3dg-c13-00018 (2)

Electronic documents, once printed, are non-controlled and may become outdated. Refer to the electronic Document in BecRef for the current revision.

Bechtel Confidential© Bechtel Corporation 2004. Contains confidential and/or proprietary information to Bechtel and its affiliate companies which shall not to be used, disclosed or reproduced in any format by any non-Bechtel party without Bechtel’s prior written permission. All rights reserved.3DG-C13-00018, Rev. 000 PAGE 1 OF 22

BECHTEL CORPORATIONENGINEERING

ENGINEERING DESIGN GUIDE FORMAT FOUNDATION DESIGN3DG-C13-00018, Rev. 000, December, 2004Prepared by: S. JanChecked by: S. Malushte / S. WuApproved by: S. Mullen

TABLE OF CONTENTS

Page No.

LIST OF SYMBOLS 3

1.0 PURPOSE 5

2.0 SUMMARY OF DESIGN GUIDELINES 5

2.1 Rigid Mat Criteria 5

2.2 Flexible Mat Finite Element Analysis 6

3.0 FOUNDATION DESIGN PARAMETERS 7

3.1 Concrete Properties 7

3.2 Soil Properties 7

3.3 Rigidity of Mat and Superstructure 8

3.4 Radius of Relative Stiffness 9

4.0 ALTERNATIVE RIGID MAT CRITERIA 10

4.1 Rigid Mat Criteria Per ACI 336.2 10



4.2 Beam on Elastic Foundation Criteria 11

4.3 Radius of Relative Stiffness Criteria 11

5.0 FOUNDATION DESIGN ON RIGID MAT 12

6.0 FOUNDATION DESIGN ON FLEXIBLE MAT 12

6.1 Finite Element Analysis Model 12

6.2 Finite Element Modeling Technique 13

6.2.1 Finite Element Types 13

6.2.2 Element Aspect Ratio 15

6.2.3 Element Mesh Size 16

6.3 Finite Element Analysis Results 17

7.0 COMPUTER PROGRAMS 18

7.1 GT STRUDL Program (CE029) 18

7.2 STAAD.Pro Program (CE242) 18

7.3 FOUNDS Program (CE224) 18

8.0 REFERENCES 19

APPENDIX A: PARAMETRIC STUDIES FOR DETERMINATION OF 20MAT RIGIDITY

APPENDIX B: TABLE FOR RADIUS OF RELATIVE STIFFNESS 22



LIST OF SYMBOLS

Bm mat width

Ec static modulus of elasticity for concrete

Es modulus of elasticity for soil

fc’ 28-day concrete compressive strength (psi)

Gs soil shear modulus

EcIm rigidity of mat per unit width (FL)

EcIc rigidity of columns per unit width (FL)

EcIw rigidity of shear walls per unit width (FL)

EcIF total rigidity of mat foundation per unit width (FL)

Ic individual moment of inertia of column cross section (L4)

Iw individual moment of inertia of shear wall cross section (L4)

Kr relative stiffness ratio of mat to soil

ks modulus of subgrade reaction of foundation (F/L3)

Lm length of mat

Lk radius of relative stiffness of mat foundation

Ma maximum calculated moment

Mxx calculated bending moments at local element x and y-axis, and twisting momentMyyMxy

tm mat thickness



wc unit concrete weight (pcf)

νc Poisson's ratio for concrete

νs Poisson's ratio for soil

γs soil weight density



1.0 PURPOSE

This Design Guide is intended to provide general guidelines for designing and analyzing a mat foundation on soil. A mat may be used when column loads are so large that more than 50 percent of the area is covered by conventional spread footings. The methods of analysis and design of mat foundations may be divided into two categories: rigid and flexible mat. This design guide provides specific criteria for determining whether a mat foundation should be treated as rigid or flexible.

A parametric study was performed to establish a rigid mat criterion. Different industrial guidelines for rigidity criteria are also provided for reference. In general, Bechtel FOUNDS program is used for rigid foundation design. A three dimensional finite element analysis is required for design of flexible mat.

This design guide is intended for mat foundation on soil. However, it may be applied to a pile supported foundation, by substituting the parameter of soil modulus of sugbrade reaction by the average pile stiffness per unit area of the foundation.

2.0 SUMMARY OF DESIGN GUIDELINES

The guidelines for mat foundation design are summarized as follows:

2.1 Rigid Mat Criteria

For practical design application, a mat is considered to be rigid when the maximum differential deflection is less than 15% of the total deflection. Based on this criterion, parametric studies have been performed to determine the rigid mat criteria as discussed in the Appendix A. From the results of the study, it is concluded that a mat can be considered as a rigid mat when

Lm < 2Lk (Eq. 2-1)

Where:

Lm = Length of mat

Lk = Radius of relative stiffness of mat foundation (Ref. 8.5), and is defined as:

Lk = 4

s

Fc

kIE

(Eq. 2-2)



The Ec IF and ks are discussed in Section 3.4.

A rigid mat approach results in a uniform or linearly varying soil bearing pressure distribution across the bottom of footing. For analysis purposes, the mat becomes an inverted and simply loaded two-way slab.

Bechtel FOUNDS is recommended for design of rigid mat foundation.

2.2 Flexible Mat Finite Element Analysis

For a flexible mat, a finite element analysis is required to obtain the design moments and displacements. The finite element modeling parameters are as follows:

a) Element types

Quadrilateral plate element is recommended. Triangular plate element may be used if necessary. The plate element can be used to model mat foundation with considerable thickness of foundation. Solid (brick) element is not recommended due to the complexity of obtaining stress resultants for design.

b) Aspect Ratio

The aspect ratio of the plate element’s longest side to the shortest side should not be greater than four (4). The internal angles of the element should be greater than 15 degrees and less than 150 degrees.

c) Mesh sizes

The maximum mesh size of the finite elements should not be greater than one half length of the relative stiffness radius of mat ( Lk ). The dimension of mesh may be several times smaller than thickness.

Reference 8.3 provides guidelines for finite element modeling of superstructure and foundation.



3.0 FOUNDATION DESIGN PARAMETERS

3.1 Concrete Parameters

The required concrete properties are:

(a) Modulus of elasticity (Ec)

For normal weight concrete, Ec =57,000 'cf (psi) (Eq. 3-1)

(b) Poisson's ratio (νc )

Typically, νc = 0.17

3.2 Soil Properties

Project soil consultant (G&HES Group) shall be consulted for obtaining the project specific soil properties. The following soil properties are required for foundation design:

(a) Soil weight density (γs);

(b) Soil Poisson's ratio (νs);

(c) Modulus of subgrade reaction of foundation (ks):

The modulus of subgrade reaction of foundation is an essential parameter for checking the mat rigidity and performing the finite element analysis. This value should be provided by project soil consultant.

The modulus of subgrade reaction of the foundation is a conceptual relationship between soil pressure (q) and deflection (δ), calculated as follows:

ks = δq (unit: F/L3) (Eq. 3-2)

The ks value is representative of the foundation settlement as a whole and it depends on parameters such as the size/aspect ratio of the foundation, soil type, and foundation embedment.



(d) Static modulus of elasticity of Soil (Es):

The static modulus of elasticity of soil (Es) is a fundamental soil property that is relevant to foundation design and settlement calculations; it should be provided by the project soil consultant.

(e) Allowable soil bearing pressure (qa ):

The allowable soil pressure, provided by project soil consultant, is used for checking the adequacy of foundation design.

The allowable soil bearing pressure is normally proportioned to the least mat dimension (B) and the foundation depth (D) below the grade:

qa = αB+βD (Eq. 3-3)

Where, α and β are coefficients determined by soil test.

3.3 Rigidity of Mat and Superstructure

(a) Mat foundation stiffness

The rigidity of mat depends on concrete properties and the following mat dimensions:

(i) Mat length: Lm

(ii) Mat width: Bm

(iii) Mat thickness: tm

The rigidity of mat per unit width is calculated as:

Ec Im = )-12(1

tE2

3mc

cν (Eq. 3-4)



(b) Superstructure stiffness

Mat supporting structures which, because of their stiffness, will reduce the amount of relative settlement between columns or shear walls. Their flexural stiffness per unit width of mat may be approximated as follows:

(i) Columns:

Ec Ic = m

cic

B)I(E∑ (Eq. 3-5)

Where, ciI = moment of inertia of individual columns.

(ii) Shear walls:

Ec Iw = m

3wwc

B/12)h(E t∑ (Eq. 3-6)

Where tw and hw are thickness and height, respectively, of individual shear walls.

(c) Combined rigidity of mat and superstructure

The total rigidity of the mat foundation per unit width is:

Ec IF = Ec Im + Ec Ic + Ec Iw (Eq. 3-7)

3.4 Radius of Relative Stiffness

The radius of relative stiffness (Ref. 8.5) is determined based on the relative stiffness between the mat foundation and the soil subgrade modulus. It is defined as: (see section 2.1)

Lk = 4

s

Fc

kIE

(Eq. 3-8)



The significance of the radius of relative stiffness becomes apparent when analyzing the effect of a load on a slab. It is found that any load that is more than 3Lk away from a given location has virtually no influence on slab stress at that location. The parameter Lkis often used to determine the degree of mat rigidity. The values of Lk for slabs on grade are tabulated in Table B1 of Appendix B for reference.

The radius of relative stiffness is adopted in this design guide as the basis for developing the rigid mat criteria (Section 2.1).

4.0 ALTERNATIVE RIGID MAT CRITERIA

4.1 Rigid Mat Criteria Per ACI 336.2

The following two criteria are provided by ACI 336.2 for determining whether a mat is rigid:

(a) Relative footing stiffness Criteria

The relative stiffness Kr is used to determine whether the footing should be considered as flexible or rigid.

Kr = 3s

Fc

BEIE

(Eq. 4-1)

A mat foundation is considered to be rigid when Kr > 0.5. When Kr < 0.5, the foundation is considered to be flexible.

(b) Column Spacing Criteria

The column spacing on continuous footings is important in determining the variation in soil pressure distributions. If the average of two adjacent spans in a continuous strip having adjacent loads and column spacing does not vary by more than 20% of the greater value, and if the average spacing is less than 1.75/λ, the footing can be considered rigid and the variation of soil pressure determined on the basis of simple statics. The factor λ is determined as follows:

λ = 4

mc

s

I4Ek

(Eq. 4-2)



4.2 Beam on Elastic Foundation Criteria

Based on the classical solution of a beam on elastic foundation, the parameter λL (where λ is defined section 4.1) may be used to determine if a foundation should be analyzed on the basis of the rigid mat procedure or as a beam on elastic foundation.

Rigid foundation: λL < 4π (Eq. 4-3)

Flexible foundation: λL > π (Eq. 4-4)

Where, L = length of foundation member

4.3 Radius of Relative Stiffness Criteria

The radius of relative stiffness was developed originally for slab design in order to determine the effective external loads that need to be included in the slab design. The approach of using the relative stiffness criteria is adopted in this design guide to determine the maximum foundation sizes that can be defined as rigid foundation.

In ACI 336.2, a footing is considered rigid when the ratio of differential to total settlement is about 0.1. However, the section moment used for practical design is normally an average value of moment over a section width of two times of mat thickness plus column width (or, concentrated load area). Therefore, a mat is considered rigid in this study when the ratio of differential deflection to the total deflection is less than 0.15.

One of parametric studies is presented in Appendix A. The mat foundation used in the study is described as follows:

Mat dimension: Lm = 18ft, Bm = 18ftMat thickness: tm = 1ft, 1.5ft, 2ft, 3ft, 3.5ft, 4ft , 5ft and 6ft.Concrete: Ec = 519200 ksf, νc = 0.17

Soil: ks , the modulus of subgrade reaction of foundation ranged from 7 to 1500kcf.

Load: P = 100 kips at mat center

Finite element results are tabulated in tables A1 and A2 of Appendix A. The analysis results show that all the differential deflections are less than 15% of total deflections when the length of mat Lm is 2 times the relative stiffness radius Lk. Therefore, it is concluded that a mat may be treated as rigid when:

Lm < 2Lk (Eq. 4-5)



5.0 FOUNDATION DESIGN ON RIGID MAT

When a mat foundation is determined to be rigid, Bechtel FOUNDS program can be used for mat foundation design. It is an integrated system of foundation design programs based on a rigid mat theory. The soil bearing pressure is assumed to be linear distribution and in static equilibrium with external applied load, The foundation types currently supported by FOUNDS are the following:

• Spread footing• Foundations for horizontal and vertical vessels• Multiples columns mat• Simple pump block• Centrifugal and reciprocating foundations

Both soil and pile supported foundations are considered by FOUNDS.

6.0 FOUNDATION DESIGN ON FLEXIBLE MAT

When a mat foundation is determined to be flexible, the finite element analysis is used to compute design moments and footing displacements. Some guidelines for the finite element modeling technique are discussed in the following sections.

6.1 Finite Element Foundation Model

A mat foundation is designed to support a superstructure for transferring heavy loads from columns, walls or piers to soil media or piles underneath the foundation in order to avoid excessive settlement and to provide stability. A computer analysis is generally required for design of a mat foundation due to the complexity of loading patterns applied to the foundation, and also to account for the flexibility of the mat foundation.

In the finite element computer modeling of a mat foundation, the foundation is simulated as an assemblage of thin plate/shell elements, and is discretized into a number of quadrilateral or triangular finite plate/shell elements. Loads from superstructure may be applied as concentrated forces at nodes or uniform pressure on elements. For framed concrete structures and shear walls, the effect of column and wall stiffness at the wall-mat junctions may require consideration. Note that the effect of the structural rigidity is automatically accounted for, when a complete three-dimensional finite element model including the superstructure is utilized in the analysis.

For a mat foundation supported on soil, Winkler type springs are used to simulate soil foundation media in order to account for the soil-foundation interaction effect. In a classical application of the Wrinkler method, the value of ks is considered constant across



mat. Soil springs attached at nodes are evaluated based on the modulus of subgrade reaction of foundation times the tributary areas of those nodes. It should be noted that a uniformly loaded mat such as an oil tank base may produce a dishing profile across the slab with a larger deflection at middle. In this case, the values of subgrade reactions at center zone of the mat will be smaller than the values at edge. Section 6.7 of ACI-336.2 provides a method to calculate the location dependent values of ks. However, the geotechnical engineers should be consulted in computing the value of subgrade reaction of the foundation.

Since soil is considered to resist compressive force only, iterations of the finite element analysis may be required to remove vertical soil springs that are under tension (unless “compression-only” nonlinear springs are used to model the soil springs). This should be applied to those load combinations that result in foundation uplifting cases.

In the region of high seismic zone and/or high wind area, the foundation may have significant uplift. In this case, the compression only spring element should be used. GT STRUDL and STAAD programs have the capability of performing the iteration process automatically so that soil reactions are all under compression. It should be pointed out that all loads such as dead load, seismic, and live loads, etc. should be combined as an independent load prior to the non-linear analysis. In other words, the result from a linear combination of a set of non-linear analysis results is invalid. The FORM LOAD command in GT STRUDL, or, the REPEAT LOAD command in STAAD should be used to combine all individual load cases to form an independent load case for analysis.

Note that computer outputs of element stress resultants should reflect the same reference or global coordinate systems, since difficulty may result in reviewing the analysis results or sizing the main reinforcement if stress resultants are defined in different element local coordinate systems. The PLANAR COORDINATE in GT STRUDL can be used to define the common coordinate system for element stress resultant output.

6.2 Finite Element Modeling Techniques

The accuracy of finite element analysis results is highly dependent on the element type, mesh sizes and aspect ratio used in the model. A parametric study has been carried out to investigate the effect of these parameters on the analysis results. The following recommendations are based on the investigation result of this study.

6.2.1 Finite Element Type

As discussed previously, a foundation mat is normally modeled as an assemblage of thin plate elements. The 4-noded (quadrilateral) and 3-noded (triangular) plate elements in STAAD program can be used for modeling. A set of plate elements is available in GT STRUDL finite element library. It is recommended that the quadrilateral SBHQ6 and the triangular SBHT6 elements in the library be used in the modeling. A study was undertaken to validate the use of thin plate elements for modeling a thick mat foundation.



As illustrated below, it was concluded that thin plate finite elements should do an adequate job of representing relatively thick mat foundations.

A square mat foundation with various thickness supported on soil is used to investigate the effect of thickness on analysis results. The parameters of the finite element model are summarized as follows:

Modulus of subgrade reaction of foundation (ks): 300 kcfMat dimension: 48ft x 48ftMat thickness: 4t and 8ftMesh size: 2ft x 2ftLoad: 100kips at mat center

Element types:

GT Strudl thin plate element: SBHQ6

GT Strudl eight node solid (brick) element: IPSL • Two layers for 4ft mat• Four layers for 8ft mat

The analysis results are summarized in the following table:

4ft Mat 8ft Mat

Plate Element(SBHQ6)

2-Layers Solid (brick)Element(IPSL)

Plate Element(SBHQ6)

4-Layers Solid (brick)Element(IPSL)

Max.displacement(inch) 0.0057 0.006 0.0025 0.0026Moments (ft-kip/ft)(4ft average) 27.5 31.3 31.8 37.3Moments (ft-kip/ft)(8ft average) 22.3 23.2 26.7 27.5



The displacements for plate element and solid element models are in very good agreement. The average bending moments across a width of one or two times of mat thickness are also in good agreement. For design purpose, the average bending stresses over the width length of two times of mat thickness is generally used for sizing the reinforcement. Therefore, it is concluded that the thin plate elements can be satisfactorily used for design of the thick mat foundation.

6.2.2 Element Aspect Ratio

In a finite element model, the aspect ratio is defined as the ratio of the longest to the shortest element dimensions.

A parametric study is performed to evaluate a reasonable maximum aspect ratio for finite element modeling of mat foundation. The finite element model used for this study is described as follows:

Modulus of subgrade reaction of foundation (ks): 300 kcf

Mat dimension: 48ft x 48ft

Mat thickness: 1ft

Mesh size: 2ft x 2ft, 2ft x 1ft, 2ft x 0.5ft

Load: 100kips at mat center

Element types: GT Strudl thin plate element: SBHQ6

From the finite element analysis results, the maximum displacements for both models are identical to be 0.0034ft. Therefore, the aspect ratio of four (4) is acceptable for modeling the mat foundation with quadrilateral plate elements. However, the aspect ratio should not be greater than 2 for a triangular element.



6.2.3 Element Mesh Sizes

The accuracy of finite element analysis results is highly depending on the mesh sizes used in modeling.

A parametric study is performed to evaluate a reasonable maximum mesh size that may be used for finite element modeling of mat foundation. The finite element model used for this study is described as follows:

Concrete : Ec = 519200 ksf, νc = 0.17

Soil: ks = 300 kcf, νs = 0.4

Mat dimension: 48ft x 48ft

Mat thickness: 1ft

Mesh size: 1ft x 1ft, 2ft x 2ft, 3ft x 3ft, 4ftx4ft, 6ftx6ft, 8ft x 8ft, 12ftx12ft, 24ft x 24ft

Load: 100kips at mat center

Element types: GT Strudl thin plate element: SBHQ6

The radius of relative stiffness is:

Lk = 4

s

Fc

kIE

= 3.49ft

The analysis results are summarized in the following table:

1’ x 1’ 2’ x 2’ 3’ x 3’ 4’ x 4’ 6’ x 6’ 8’x8’ 12’x 12’ 24’x24’Max. disp.(ft) 0.0034 0.0034 0.0034 0.0033 0.0031 0.0028 0.0019 0.0006

From the above table, the displacements are identical for models with mesh sizes up to 3ft. The displacement starts to decrease for mesh size greater than 4ft. It is noted that the radius of relative stiffness for the one foot mat is 3.49ft. Therefore, it is justified to



conclude that the maximum mesh size should not be greater than the radius of relative stiffness for determining the foundation displacement or bearing pressure.

For determining the design bending moment for sizing the reinforcement, the mesh size should not be greater than one half of the radius of relative stiffness.

6.3 Finite Element Analysis Results

Soil reactions obtained from a finite element foundation analysis is used to calculate the maximum soil contact pressure to ensure that it does not exceed the allowable.

For design purpose, displacements and moment contours should be plotted for checking the settlements and bearing pressures and to find the critical location of stress concentrations. The analysis results of moments and shears for finite plate elements are used to size the foundation reinforcement.

Note that computer outputs of element stress resultants should reflect the same reference or global coordinate systems, since difficulty may arise in reviewing the analysis results or sizing the main reinforcement if stress resultants are defined in different element local coordinate systems. The PLANAR COORDINATE in GT STRUDL can be used to define the common coordinate system for element stress resultant output. The outputs of PLATE/SHELL elements from a finite element analysis include the bending moments Mxx and Myy, twisting moment Mxy, transverse shear Vz, in-plane shear Vxy and axial force Nxx. For design purpose, an average resultant over a section width of two times of element thickness plus column width (or, concentrated load area) may be used. The radius of relative stiffness (Lk) may also be used as the cross section width for stress resultant average. Contour plots of stress resultants may also be used to evaluate the design forces and moments.

In order to account for twisting moment effect, the design moments Mx and My can be conservatively calculated based on the following:

Mx = ABS(Mxx) + ABS(Mxy) (Eq. 6-1)

My = ABS(Myy) + ABS(Mxy) (Eq. 6-2)

The signs of the design moments Mx and My should be the same as those for Mxx and Myy, respectively. It is noted that Mx and Mxy must be the moments in an element under the same load combinations.



7.0 COMPUTER PROGRAMS

GT STRUDL, STAAD.Pro and FOUNDS are Bechtel Standard Computer Programs. They are validated and documented in accordance with various QA code requirements.

7.1 GT STRUDL (CE029)

GT STRUDL is a Bechtel Standard Application Program developed by Georgia Tech Research Corporation. It is a computer-aided structural engineering software system for assisting engineers in the structural analysis and design process. It completely integrates graphical modeling, analysis, design and structural database management into a powerful menu-driven information processing system.

GT STRUDL is validated and certified in full conformance with the applicable provisions of the United States Nuclear Regulatory Commission software quality assurance and quality control regulations. It performs general structural analysis and design, as well as structural database processing, on a very broad range of structural problems.

7.2 STAAD.Pro (CE242)

STAAD.Pro is a Bechtel Standard Application Program developed by Research Engineers International. It is a computer-aided structural engineering software system for assisting engineers in the structural analysis and design process. STAAD.Pro completely integrates graphical modeling, frame and static, dynamic, and nonlinear analysis, finite element analysis, structural frame design, graphical result display, and structural database management into a powerful menu-driven information processing system.

STAAD.Pro is validated and certified in full conformance with the applicable provisions of the United States Nuclear Regulatory Commission software quality assurance and quality control regulations. It performs general structural analysis and design, as well as structural database processing, on a very broad range of structural problems.

7.3 FOUNDS Program (CE224)

FOUNDS is a Bechtel in-house developed Standard computer program. It is an integrated system of foundation design programs. It consists of a set of foundation design programs and a set of programs for drawings. All foundation design modulus are based on the rigid mat assumption. The foundation types supported in FOUNDS include spread footing, multiple column mats, combined footing, dual footings and block foundations. Both soil and pile supported foundation are considered.



8.0 REFERENCES

8.1 ACI 318-05, Building Code Requirements for Reinforced Concrete and Commentary.

8.2 J.E. Boweles, “Foundation Analysis and Design”, fourth Edition, 1988.

8.3 Civil Design Guide 3DG-C01-00008, "Finite Element Modeling of concrete Structures”

8.4 ACI 336.2R-88, "Suggested Analysis and Design Procedures for combined Footing and Mats”.

8.5 B. C. Ringo and R. B. Anderson, “Designing floor slabs on Grade”, 2nd Edition, 1996

8.6 GT STRUDL User Reference Manual, Georgia Institute of Technology, Rev. R, 2002

8.7 STAAD.Pro Technical Reference Manual, Research Engineers International, 2004

8.8 FOUNDS Users / Theoretical manual, Bechtel Corp., 2001



APPENDIX A

PARAMETRIC STUDIES DETERMINATION OF MAT RIGIDITY

A parametric study with finite element analysis has shown that the radius of relative stiffness is the best parameter to classify a mat as a rigid or flexible.

The mat foundation used in this study is described as follows:

Mat dimension: Lm = 18ft, Bm = 18ft

Mat thickness: tm = 1ft, 1.5ft, 2ft, 3ft, 3.5 ft, 4ft and 5ftConcrete : Ec = 519200 ksf, νc = 0.17

Soil: ks = (Range from 7 to 900kcf)

νs = 0.4

Load: P = 100 kips at mat center

The rigidity of mat per unit width is calculated as:

D = )-12(1

tE2

3mc

cν(k-ft) (Eq. A-1)

The finite element analysis results are summarized in following tables:



TABLE A1 (Lm = 18ft, ks =300 kcf)

tm(ft.)

Mat rigidity per unit widthD(k-ft)

Radius of relative stiffnessLk (ft)

Lm/2Lk Min. Disp.(ft)

Max. Disp.(ft)

Ratio of DifferentialTo Total Deflection(%)

Remarks

1 1.0 44500 3.49 2.58 -0.0038 -0.0002 95% Flexible

2 1.5 150400 4.73 1.90 -0.0022 -0.0003 86% Flexible

3 2.0 356000 5.87 1.53 -0.0016 -0.0009 44% Flexible

4 3.0 1168200 7.90 1.14 -0.0012 -0.0010 19% Flexible

5 3.5 1910300 8.93 1.01 -0.0011 -0.0010 13% Rigid

6 4.0 2851500 9.87 0.91 -0.0011 -0.0010 10% Rigid

7 5.0 5569000 11.67 0.77 -0.00106 -0.00097 8% Rigid

TABLE A2 (Lm = 18ft )

tm(ft.)

SubgradeReaction(kcf)

Mat rigidity per unit widthD(k-ft)

Radius of relative stiffnessLk (ft)

Max. Disp.(ft)

Min.. Disp.(ft)

Ratio of DifferentialTo Total Deflection(%)

Lm/2LkRemarks

1 1.0 7 44500 8.93 -0.5878 -0.5100 13% 1.01 Rigid

2 1.5 24 150400 8.90 -0.1716 -0.1480 14% 1.01 Rigid

3 2.0 56 356000 8.93 -0.0734 -0.0638 13% 1.01 Rigid

4 3.0 190 1168200 8.92 -0.0217 -0.0187 14% 1.01 Rigid

5 4.0 450 2851500 8.92 -0.0091 -0.0079 13% 1.01 Rigid

6 5.0 900 5569000 8.87 -0.0046 -0.004 13% 1.01 Rigid

Based on the above tables, the differential deflections are less than 15% when the length of mat Lm is 2 times the relative stiffness radius Lk .

Therefore, the rigid mat criterion is:

Lm < 2Lk (rigid mat) (Eq. A-2)



APPENDICE B

TABLE B1: RADIUS OF RELATIVE STIFFNESS ( Lk , feet )

Ks (kcf) 25 50 75 100 150 200 250 300 350 400 450 500tm (ft)

0.5 3.86 3.25 2.94 2.73 2.47 2.30 2.17 2.08 2.00 1.93 1.88 1.831.0 6.50 5.46 4.94 4.59 4.15 3.86 3.65 3.49 3.36 3.25 3.15 3.071.5 8.81 7.41 6.69 6.23 5.63 5.24 4.95 4.73 4.55 4.40 4.28 4.162.0 10.93 9.19 8.30 7.73 6.98 6.50 6.14 5.87 5.65 5.46 5.31 5.172.5 12.92 10.86 9.82 9.13 8.25 7.68 7.26 6.94 6.68 6.46 6.27 6.113.0 14.81 12.45 11.25 10.47 9.46 8.81 8.33 7.96 7.66 7.41 7.19 7.003.5 16.63 13.98 12.63 11.76 10.62 9.89 9.35 8.93 8.60 8.31 8.07 7.864.0 18.38 15.45 13.96 12.99 11.74 10.93 10.33 9.87 9.50 9.19 8.92 8.694.5 20.07 16.88 15.25 14.19 12.83 11.94 11.29 10.79 10.38 10.04 9.75 9.495.0 21.73 18.27 16.51 15.36 13.88 12.92 12.22 11.67 11.23 10.86 10.55 10.275.5 23.34 19.62 17.73 16.50 14.91 13.88 13.12 12.54 12.06 11.67 11.33 11.036.0 24.91 20.95 18.93 17.61 15.92 14.81 14.01 13.38 12.88 12.45 12.09 11.786.5 26.45 22.24 20.10 18.70 16.90 15.73 14.87 14.21 13.67 13.22 12.84 12.517.0 27.96 23.51 21.25 19.77 17.87 16.63 15.72 15.02 14.46 13.98 13.58 13.227.5 29.45 24.76 22.37 20.82 18.81 17.51 16.56 15.82 15.22 14.72 14.30 13.928.0 30.91 25.99 23.48 21.85 19.75 18.38 17.38 16.61 15.98 15.45 15.01 14.618.5 32.34 27.20 24.58 22.87 20.67 19.23 18.19 17.38 16.72 16.17 15.70 15.299.0 33.76 28.39 25.65 23.87 21.57 20.07 18.99 18.14 17.45 16.88 16.39 15.969.5 35.16 29.56 26.71 24.86 22.46 20.91 19.77 18.89 18.18 17.58 17.07 16.63

10.0 36.54 30.72 27.76 25.84 23.35 21.73 20.55 19.63 18.89 18.27 17.74 17.28

Note: fc’ = 4000psi , Ec = 519200 ksf, νc =0.17,

tm = Mat thickness (ft),

Ks = Foudation modulus of subgrade reaction (kcf)

3dg-c13-00018 (2)

Documents