Creep and Shrinkage Code Comparison / LARSA, Inc.

LARSA, Inc. develops advanced software for the analysis and design of bridges and structures based on the finite element method.

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Aug 12, 2021

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specimen = ({

//////////////

// MATERIAL //

//////////////

f_cm: 40, // Mean Compressive Strength at 28th day (MPa)

E_cm: 35000, // Elastic Modulus at 28th day (MPa)

cement_hardtype: "N", // Cement Hardening Type (CEB-FIP 90 only; Choices: "SL", "N", "R", "RS")

cement_strengthclass: "32.5N", // Strength Class (fib MC 2010 only)

// Choices: "32.5N", "32.5R", "42.5N", "42.5R", "52.5N", "52.5R"

cement_type: "I", // Cement Type (CEB-FIP 90 Updated Knowledge and Model B3 only)

// Choices: "I", "II", "III"

// (Model BAZANT B4 uses different notation for cement type and for this

// model according to explanation just after the equation 43 (RILEM-B4 document)

// R: Type I, SL: Type II, RS: Type III are assumed to be consistent with the

// other codes.)

//////////////

// GEOMETRY //

//////////////

V_S: 150, // Volume to surface area ratio (mm)

L: 1000, // Specimen Length (mm)

notional_thickness_coef: 1.5, // notional thickness coefficient (CEB-FIP 78 only)

/////////////////

// ENVIRONMENT //

/////////////////

RH: 60, // Relative Humidity (%)

T: 35, // Temperature (C; CEB-FIP90, CEB-FIP2010, EN1992, and IRC2020 only)

Consider_Temperature_Adjusted_Age_of_Concrete: "No", // Options : "Yes" , "No"

// For CEB-FIP90, CEB-FIP2010,

// IRC112 2020 and EN1992/Eurocode 2004

includeHighStressEffect: "No", // Options: "Yes", "No"

// For CEB-FIP90, CEB-FIP2010, and EN1992/Eurocode 2004

//////////////////

// CONSTRUCTION //

//////////////////

t_s: 0, // age when shrinkage starts

t_0: 16, // age of loading

//////////

// LOAD //

//////////

P: -10000000, // Applied axial load (N)

Sigma: -20.833333, // Axial Compressive Stress (MPa) (P/(b*d))

////////////////////////////////////////////////

// ADDITIONAL PARAMETERS FOR MODELS B3 and B4 //

////////////////////////////////////////////////

// Material

c: 350, // Cement content (in kg/m^3) = 13.69 lb/ft^3

a_c: 5, // Aggregate to cement ratio

w_c: 0.5, // Water to cement ratio

w: 175, // Water content (kg/m^3; Model B3 only)

aggregate_type: "Unknown", // Aggregate type of concrete (Model B4 only)

// Choices: Diabase, Quartzite, Limestone, Sandstone, Granite, QuartzDiorite, Unknown

density: 2350, // density of concrete (Model B4 only)

simplifiedDesign: true, // (Model B4 only)

//If designer knows admixture class composition of concrete

admixtureClass_Shrinkage: "", // Admixture Class

admixtureClass_Creep: "",

// Geometry

specimen_geometry: "infinite square prism", // "infinite slab", "infinite cylinder", "infinite square prism", "sphere", "cube"

// Environment

T_cur: 20, // Ambient temperature while curing (Model B4 only)

curing_condition: "normalcuring", // Choices: "normalcuring", "steamcuring", "curedinwater" (Model B3 only)

// Construction

t_c: 16, // age when drying starts (for creep)

UH_R: 4000, // activation energy of hydration where R is the gas constant (Model B4 only)

US_R: 4000, // activation energy of moisture diffusion and of creep where R is the gas constant (Model B4 only)

///////////////////////////////////////////

// ADDITIONAL PARAMETERS FOR AS3600-2009 //

///////////////////////////////////////////

environmentVariable: 0.6, // (k4) Choices: 0.7 for arid, 0.65 for interior, 0.60 for temperate inland

basicCreepCoef: 0, // 3.1.8.2 (phi_cbb) if "basicCreepCoef: 0", default values are used based on Table 3.1.8.2

basicDryingShrinkageStrain: 0.0008, //3.1.7.2

});

CEB_FIP_78_Eps_cc = function(material, t) {

let msg = "";

let dbg = "CEB FIP 78 Creep";

let h = 2*material.V_S;

dbg = Utility_Add(dbg, "h", h);

let h_0 = (h *material.notional_thickness_coef) / 10; // [e.9]

dbg = Utility_Add(dbg, "h_0", h_0);

let K_1 = Math.exp(5.02 / h_0 + Math.log(6.95 * h_0 ** 1.25)); // (D-5.2)

dbg = Utility_Add(dbg, "K_1", K_1);

let K_2 = Math.exp(0.00144 * h_0 - 1.1 / h_0 - Math.log(1.005 * h_0 ** 0.2954)); // (D-5.3)

dbg = Utility_Add(dbg, "K_2", K_2);

let alpha; // Clause e.1.5

if (material.cement_hardtype == "SL" || material.cement_hardtype == "N")

alpha = 1;

else if (material.cement_hardtype == "R")

alpha = 2;

else if (material.cement_hardtype == "RS")

alpha = 3;

let t_adj; // Clause e.1.3.2 & [e.8]

if (material.Consider_Temperature_Adjusted_Age_of_Concrete == "Yes")

t_adj = alpha / 30 * (material.T + 10) * t;

else

t_adj = t * alpha;

dbg = Utility_Add(dbg, "t_adj", t_adj);

let t0_adj; // Clause e.1.3.2 & [e.8]

if (material.Consider_Temperature_Adjusted_Age_of_Concrete == "Yes")

t0_adj = alpha / 30 * (material.T + 10) * material.t_0;

else

t0_adj = material.t_0 * alpha;

dbg = Utility_Add(dbg, "t0_adj", t0_adj);

let Beta_f_t = (t_adj / (t_adj + K_1)) ** K_2; // (D-5.1)

dbg = Utility_Add(dbg, "Beta_f_t", Beta_f_t);

let Beta_f_t0 = (t0_adj / (t0_adj + K_1)) ** K_2; // (D-5.1)

dbg = Utility_Add(dbg, "Beta_f_t0", Beta_f_t0);

let Beta_d = ((t_adj - t0_adj) / (t_adj - t0_adj + 328)) ** (1/4.2); //(D-4)

dbg = Utility_Add(dbg, "Beta_d", Beta_d);

let Beta_a = 0.8 * (1 - (t0_adj / (t0_adj + 47)) ** (1 / 2.45)); // [e.4]

Beta_a = 0.0; // (LARSA 4D assumption)

msg += "Beta_a is taken as 0 (LARSA 4D assumption), ";

dbg = Utility_Add(dbg, "Beta_a", Beta_a);

let Phi_f1 = 4.45 - 0.035 * material.RH; //(D-6)

dbg = Utility_Add(dbg, "Phi_f1", Phi_f1);

let Phi_f2 = Math.exp(4.4 * 0.00001 * h_0 - 0.35 / h_0 - Math.log(h_0 ** 0.1667 / 2.6)); // (D-7)

dbg = Utility_Add(dbg, "Phi_f2", Phi_f2);

let Phi_f = Phi_f1 * Phi_f2; // taken form expalantion of [e.4]

dbg = Utility_Add(dbg, "Phi_f", Phi_f);

let Phi_d = 0.4; //denotes delayed modulus of elasticity, taken form expalantion of [e.4]

dbg = Utility_Add(dbg, "Phi_d", Phi_d);

let Phi_t_t0 = Beta_a + Phi_d * Beta_d + Phi_f * (Beta_f_t - Beta_f_t0); // [e.4]

dbg = Utility_Add(dbg, "Phi_t_t0", Phi_t_t0);

let CEB_FIP_78_Eps_cc = (material.Sigma * Phi_t_t0) / material.E_cm; // [e.1]

let disp = CEB_FIP_78_Eps_cc*material.L;

if (-material.Sigma > 0.4*(material.f_cm-8)) msg += "Applied stress is larger than 0.4f<sub>ck</sub>";

return ({value:disp, message:msg, debug:dbg});

}

CEB_FIP_90_upd_Eps_sh = function(material,t) {

let msg = ""; // holds the warning messages

let Alpha_as; // talen from explanation of eq (3.1-16 b)

if (material.cement_type == "I") Alpha_as = 700;

else if (material.cement_type == "II") Alpha_as = 800;

else if (material.cement_type == "III") Alpha_as = 600;

else return "Undefined Cement Type";

let t_1 = 1;

let f_cm_0 = 10;

let RH_0 = 100;

let h_0 = 100;

let Beta_as = 1-Math.exp(-0.2*(t/t_1)**0.5); // eq(3.1-16 b)

let Eps_caso = -Alpha_as*((material.f_cm/f_cm_0)/(6+material.f_cm/f_cm_0))**2.5 *10**-6; // eq(3.1-16 a)

//Autogeneous shrinkage

let Eps_cas = Eps_caso * Beta_as; // eq(3.1-15 b)

let alpha_ds1; // taken from explanation of eq(3.1-17 d)

if (material.cement_type == "I") alpha_ds1 = 4;

else if (material.cement_type == "II") alpha_ds1 = 3;

else if (material.cement_type == "III") alpha_ds1 = 6;

else return "Undefined Cement Type";

let alpha_ds2; // taken from explanation of eq(3.1-17 d)

if (material.cement_type == "I") alpha_ds2 = 0.11;

else if (material.cement_type == "II") alpha_ds2 = 0.13;

else if (material.cement_type == "III") alpha_ds2 =0.12;

else return "Undefined Cement Type";

let Eps_cdso = (220+110*alpha_ds1)*Math.exp((-alpha_ds2*material.f_cm)/f_cm_0)*0.000001; // eq(3.1-17 a)

let Beta_s1 = ((3.5*f_cm_0)/material.f_cm)** 0.1; // eq(3.1-17 d)

let Beta_RH; // eq(3.1-17 b)

if (material.RH < 99*Beta_s1) Beta_RH = -1.55*(1 -(material.RH/RH_0)**3);

else Beta_RH = 0.25;

let h = 2*material.V_S;

let Beta_ds =((t-material.t_s)/t_1/(350*(h/h_0)**2+(t-material.t_s)/t_1))**0.5; // eq(3.1-17 c)

// Drying shrinkage

let Eps_cds = Eps_cdso * Beta_RH * Beta_ds; // eq(3.1-15 c)

let CEB_FIP_90_upd_Eps_sh = Eps_cas + Eps_cds; // eq(3.1-15 a)

let disp = CEB_FIP_90_upd_Eps_sh*material.L;

return {value:disp, message: msg};

}

CEB_FIP_90_Eps_cc = function(material, t) {

let msg = "";

let dbgOutput = "CEB-FIP 90 Creep:";

let t_0_adj = material.t_0;

dbgOutput = Utility_Add(dbgOutput, "TempAdjTime",t_0_adj);

if (material.Consider_Temperature_Adjusted_Age_of_Concrete == "Yes")

t_0_adj = t_0_adj * Math.exp(13.65-(4000./(273.+material.T))); // eq(2.1-86)

dbgOutput = Utility_Add(dbgOutput, "TempAdjTime",t_0_adj);

let Alpha; // taken from explanation of eq(9-40)

if (material.cement_hardtype =="SL")

Alpha = -1;

else if (material.cement_hardtype == "R" || material.cement_hardtype == "N")

Alpha = 0;

else if (material.cement_hardtype == "RS")

Alpha = 1;

else return ({value:0.0, message:"Undefined Strength Class - Alpha parameter", debug:dbgOutput});

t_0_adj = t_0_adj*((9/(2+t_0_adj**(1.2)))+1)**Alpha; // eq(2.1-72)

dbgOutput = Utility_Add(dbgOutput, "t0",t_0_adj);

let RH_0 =100; // taken from explanation on page 55

let f_cm_0 = 10; // taken from explanation on page 55

let h_0 = 100; // taken from explanation on page 55

let t_1= 1; // taken from explanation on page 55

let h = 2*material.V_S;

let Beta_H; // eq(2.1-71)

if ((150*(1+(1.2*material.RH/RH_0)** 18)*(h/h_0) +250) <= 1500)

Beta_H =150*(1+(1.2*material.RH / RH_0)** 18)*(h/h_0)+250;

else

Beta_H = 1500;

dbgOutput = Utility_Add(dbgOutput, "Beta_H", Beta_H);

let Beta_c =(((t - t_0_adj)/t_1)/(Beta_H + (t-t_0_adj)/t_1))**0.3; // eq(2.1-70)

dbgOutput = Utility_Add(dbgOutput, "Beta_c", Beta_c);

let Beta_t0 = 1 / (0.1+(t_0_adj / t_1)**0.2); //eq (2.1-68)

dbgOutput = Utility_Add(dbgOutput, "Beta_t0", Beta_t0);

let Beta_fcm = 5.3/(material.f_cm/f_cm_0)**0.5; // eq(2.1-67)

dbgOutput = Utility_Add(dbgOutput, "Beta_fcm", Beta_fcm);

let Phi_RH =1 +(1-material.RH/RH_0)/(0.46 *(h/h_0)**(1/3)); // eq(2.1-66)

dbgOutput = Utility_Add(dbgOutput, "Phi_RH", Phi_RH);

let Phi_0 = Phi_RH * Beta_fcm * Beta_t0; // eq(2.1-65)

dbgOutput = Utility_Add(dbgOutput, "Phi_0", Phi_0);

let Phi = Phi_0 * Beta_c; // eq(2.1-64)

dbgOutput = Utility_Add(dbgOutput, "Phi", Phi);

//Effect of High Stress

let Phi_corrected = Phi;

if (material.includeHighStressEffect == "Yes") // if high stress effect is included

{

if (-material.Sigma<=0.4*material.f_cm) Phi_corrected = Phi; // eq(2.1-73b)

else Phi_corrected = Phi*Math.exp(1.5*(-material.Sigma/material.f_cm-0.4)); // eq(2.1-73a)

}

dbgOutput = Utility_Add(dbgOutput, "Phi_corrected", Phi_corrected);

let CEB_FIP_90_Eps_cc = (material.Sigma * Phi_corrected) / material.E_cm; // eq(2.1-61)

let disp = CEB_FIP_90_Eps_cc *material.L;

if (-material.Sigma> 0.6*material.f_cm) msg += "Applied stress is larger than 0.6f<sub>cm</sub>";

return ({value:disp, message:msg, debug:dbgOutput});

}

CEB_FIP_2010_Eps_sh = function(material,t,t_s) {

let msg = ""; // holds the warning messages

let Beta_s1; // eq(9-14)

if ((35 / material.f_cm) ** 0.1 <= 1) Beta_s1 = (35 / material.f_cm) ** 0.1;

else Beta_s1 = 1;

let Beta_RH; // eq(9-14)

if (material.RH < 99 * Beta_s1 && material.RH >= 40 * Beta_s1)

Beta_RH = -1.55 * (1 - (material.RH / 100) ** 3);

else if (material.RH >= 99 * Beta_s1) Beta_RH = 0.25;

else return "Undefined Relative Humidity - Beta_RH parameter";

let h = 2*material.V_S;

let Beta_ds =((t -t_s) /(0.035 * h ** 2 + (t -t_s))) ** 0.5; //eq(9-15)

let Alpha_ds1; // Table(9-2)

if (material.cement_strengthclass == "32.5N") Alpha_ds1 = 3;

else if (material.cement_strengthclass == "32.5R" || material.cement_strengthclass == "42.5N")

Alpha_ds1 = 4;

else if (material.cement_strengthclass == "42.5R" ||material.cement_strengthclass == "52.5N" ||material.cement_strengthclass == "52.5R")

Alpha_ds1 = 6;

else return "Undefined Cement Type - Alpha_ds1 parameter";

let Alpha_ds2; // Table(9-2)

if (material.cement_strengthclass == "32.5N") Alpha_ds2 = 0.013;

else if (material.cement_strengthclass == "32.5R" || material.cement_strengthclass == "42.5N")

Alpha_ds2 = 0.012;

else if (material.cement_strengthclass == "42.5R" ||material.cement_strengthclass == "52.5N" ||material.cement_strengthclass == "52.5R")

Alpha_ds2 = 0.012;

else return "Undefined Cement Type - Alpha_ds2 parameter";

let Eps_cds0 = ((220 + 110 * Alpha_ds1) * Math.exp(-Alpha_ds2 * material.f_cm) )* 0.000001; // eq(9-13)

let Eps_cds = Eps_cds0 * Beta_RH * Beta_ds; //drying shrinkage at time t. eq(9-10 c)

let Alpha_bs; // Table(9-2)

if (material.cement_strengthclass == "32.5N") Alpha_bs = 800;

else if (material.cement_strengthclass == "32.5R" || material.cement_strengthclass == "42.5N")

Alpha_bs = 700;

else if (material.cement_strengthclass == "42.5R" ||material.cement_strengthclass == "52.5N" ||material.cement_strengthclass == "52.5R")

Alpha_bs = 600;

else return "Undefined Cement Type - Alpha_bs parameter";

if (material.cement_hardtype == "SL")

Alpha_ds2 = 0.013;

else if (material.cement_hardtype == "N")

Alpha_ds2 = 0.012;

else

Alpha_ds2 = 0.012;

let Eps_cbs0 = -Alpha_bs * (((material.f_cm / 10 )/ (6 + material.f_cm / 10))**2.5) * 0.000001; // eq(9-11)

let Beta_bs = (1-Math.exp(-0.2*Math.sqrt(t))); // eq(9.12)

let Eps_cbs = Eps_cbs0 * Beta_bs; // basic shrinkage at time t. eq(9-10 b)

let CEB_FIP_2010_Eps_sh = Eps_cbs + Eps_cds; // eq(9-10 a)

let disp = CEB_FIP_2010_Eps_sh*material.L;

return {value: disp, message: msg};

}

IRC_112_2020_Eps_cc = function(material,t){

let msg = ""; // holds the warning messages

let dbgOutput = "IRC_112_2020 Creep"

let f_cm = material.f_cm; // mean compressive strength at age of 28 days !!! fcm=fck+10 in IRC !!!

let h_0 = 2 * material.V_S; // notional thickness, should be in mm

let t_0_adj = material.t_0; // age of loading

if(material.Consider_Temperature_Adjusted_Age_of_Concrete == "Yes") {

t_0_adj = (Math.exp(-(4000/(273+material.T)-13.65)))*t_0_adj; // eq(B.10)

dbgOutput = Utility_Add(dbgOutput, "Temp_Adj_T0",t_0_adj);

}

let a; // taken from explanation of (B.9)

if (material.cement_hardtype == "SL") a = -1;

else if (material.cement_hardtype == "N") a = 0;

else if (material.cement_hardtype == "R" || material.cement_hardtype == "RS") a =1;

else return ({value:0.0, mesage:"Undefined Cement Type - Alpha parameter", debug:dbgOutput});

t_0_adj = t_0_adj*(9/(2+t_0_adj**1.2)+1)**a; // eq(B.9)

if (t_0_adj < 0.5) t_0_adj = 0.5;

dbgOutput = Utility_Add(dbgOutput, "t_0",t_0_adj);

let RH = material.RH; // relative humidity

let sigma = material.sigma; //MPa

let E_cm= 35000; // Elastic Modulus at 28th day (MPa)

dbgOutput = Utility_Add(dbgOutput, "f_cm",f_cm);

dbgOutput = Utility_Add(dbgOutput, "h_0",h_0);

dbgOutput = Utility_Add(dbgOutput, "RH",RH);

let beta_f_cm = 18.78/ (f_cm**(0.5));

dbgOutput = Utility_Add(dbgOutput, "beta_f_cm",beta_f_cm);

let beta_t_0 = 1/(0.1+(t_0_adj**(0.2)));

dbgOutput = Utility_Add(dbgOutput, "beta_t_0",beta_t_0);

let alpha_1 = (43.75/f_cm)**(0.7);

dbgOutput = Utility_Add(dbgOutput, "alpha_1",alpha_1);

let alpha_2 = (43.75/f_cm)**(0.2);

dbgOutput = Utility_Add(dbgOutput, "alpha_2",alpha_2);

let alpha_3 = (43.75/f_cm)**(0.5); // Where 45 in numerator and fcm in denominator has units of MPa

dbgOutput = Utility_Add(dbgOutput, "alpha_3",alpha_3);

let beta_H;

if (f_cm <= 45 && 1.5 * (1 + (0.012*RH)**18) * h_0 + 250 <= 1500) {

beta_H = 1.5 * (1 + (0.012*RH)**18) * h_0 + 250; //<=1500 for f_cm <= 45 MPa

}

else if (f_cm <= 45 && 1.5 * (1 + (0.012*RH)**18) * h_0 + 250 > 1500) beta_H =1500;

else if (f_cm>45 && 1.5 * (1 + (0.012*RH)** 18) * h_0 + 250 * alpha_3<= 1500*alpha_3) {

beta_H = 1.5 * (1 + (0.012*RH)** 18) * h_0 + 250 * alpha_3; //<=1500*alpha_3 for f_cm >= 45 MPa

}

else if (f_cm>45 && 1.5 * (1 + (0.012*RH)** 18) * h_0 + 250 * alpha_3> 1500*alpha_3) beta_H = 1500*alpha_3;

dbgOutput = Utility_Add(dbgOutput, "beta_H",beta_H);

let phi_RH;

if (f_cm <= 45) phi_RH = 1+ ((1-RH/100)/(0.1*(h_0**(1/3))));

else phi_RH = (1+ ((1-RH/100)/(0.1*(h_0**(1/3))))*alpha_1)*alpha_2;

dbgOutput = Utility_Add(dbgOutput, "phi_RH",phi_RH);

let phi_0 = phi_RH*beta_f_cm*beta_t_0;

dbgOutput = Utility_Add(dbgOutput, "phi_0",phi_0);

let beta_c = ((t - material.t_0) / (beta_H + (t - material.t_0)))** 0.3;

dbgOutput = Utility_Add(dbgOutput, "beta_c",beta_c);

let phi = phi_0*beta_c;

dbgOutput = Utility_Add(dbgOutput, "phi",phi);

let IRC_112_2020_Eps_cc = phi* material.Sigma / material.E_cm;

dbgOutput = Utility_Add(dbgOutput, "IRC_112_2020_Eps_cc",IRC_112_2020_Eps_cc);

let disp = IRC_112_2020_Eps_cc * material.L;

dbgOutput = Utility_Add(dbgOutput, "disp",disp);

return ({value:disp, message:msg, debug:dbgOutput});

}

md `# Utility Functions`

_ = require('lodash')

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