u-* (beta-point) :
(n ; 1; -0.1503 ) (Do ; 2; 6.8246E-02) (cs ; 3; 6.0705E-02) (cx ; 4; -3.4298E-02) (x ; 5; -0.1742 )
Normalized U-space gradient (alfa-U) with norm = 4.032 : (n ; 1; 0.6014 ) (Do ; 2; -0.2731 ) (cs ; 3; -0.2430 ) (cx ; 4; 0.1373 ) (x ; 5; 0.6971 )
Normalized Representative alfa-values with norm = 1.000 : (n ; 1; 0.6014 ) (Do ; 2; -0.2731 ) (cs ; 3; -0.2429 ) (cx ; 4; 0.1372 ) (x ; 5; 0.6971 )
--- Solution in Basic- (X-) space (x-*):
(n ; 1; 0.4925 ) (Do ; 2; 11.01 ) (cs ; 3; 3.322 ) (cx ; 4; 0.5979 ) (x ; 5; 5.326 )
Gradient in Basic- (X-) space (scaled by 1/SCAL, see above):
(n ; 1; 48.50 ) (Do ; 2; -0.6798 ) (cs ; 3; -1.661 ) (cx ; 4; 9.225 ) (x ; 5; 2.811 )
--- Constant Parameters (PVEC):
(t ; 1; 50.00 )
--- Statistics after beta-point search
Gradient evaluations : 3 Calls of state-function : 20
--- *****************************************************
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 :
-12.900 -29.464 147.550 16.038
--- Results of Second-Order improvement--- Second-Order reliability index = 0.268
Corresponding prob. of failure = 0.39423
--- Importance Sampling scheme based on SORM results --- Initialize Rand.Numb.Gen. with set no. 1
Importance sampling: Sample no. 10 E(Sim)= 0.994 C.o.V.= 0.53 (%) Importance sampling: Sample no. 20 E(Sim)= 0.994 C.o.V.= 0.45 (%) Importance sampling: Sample no. 30 E(Sim)= 0.997 C.o.V.= 0.65 (%) Importance sampling: Sample no. 40 E(Sim)= 0.995 C.o.V.= 0.61 (%) Importance sampling: Sample no. 50 E(Sim)= 1.00 C.o.V.= 0.61 (%) Importance sampling: Sample no. 60 E(Sim)= 1.00 C.o.V.= 0.54 (%) Importance sampling: Sample no. 70 E(Sim)= 1.00 C.o.V.= 0.56 (%) Importance sampling: Sample no. 80 E(Sim)= 1.00 C.o.V.= 0.50 (%) Importance sampling: Sample no. 90 E(Sim)= 1.00 C.o.V.= 0.47 (%)
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II –Rec.=5.5 cm.‐ a/c=0.55
--- Results of importance sampling --- Corrected reliability index = 0.267
Corresponding prob. of failure = 0.39486 Correction factor by simulation = 1.002 Coefficient of Variation in % = 0.482
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) 0.491932 0.500000 0.984 (Do : 2) 11.0187 10.9000 1.011 (cs : 3) 3.32446 3.28600 1.012 (cx : 4) 0.597790 0.600000 0.996 (x : 5) 5.31297 5.50000 0.966 --- Parameter study for Parameter: t ---
Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 3.816 6.78E-05 -0.8920 -0.1172 3.000 2.777 2.74E-03 -0.2424 -0.2627 5.500 2.304 1.06E-02 -0.1508 -0.3612 8.000 1.983 2.37E-02 -0.1104 -0.4471 10.50 1.739 4.10E-02 -0.8706E-01 -0.5283 13.00 1.542 6.16E-02 -0.7179E-01 -0.6087 15.50 1.377 8.42E-02 -0.6097E-01 -0.6910 18.00 1.236 0.11 -0.5291E-01 -0.7770 20.50 1.112 0.13 -0.4667E-01 -0.8685 23.00 1.003 0.16 -0.4170E-01 -0.9674 25.50 0.9044 0.18 -0.3765E-01 -1.076 28.00 0.8151 0.21 -0.3428E-01 -1.196 30.50 0.7337 0.23 -0.3144E-01 -1.331 33.00 0.6587 0.26 -0.2902E-01 -1.485 35.50 0.5893 0.28 -0.2693E-01 -1.662 38.00 0.5248 0.30 -0.2510E-01 -1.870 40.50 0.4646 0.32 -0.2350E-01 -2.117 43.00 0.4081 0.34 -0.2207E-01 -2.417 45.50 0.3550 0.36 -0.2080E-01 -2.792 48.00 0.3049 0.38 -0.1967E-01 -3.272 50.50 0.2574 0.40 -0.1864E-01 -3.913 53.00 0.2123 0.42 -0.1771E-01 -4.810
n
0.60
Do
-0.27
cs
-0.24
cx
0.14
x
0.70
Sum of a² 1.00
Representative Alphas of Variables FLIM(1), 5º -4.pti
Coeficiente de Difusión Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II –Rec.=5.5 cm.‐ a/c=0.55
Reliability Index FLIM(1), 5º -4.pti
0.50 5.75 11.00 16.25 21.50 26.75 32.00 37.25 42.50 47.75 53.00 0.21 0.57 0.93 1.29 1.65 2.01 2.37 2.73 3.10 3.46 3.82 Beta t
Failure Probability FLIM(1), 5º -4.pti
0.50 5.75 11.00 16.25 21.50 26.75 32.00 37.25 42.50 47.75 53.00 0.00 0.04 0.08 0.12 0.17 0.21 0.25 0.29 0.33 0.37 0.42 Failure Probability t
Partial Safety Factors FLIM(1), 5º -4.pti
0.50 5.75 11.00 16.25 21.50 26.75 32.00 37.25 42.50 47.75 53.00 0.32 0.39 0.47 0.55 0.62 0.70 0.77 0.85 0.93 1.00 1.08 P.S.F. t n 0.00 Do 1.75 cs -107374184.00 cx 2.59 x 3265073720837799900.00
Coeficiente de Difusión CV=5% Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.45
Job name ... : 5cv-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... = 6.900 ( 0.690000000000000E+01) Standard deviation... = 0.3450 ( 0.345000000000000E+00) Coefficient of Variation.. = 5.0000E-02 ( 0.500000000000000E-01) Distr.Param.no.1 : m = 6.900 ( 0.690000000000000E+01) Distr.Param.no.2 : sigma = 0.3450 ( 0.345000000000000E+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... = 3.286 ( 0.328600000000000E+01) Standard deviation... = 0.5900 ( 0.590000000000000E+00) Coefficient of Variation.. = 0.1795 ( 0.179549604382228E+00) Distr.Param.no.1 : m = 3.286 ( 0.328600000000000E+01) Distr.Param.no.2 : sigma = 0.5900 ( 0.590000000000000E+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... = 5.500 ( 0.550000000000000E+01) Standard deviation... = 1.000 ( 0.100000000000000E+01) Coefficient of Variation.. = 0.1818 ( 0.181818181818182E+00) Distr.Param.no.1 : m = 5.500 ( 0.550000000000000E+01) Distr.Param.no.2 : sigma = 1.000 ( 0.100000000000000E+01) ---
-- Constant (deterministic) Parameters --
Parameter :t ; No. on PVEC= 1 with value = 50.00
Comment : tiempo en años ---
(Lower 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 )
--- Default U-start = Origin (U=0) ----
(n ; 1; 0.000 ) (Do ; 2; 0.000 ) (cs ; 3; 0.000 ) (cx ; 4; 0.000 ) (x ; 5; 0.000 )
Coeficiente de Difusión CV=5% Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.45
(n ; 1; 0.5000 ) (Do ; 2; 6.900 )(cs ; 3; 3.286 ) (cx ; 4; 0.6000 ) (x ; 5; 5.500 )
(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) = 1.407
********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.108
Corresponding approximate prob.of failure = 0.1340
--- Scaled State-Function value at x-*(u-*)= -0.1279E-08
and Vector u-* (beta-point) :
(n ; 1; -0.6417 ) (Do ; 2; 9.8539E-02) (cs ; 3; 0.2421 ) (cx ; 4; -0.1427 ) (x ; 5; -0.8523 )
Normalized U-space gradient (alfa-U) with norm = 0.9236 : (n ; 1; 0.5793 ) (Do ; 2; -8.8967E-02) (cs ; 3; -0.2186 ) (cx ; 4; 0.1289 ) (x ; 5; 0.7695 )
Normalized Representative alfa-values with norm = 1.000 : (n ; 1; 0.5793 ) (Do ; 2; -8.8967E-02) (cs ; 3; -0.2186 ) (cx ; 4; 0.1289 ) (x ; 5; 0.7695 )
--- Solution in Basic- (X-) space (x-*):
(n ; 1; 0.4679 ) (Do ; 2; 6.934 ) (cs ; 3; 3.429 ) (cx ; 4; 0.5914 ) (x ; 5; 4.648 )
Gradient in Basic- (X-) space (scaled by 1/SCAL, see above):
(n ; 1; 10.70 ) (Do ; 2; -0.2382 ) (cs ; 3; -0.3421 ) (cx ; 4; 1.983 ) (x ; 5; 0.7107 )
--- Constant Parameters (PVEC):
(t ; 1; 50.00 )
--- Statistics after beta-point search
Gradient evaluations : 4 Calls of state-function : 25
--- --- Second-Order Improvement : ---
radii of curvature in U-space :
-15.006 -232.070 154.816 15.567
--- Results of Second-Order improvement--- Second-Order reliability index = 1.104
Corresponding prob. of failure = 0.13475
--- Importance Sampling scheme based on SORM results --- Initialize Rand.Numb.Gen. with set no. 1
Importance sampling: Sample no. 10 E(Sim)= 0.995 C.o.V.= 0.87 (%) Importance sampling: Sample no. 20 E(Sim)= 0.991 C.o.V.= 0.87 (%) Importance sampling: Sample no. 30 E(Sim)= 0.987 C.o.V.= 1.17 (%) Importance sampling: Sample no. 40 E(Sim)= 0.985 C.o.V.= 1.11 (%) Importance sampling: Sample no. 50 E(Sim)= 0.999 C.o.V.= 1.14 (%) Importance sampling: Sample no. 60 E(Sim)= 1.01 C.o.V.= 1.02 (%) Importance sampling: Sample no. 70 E(Sim)= 1.01 C.o.V.= 1.16 (%) Importance sampling: Sample no. 80 E(Sim)= 1.01 C.o.V.= 1.04 (%) Importance sampling: Sample no. 90 E(Sim)= 1.01 C.o.V.= 0.98 (%) --- Results of importance sampling --- Corrected reliability index = 1.101
Corresponding prob. of failure = 0.13541 Correction factor by simulation = 1.005 Coefficient of Variation in % = 0.979
Coeficiente de Difusión CV=5% Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.45
---Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (n : 1) 0.468014 0.500000 0.936 (Do : 2) 6.93389 6.90000 1.005 (cs : 3) 3.42839 3.28600 1.043 (cx : 4) 0.591463 0.600000 0.986 (x : 5) 4.65033 5.50000 0.846 --- Parameter study for Parameter: t ---
Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 0.5000 4.182 1.45E-05 -0.6892 -0.8251E-01 3.000 3.370 3.76E-04 -0.1928 -0.1717 5.500 2.984 1.42E-03 -0.1243 -0.2290 8.000 2.713 3.33E-03 -0.9389E-01 -0.2765 10.50 2.501 6.19E-03 -0.7602E-01 -0.3185 13.00 2.326 1.00E-02 -0.6407E-01 -0.3572 15.50 2.177 1.48E-02 -0.5542E-01 -0.3935 18.00 2.046 2.04E-02 -0.4884E-01 -0.4282 20.50 1.930 2.68E-02 -0.4366E-01 -0.4619 23.00 1.827 3.39E-02 -0.3945E-01 -0.4948 25.50 1.732 4.16E-02 -0.3597E-01 -0.5273 28.00 1.646 4.99E-02 -0.3304E-01 -0.5595 30.50 1.567 5.86E-02 -0.3054E-01 -0.5918 33.00 1.493 6.77E-02 -0.2838E-01 -0.6242 35.50 1.425 7.71E-02 -0.2650E-01 -0.6569 38.00 1.361 8.68E-02 -0.2484E-01 -0.6901 40.50 1.301 9.67E-02 -0.2337E-01 -0.7237 43.00 1.244 0.11 -0.2205E-01 -0.7581 45.50 1.191 0.12 -0.2087E-01 -0.7933 48.00 1.140 0.13 -0.1981E-01 -0.8294 50.50 1.092 0.14 -0.1884E-01 -0.8665 53.00 1.046 0.15 -0.1796E-01 -0.9047
n
0.58
Do
-0.09
cs
-0.22
cx
0.13
x
0.77
Sum of a² 1.00
Representative Alphas of Variables FLIM(1), 5cv-1.pti
Coeficiente de Difusión CV=5% Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.45
Reliability Index FLIM(1), 5cv-1.pti
0.50 5.75 11.00 16.25 21.50 26.75 32.00 37.25 42.50 47.75 53.00 1.05 1.36 1.67 1.99 2.30 2.61 2.93 3.24 3.55 3.87 4.18 Beta t
Failure Probability FLIM(1), 5cv-1.pti
0.50 5.75 11.00 16.25 21.50 26.75 32.00 37.25 42.50 47.75 53.00 0.00 0.02 0.03 0.05 0.07 0.09 0.10 0.12 0.14 0.15 0.17 Failure Probability t
Partial Safety Factors FLIM(1), 5cv-1.pti
0.50 5.75 11.00 16.25 21.50 26.75 32.00 37.25 42.50 47.75 53.00 0.24 0.33 0.41 0.49 0.58 0.66 0.74 0.83 0.91 0.99 1.08 P.S.F. t n 0.00 Do 1.75 cs -0.00 cx 2.43 x 3265073720837799900.00
Coeficiente de Difusión CV=10% Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.45
Job name ... : 5cv-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... = 6.900 ( 0.690000000000000E+01) Standard deviation... = 0.6900 ( 0.690000000000000E+00) Coefficient of Variation.. = 0.1000 ( 0.100000000000000E+00) Distr.Param.no.1 : m = 6.900 ( 0.690000000000000E+01) Distr.Param.no.2 : sigma = 0.6900 ( 0.690000000000000E+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... = 3.286 ( 0.328600000000000E+01) Standard deviation... = 0.5900 ( 0.590000000000000E+00) Coefficient of Variation.. = 0.1795 ( 0.179549604382228E+00) Distr.Param.no.1 : m = 3.286 ( 0.328600000000000E+01) Distr.Param.no.2 : sigma = 0.5900 ( 0.590000000000000E+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... = 5.500 ( 0.550000000000000E+01) Standard deviation... = 1.000 ( 0.100000000000000E+01) Coefficient of Variation.. = 0.1818 ( 0.181818181818182E+00) Distr.Param.no.1 : m = 5.500 ( 0.550000000000000E+01) Distr.Param.no.2 : sigma = 1.000 ( 0.100000000000000E+01) ---
-- Constant (deterministic) Parameters --
Parameter :t ; No. on PVEC= 1 with value = 50.00
Comment : tiempo en años ---
(Lower 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 )
--- Default U-start = Origin (U=0) ----
(n ; 1; 0.000 ) (Do ; 2; 0.000 ) (cs ; 3; 0.000 ) (cx ; 4; 0.000 ) (x ; 5; 0.000 )
Coeficiente de Difusión CV=10% Ambiente IIIc‐ Cc=350 Kg/m3‐CEM II/AV –Rec.=5.5 cm.‐ a/c=0.45
(n ; 1; 0.5000 ) (Do ; 2; 6.900 )(cs ; 3; 3.286 ) (cx ; 4; 0.6000 ) (x ; 5; 5.500 )
(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) = 1.407
********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.095
Corresponding approximate prob.of failure = 0.1368
--- Scaled State-Function value at x-*(u-*)= -0.1369E-08
and Vector u-* (beta-point) :
(n ; 1; -0.6287 ) (Do ; 2; 0.1904 ) (cs ; 3; 0.2376 ) (cx ; 4; -0.1399 ) (x ; 5; -0.8313 )
Normalized U-space gradient (alfa-U) with norm = 0.9360 : (n ; 1; 0.5743 ) (Do ; 2; -0.1739 ) (cs ; 3; -0.2170 ) (cx ; 4; 0.1278 ) (x ; 5; 0.7593 )
Normalized Representative alfa-values with norm = 1.000 : (n ; 1; 0.5743 ) (Do ; 2; -0.1739 ) (cs ; 3; -0.2170 ) (cx ; 4; 0.1278 ) (x ; 5; 0.7593 )
--- Solution in Basic- (X-) space (x-*):
(n ; 1; 0.4686 ) (Do ; 2; 7.031 ) (cs ; 3; 3.426 ) (cx ; 4; 0.5916 ) (x ; 5; 4.669 )
Gradient in Basic- (X-) space (scaled by 1/SCAL, see above):
(n ; 1; 10.75 ) (Do ; 2; -0.2359 ) (cs ; 3; -0.3442 ) (cx ; 4; 1.994 ) (x ; 5; 0.7107 )
--- Constant Parameters (PVEC):
(t ; 1; 50.00 )
--- Statistics after beta-point search
Gradient evaluations : 4 Calls of state-function : 25
--- --- Second-Order Improvement : ---
radii of curvature in U-space :
-15.010 -63.700 156.125 15.341
--- Results of Second-Order improvement--- Second-Order reliability index = 1.097
Corresponding prob. of failure = 0.13641
--- Importance Sampling scheme based on SORM results --- Initialize Rand.Numb.Gen. with set no. 1
Importance sampling: Sample no. 10 E(Sim)= 0.993 C.o.V.= 0.80 (%) Importance sampling: Sample no. 20 E(Sim)= 0.990 C.o.V.= 0.77 (%) Importance sampling: Sample no. 30 E(Sim)= 0.991 C.o.V.= 1.07 (%) Importance sampling: Sample no. 40 E(Sim)= 0.989 C.o.V.= 1.00 (%) Importance sampling: Sample no. 50 E(Sim)= 1.00 C.o.V.= 1.04 (%) Importance sampling: Sample no. 60 E(Sim)= 1.01 C.o.V.= 0.93 (%) Importance sampling: Sample no. 70 E(Sim)= 1.01 C.o.V.= 0.99 (%) Importance sampling: Sample no. 80 E(Sim)= 1.01 C.o.V.= 0.89 (%) Importance sampling: Sample no. 90 E(Sim)= 1.01 C.o.V.= 0.83 (%) --- Results of importance sampling --- Corrected reliability index = 1.094