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DISCLAIMER

This report was prepared as an account of work sponsored by anagency of the United States Government. Neither the United StatesGovernment nor any agency Thereof, nor any of their employees,makes any warranty, express or implied, or assumes any legalliability or responsibility for the accuracy, completeness, orusefulness of any information, apparatus, product, or processdisclosed, or represents that its use would not infringe privatelyowned rights. Reference herein to any specific commercial product,process, or service by trade name, trademark, manufacturer, orotherwise does not necessarily constitute or imply its endorsement,recommendation, or favoring by the United States Government or anyagency thereof. The views and opinions of authors expressed hereindo not necessarily state or reflect those of the United StatesGovernment or any agency thereof.

DISCLAIMER

Portions of this document may be illegible inelectronic image products. Images are producedfrom the best available original document.

ARH-R-172

ANALYSIS OF UNDERGROUND

WASTE STORAGE TANKS 241-SY

AT HANFORD, WASHINGTON

prepared for

Atlantic Richfield Hanford Company

Richland, Washington

October 1974

NOTICE I1 This report was prepared as an account of work2 sponsored by the United States Government, Neither

the United States nor the United States Atomic EnergyCommission, nor any of their employees, nor any oftheir contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes anylegal liability or responsibility for the accuracy, com-pleteness or usefulness of any information, apparatus,product or process disclosed, or represents that its usewould not infringe privately owned rights.

by

URS/John A. Blume & Associates, Engineers

Sheraton-Palace Hotel

130 Jessie Street

San Francisco, California

MASTER12' Lgw,»«, :1.1 » t 441 11 111,2 Mena:'EVV FYUMITES

ARH-R-172

CONTENTS

22211. INTRODUCTION ......................... ............................ 1

1.1 Purpose ..................................................... 1

1.2 Description of Tanks ........................................ 11.3 Scope of Investigation ........... ........................... 21.4 Safe Shutdown Earthquake (SSE) ..... ......................... 3

2. SOIL PROPERTIES .................. ................................ 5

3. COMPUTATION OF BASE MOTION (DECONVOLUTION) ....................... 6

4. ANALYSIS APPROACH .................... ............................ 8

4.1 General Assumptions ......................................... 84.2 Finite Element Models ......................... .............. 94.3 Load Conditions for Analyses ................................ 11

4.3.1 Gravity Loads .......... .............................. 124.3.2 Hydromechanical Loads ................................ 124.3.3 Thermal Loads ........................................ 144.3.4 Earthquake Ground Motion ............................. 15

4.4 Computer Programs ......................... .... 154.5 Load Combinations and Computation of Stresses ............... 17

5. RESULTS OF ANALYSIS .............................................. 20

5.1 Primary Steel Tank .......................................... 205.2 Concrete Tank ............................................... 22

6. SUMMARY AND CONCLUSIONS ......... ............ ........... 26

7. REFERENCES ....................................................... 27

APPENDIX A: THERMAL-CREEP ANALYSIS OF 241-SY UNDERGROUNDREINFORCED CONCRETE TANK STRUCTURE AT HANFORD,WASHINGTON, by Y. R. Rashid ................... . 56

INVESTIGATION TO DETERMINE DYNAMIC SOIL PROPERTIES AT THE241-SY TANK SITE .............................. following Appendix A

TABLES

1. Soil Properties Based on Geophysical Data ... . . 29

2. Soil Properties Used in Deconvolution ....... . 30

3. Soil-Tank Model Properties .................. 31

- ii - U[ le/IMBS&DWAIN

CONTENTS (continued)

23214. Hydrostatic and Hydrodynamic Pressures ...... ...................... 32

5. Longitudinal Internal Forces in Primary Tank .................. .... 33

6. Circumferential Internal Forces in Primary Tank ................... 34

7. Internal Forces in Concrete Tank Due to Earthquake ................ 35

FIGURES

1. Site Plan ........................................................ 36

2. Section A-A ...................................................... 37

3. Half Vertical Section Through Tank .... ........................... 38

4. Comparison of SSE and Synthetic Time-History Spectra ............. 39

5. Free-Field Surface Motion, Design Basis Earthquake ............... 40

6. Comparison of Response Spectra of Original and RecomputedSurface Motion ................................................. 41

7. Acceleration Time-History of Computed Base Motion ................ 42

8. Axisymmetric Finite Elements ..... 43

9. Soil-Tank Finite Element Model ................................... 44

10a. Detail Near Tank of Soil-Tank Finite Element Model ............... 45

1 Ob. Detail Near Tank of Soil-Tank Finite Element Model ............... 46

11. Assumed Soil Layering in Soil-Tank Finite Element Model .......... 47

12. Primary Steel Tank Model .......................... ............... 48

13· Axisymmetric Shell Elements, Forces and Moments .................. 49

14. Radial Displacements of Primary Steel Tank ........... ............ 50

15· Longitudinal Moments and Forces on Primary Steel Tank ....... "··· 51

16. Circumferential M6ments and Forces on Primary Steel Tank.......... 52

17· Earthquake Longitudinal Moments and Forces on Concrete Tank ...... 53

18. Earthquake Circumferential Moments and Forces on Concrete Tank ... 54

19. Gravity Load Moments and Forces on Base Slab ............. ........ 55

- iii -UNl#3/IMBO=QOMME

1. INTRODUCTION

1.1 Purpose

High level radioactive wastes are generated by the chemical separations

plant at Hanford, Washington. These wastes are stored for long periods in

large underground tanks on the Hanford Project in accordance with the Waste

Management Program being carried out by the Atlantic Richfield Hanford Com-

pany (ARHCO). The 241-SY tank farm is being built to expand the waste stor-

age capacity at Hanford. The 241-SY tanks have to be designed to withstand

all credible load conditions during their use and maintain integrity such

that no leakage to the surrounding soil occurs. URS/John A. Blume & Associ-

ates, Engineers conducted a Phase I review of the tanks and presented the

results of this review in a report (ARHCO Waste Storage Tanks, 241-SY Tank

Farm, Phase I Review) dated February 26, 1974. The report presented a qual-

itative analysis of the tank structure, reviewed the applicability of the

seismic analysis of 241-AZ tanks that are identical to the 241-SY tanks, and

recommended a detailed (Phase II) analysis required for the 241-SY tanks.

URS/Blume was then contracted by ARHCO to make a detailed engineering an-

alysis study as recommended in the Phase I review report, of the proposed

241-SY tank structure for long-term dead, live, and thermal loads plus the

Safe Shutdown Earthquake (SSE) ground motions. The purpose of this report

is to describe and present the results of this study.

1.2 Description of Tanks

The proposed 241-SY tank farm consists of three cylindrical, dome-roofed tanks

(tanks 101, 102, and 103) and is located in the 200 West Area near the 242-S

Evaporator Crystallizer building. The three tanks are eksentially identical

to each other and to the 241-AZ tanksl in the 200 East Area, located approxi-

mately 5 miles east of the 200 West Area. Figures 1 and 2 show the layout of

the tanks and a vertical section through the tanks and the surrounding soil.

Each tank is 56 feet high overall with a minimum height of overburden of

6-1/2 feet above its dome. The outside diameter of each tank is approximately

83 feet and there is a minimum of a 24-foot clear separation between the walls

of adjacent tanks.

-1- 06 [* 9#/IMB L[!=0 [R:A] IN

A half vertical cross section of one of the tanks is shown in Figure 3. The

tank provides dual containment for the liquid waste. The primary contain-

ment is provided by a primary steel tank with plate thickness varying from

3/8 inch in the dome region to 7/8 inch in the base knuckle region. The

secondary containment is provided by a reinforced concrete tank with a steel

plate liner on the inside face. The concrete tank wall is 18 inches thick,

and the thickness of the base slab is generally 11-1/2 inches with a increase

to 24 inches in the circumferential and central areas. The secondary steel

liner is 3/8-inch thick. The concrete cylindrical wall-to-base slab connec-

tion is of the sliding type with a curb on the exterior side of the base slab

limiting the motion of the tank wall. The concrete dome is an ellipsoid, hav-

ing a major diameter of 80 feet and a minor diameter of 30 feet on the inside

face. The thickness of the concrete dome varies from approximately 30 inches

near the wall to 15 inches at the crown. There are several penetrations in

the dome roof of the tank, ranging in diameter from 4 inches to 42 inches,

required for various purposes. The primary and secondary tanks are separated

by a 30-inch annulus of air in the cylindrical region and by an 8-inch-thick

layer of insulating concrete in the base region. In the dome region, the

primary steel tank is directly attached to the secondary concrete tank form-

ing a liner of the latter. Further details of the tank structure may be ob-

tained from Reference 2 drawings.

1.3 Scope of Investigation

The basic purpose of the present investigation was to determine the combined

effects of long-term dead, live, and thermal loads and the SSE ground motions

on the proposed 241-SY Waste Tank Structure. To analyze the structure for

each of the above load conditions, an axisymmetric finite element model of

the tank, with or without the surrounding soil, was used. The axisymmetric

finite element model of the tank with the surrounding soils consists of shell

and solid elements. Although the soil extends infinitely around the tank,

the boundaries of the model were taken only sufficiently far from the tank as

to affect the results of the analysis in and near the tank minimally. The

model was used for the dynamic analysis of the tank-soil interaction during

an earthquake as well as for the static analysis under gravity loads.

The primary steel tank alone, modeled by axisymmetric finite elements, was

used for hydromechanical analyses. Stresses in the primary steel tank due

-2- LD ME%/MBL[LJ] [1 0 IM

to thermal loads were also computed using this model.

The seismic analysis was conducted in two parts. In one part the interac-

tion of the empty tank with the surrounding soil was considered; in the

other the effect of the sloshing liquid on the tank was examined. It was

assumed that the responses of the tank to these two earthquake-induced pheno-

mena are not coupled and may be computed separately. The hydrodynamic effect

of sloshing fluid was considered approximately by a quasistatic approach.

The problem of interaction of tank and soil during earthquake motion was

treated as a dynamic problem using a time-history approach. In this dynamic

analysis, the time-history of responses was computed for the soil-tank finite

element model subjected to a time-history of earthquake motion at its base.

The design earthquake (SSE) has been specified as a time-history of free-

field ground motion at the surface. The equivalent SSE motions at the base

of the soil-tank model were computed by a deconvolution procedure.

A gravity load analysis was also carried out with the same soil-tank

model used in the seismic analysis with some minor changes. The gravity

load condition includes the dead load of tank and soil, live load (surcharge)

and weight of tank contents.

A separate nonlinear thermal-creep analysis of the concrete tank was carried

out by our consultant Dr. Y. R. Rashid. A finite element model of the con-

crete tank and dome, including the secondary steel liner, was used for this

analysis. Gravity load (overburden and lateral soil pressures) was also in-

cluded as the initial mechanical load on the tank. Dr. Rashid's report on

this analysis is included as Appendix A of this report.

1.4 Safe Shutdown Earthquake (SSE)

The 241-SY tanks are located in the 200 West Area, approximately 5 miles

west of the 241-AZ tanks in the 200 East Area. A site seismicity study for

the 241-AZ tanks is reported in the Appendix of Reference 1. Due to the

proximity of the two sites, the SSE (referred to as Design Earthquake in

Reference 1) proposed for the 241-AZ tanks was considered applicable to the

241-SY tank site. The design response spectrum of the SSE for 5% damping is

shown in Figure 4. A synthetic free-field ground acceleration time-history

correlated to the SSE design response spectrum has been developed by URS/John

G=0 [ e/MBO=GLWAIN-3-

A. Blume & Associates, Engineers, and is shown in Figure 5. The 5% damping

response spectrum of the synthetic time-history is compared with the corres-

ponding SSE design spectrum in Figure 4.

-4-01 [ 3 #3/MB & 0=0 [i ] IME

2. SOIL PROPERTIES

A subsurface geophysical investigation was conducted at the 241-SY tank site

to determine the dynamic soil properties. The results of that study are re-

ported in Reference 3. Soil properties to a depth of 150 feet from the sur-

face were obtained. Data beyond that depth were developed from other avail-

able geologic data.4 From these data, it is believed that the surface of

the Ringold formation is at a depth of approximately 155 feet. The Ringold

formation consists of cemented and very dense conglomerate whose stiffness

is estimated to be almost 20 times that of the soil layers (silty sand) just

above. Thus the Ringold formation may be interpreted as bedrock for the

purpose of analysis and was taken as the base of the soil-tank model.

It has been established by many investigators5 that soil behavior under

earthquake forces is nonlinear, i.e., the stress-strain relations are not

linearly proportional. However, a direct nonlinear dynamic analysis of the

soil-tank structure was beyond the scope of this investigation. Instead, an

equivalent linear dynamic analysis approach6 was used. In this approach,

soil moduli are assumed to depend on the average maximum strain levels occur-

ring over the duration of earthquake motion. Thus, an initial guess is made

at these strain levels, and the soil properties based on them are used in

the first analysis. If the assumed strain levels are much different from I

the computed values, the latter are then used as the basis for soil proper-

ties for the next analysis, and so on. Such an approach has been shown to

lead to results comparable to those obtained from direct nonlinear analysis.6

The shear modulus data given in Figure 5 of Reference 3 are obtained from

geophysical tests where very low strain levels (10-4%) are involved. Fig-

ure 6 of Reference 3 gives the variation of shear modulus, in a non-dimen-

sional form, with shear strain levels. The data on variation of damping with

strain levels for sandy material given in Reference 5 were also used in the

present analysis.

-5-aD IN IM/IMB L &0 WA IM

3. COMPUTATION OF BASE MOTION (DECONVOLUTION)

The SSE has been specified in terms of free-field spectra (Figure 4) and

was represented by synthetic free-field acceleration time-history (Figure 5).

To evaluate the response during the SSE of an underground tank and the soil

surrounding it, the input motion must be applied at the base of the soil-

tank model. This base motion should be equivalent to the specified surface

motion.

Such a computation of the motion at the base of soil layers that will pro-

duce a given surface response motion is the reverse of the usual problem of

computing the surface response of soil layers subjected to a given base mo-

tion. It is difficult if not impossible to solve such a problem in the time

domain. However, for stable linear elastic systems, there exists a simple

relationship between the output motion (motion at the surface or any inter-

mediate point) and the input (base) motion in the frequency domain:

Y(W) H(w) · X(w)

where Y(w) and X(w) are the Fourier transforms of the output motion y(t) and

input motion x(t), respectively, and H(w) is the frequency response function

of the system and is solely dependent on the system properties. Here, Y(w)

can be computed because the surface motion y(t) is known. H(w) is simply

the Fourier transform of the. surface response of the soil layers to unit

impulse input at the base. Thus, X(w) may be computed from the above equa-

tion and then x(t) may be obtained by inverse Fourier transform of X(w).

The 155-foot deep soil layers down to the Ringold formation (which was taken

as the bedrock base of the soil-tank model as explained in Section 2) were

modeled by a soil column of unit area for the deconvolution analysis described

above to obtain the base motion time-history at the surface of Ringold forma-

tion. The acceleration time-history at the surface of the soil column was

recomputed using the computed base motion as input. The acceleration response

spectra of the recomputed surface motion and the original free-field motion

are compared in Figure 6.

-6-06 e/IMB LUMIE

The soil properties used in the deconvolution analysis are shown in Table 2.

*As explained in Section 2, the soil properties are strain dependent; conse-

quently, an iterative elastic approach was used. The strain levels are also

shown in Table 2. The computed base acceleration time-history is shown in

Figure 7.

-7-9 £#3/IMB L &9 MI IN

4. ANALYSIS APPROACH

4.1 General Assumptions

Structural analysis of underground tanks with liquid contents subjected to

long-term gravity, thermal, and creep loads, as well as the transient earth-

quake ground motion is a complex problem. The recent development of the

finite element method of analysis of structures has made such analyses pos-

sible. However, a few simplifying assumptions regarding the structure and

the loads were necessary to make such analyses practicable within reasonable

budget limits. Two basic assumptions made in the present analysis are out-

lined below. Several other assumptions will be mentioned in the remainder

of this section.

Each tank was assumed to be axisymmetric. The nonaxisymmetric features of

the tank were either ignored or modeled approximately by equivalent axisym-

metric elements. The soil surrounding the tank was also assumed to extend

axisymmetrically for a large radius (large in relation to tank size). The

effects of neighboring tanks and nonaxisymmetric soil profile were ignored.

It is difficult to estimate the effect of this assumption ori the computed

responses, especially in the case of earthquake forces. When considering

gravity loads, it seems that ignoring the existence of adjacent tanks will

lead to conservative results with regard to lateral soil pressures on the

concrete tank walls; effects elsewhere should be minimal. Also, as will be

observed from the results presented later in this report, the earthquake-

generated stresses are generally much smaller than those caused by static

loads. The computed results should, therefore, be conservative.

The hydrodynamic problem of liquid pressures on the tank due to oscillating

liquid contents was solved separately from the soil-tank interaction problem.

That is, the coupling between the liquid motion and the tank motion was

assumed to be negligible because the frequency differences of the two motions

are large. Hydfodynamic forces computed on the basis of this assumption will

be quite conservative. 7

-8-[U] M) #3/IMB & &0 [R ] ME

4.2 Finite Element Models

The tank and the surrounding soil were modeled as an assemblage of axisymme-

tric, thin, conical shell and toroidal solid finite elements. The shell ele-

ment has, in general, the shape of a conical frustum, but can also represent

a segment of a vertical cylindrical shell and a flat, horizontally oriented

plate at extreme orientations. The solid elements are toroids of triangular

or quadrilateral cross section. A shell element and a quadrilateral solid

element are shown in Figure 8 along with the global reference axes (Z, R,

and 0) and the degrees of freedom involved at each nodal point. For a

description of the finite element method, see Reference 8. Reference 9 devel-

ops the finite element method for axisymmetric structures under axisymmetric

and nonaxisymmetric loading, the particular area of interest in the present

investigation.

The entire soil-tank finite element model is shown in Figure 9. Detail near

the tank region is shown in Figures 10a and 1Ob. The concrete tank, includ-

ing the dome and the base slab, was represented by thin shell elements. The

secondary steel liner attached to the concrete tank was ignored, because it

will contribute very little to the stiffness of the shell. The primary steel

tank was included in the model and was also represented by thin shell ele-

ments. The primary steel tank was assumed to be rigidly attached to the con-

crete shell in the dome region. In the base slab region, the layer of insu-

lating concrete between the primary steel tank and the concrete tank wasrlmodeled by solid elements. The primary tank was assumed to»rigidly attachedto the insulating concrete. This will be the behavior in reality because of

self weight of the tank and the weight of the contents.

The concrete tank dome, wall, and slab were represented by shell elements at

their middle surfaces. To maintain actual geometry, the nodal points of the

shell elements on the middle surface and the nodal points of the adjacent

solid soil elements at the soil-tank boundary were connected by thin shell

elements of appropriate length (usually half the thickness of the concrete

wall or slab), stiffness, and weightless material. Similar solid connector

elements were used in the cantilever portion of the wall footing to maintain

its actual geometry. For dead load analysis, the shell connectors between

concrete walls and adjacent soil were assumed to be pin-connected to elimi-

-9- LDME#l/BLLD[MIE

nate the drag-down effect (transfer of weight of soil) on the concrete wall

from the surrounding soil. This assumption closely simulates actual condi-

tions, because the drag-down effect due to consolidation of the fill around

the tanks diminishes with time after initial construction.

Except for the materials used to define the properties of the cracked con-

crete elements in the dome for the dynamic analysis, all materials, i.e.,

soil, concrete, insulating concrete, steel, etc., were assumed homogeneous

and isotropic for a given analysis run. As indicated in Section 2, the soil

properties were assumed to be dependent on expected strain levels. The

properties used in the analysis for various materials are given in Table 3.

Results of the thermal-creep analysis by Dr. Rashid show some cracking near

the center and in the haunched portion of the dome. The cracking is due to

tensile forces in the circumferential direction. Consequently, in the

dynamic analysis, the cracked concrete was modeled by material having equiv-

alent orthotropic properties with reduced stiffness of only the hoop rein-

forcement in the circumferential direction and the stiffness of the concrete

in the other directions.

Only a finite extent of soil around the tank could be included in the model.

The bottom boundary of the model was assumed to be 155 feet below the ground

surface. The vertical boundary was assumed to be at a radius of 240 feet

from the axis of symmetry of the soil-tank model. The bottom boundary was

at the surface of the Ringold formation, which, as explained in Section 2,

consists of a much sti ffer material than the soil above and thus forms a

natural boundary. The vertical boundary was somewhat artificial; however,

it was sufficiently far from the tank region that the stresses and displace-

ments in this region were little affected by the artificial boundary. Fur-

thermore, to simulate continuity at the vertical boundary, appropriate bound-

ary conditions were assumed: lateral support but freedom of vertical move-

ment under vertical loads, and exactly the reverse under lateral loads. Also,

in the earthquake analysis, dampers were used at the vertical boundary to

simulate radiation dampinglo (loss of energy due to radiation of wave energy

into soil beyond the boundary). The bottom boundary was assumed to be

fixed for all load cases.

- 10 -&DIAO#3/MBLLDOME

No geophysical test data for the tank site were available at the start of

the present investigation, so initially the soil-tank finite element model

was made to extend down to 200 feet below the surface. The model had been

finalized and the input data cards had been punched when the geophysical

investigation results were obtained. The very dense and cemented Ringold

formation is believed to be 155 feet below the surface. It was decided, as

explained in Section 2, that the surface of this formation forms a natural

bottom boundary. To avoid delaying the present investigation, instead of

developing a new model, all nodal points below the 155-foot level were

assumed fixed. The soil-tank model given in Figure 9 shows the model down

to the 155-foot level only.

A separate model of the primary steel tank was used for analysis under hydro-

mechanical pressures that act directly on the primary tank and have very

little effect on the secondary tank. Also, a more refined model of the

primary tank was made possible by analyzing it independently. The model used

in hydromechanical analysis is shown in Figure 12, with the tank liner plate

represented by axixymmetric shell elements. The thermal stress analysis was

darried out with a separate computer program (see Section 4.4) whose limita-

tions made it necessary to model the tank liner plate by axisymmetric solid

elements (5 layers across the thickness).

A separate model of the concrete tank wall and dome was used in thermal-creep

analysis conducted by Dr. Rashid and is described in Appendix A.

The wall-to-base slab joint in the concrete tank is of the sliding type. The

wall was therefore assumed to be free to move laterally with respect to the

base slab under long term loads such as gravity, lateral soil pressure and

thermal loads and under creep effects. However, for the transient earth-

quake ground motion loading, which generally lasts for less than a minute,

the wall and the base slab were assumed to be pin-connected, i.e., free to

rotate but prevented from sliding with respect to each other.

4.3 Load Conditions for Analyses

In addition to the two dynamic load cases, i.e., hydrodynamic loads and earth-

quake ground motion, the gravity (i.e., dead and live), hydrostatic, thermal,

- 11 -[LI] [R)#S/IBLLI][1 0 IM

and vapor pressure (in the primary tank vapor space) loads must also be con-

sidered to obtain the proper combined stress for checking the steel and con-

crete tank sections. A separate thermal-creep analysis of the concrete tank

was conducted by Dr. Y. R. Rashid.

4.3.1 Gravity Loads

Under gravity loads, the weight of the tank and the soil in the model were

considered. The weight of the 1,000,000 gallons of liquid waste (specific

gravity of 1.7) was also considered as was the live load at the ground sur-

face, which consists of a uniform load of 40 psf and a concentrated load of

50 tons. The 50-ton concentrated load was applied only in the central region

at the axis of symmetry. Its application elsewhere makes it a nonaxisymmet-

ric load which cannot be easily modeled by equivalent axisymmetric loads.

The soil-tank model was used in the analysis for gravity loads.

4.3.2 Hydromechanical Loads

The liquid waste to be contained in the primary steel tank will exert hydro-

static pressures on that tank. Vapor in the space above the liquid surface

will also exert pressures on the tank dome. These pressures are long-term in

nature. The motion of the tank under seismic excitation will cause sloshing

of the liquid in the tank, resulting in hydrodynamic pressures on the tank.

Such hydrodynamic pressures will be exerted only for a short time during

an earthquake.

The hydromechanical pressures act directly on the primary steel tank, which

then transfers them to the surrounding soil through connections to the con-

crete tank dome and base slab. The effect of these loads on the concretetank and soil is expected to be minimal. Thus, the primary tanks were ana-

lyzed under such loads under the assumption that the dome and base slab of

the concrete tank provide it rigid supports. An analysis of the entire soil-

tank model under hydrostatic loads confirmed this assumption.

In computing the hydrostatic pressures, the specific gravity of the liquid

contents was assumed to be 1.7. Vapor pressure has been specified as rang-

ing between -6 inches of water to +60 inches of water. Vapor pressure of +60

- 12 -9 R e/BL 013 040 IN

inches of water acts in the same direction as the hydrostatic pressures and

the weight of liquid, and was therefore used in the analysis simultaneously

with the hydrostatic pressures.

Hydrodynamic pressures caused by the sloshing motion of the liquid contents

were computed by a method developed in Reference 7 that is essentially simi-11lar to that developed by Housner. This method assumes that the tank is

rigid; the liquid is nonviscous, incompressible, and homogeneous; the dis-

placements, velocities, and slopes of the free surface of the liquid are all

small; and the flow field is irrotational. From the expression for hydro-

dynamic pressure developed in Reference 7, using only the first sloshing mode

and assuming that the spectral acceleration value at the first mode period

(which is greater than 5 seconds) equals half the maximum ground acceleration,

0 , the pressure on the tank wall at radius R is computed to beg

p (z,0)PR09 {1-fl(R, z)} cos 0

where

H-zcosh 1.84 -

fl(R,Z)R

1.84H2.38 cosh R

In the above expression, H is the height of liquid surface from the base of

the tank, z is the coordinate of depth measured from the surface of the

liquid (positive downward), p is the mass density of the liquid, and 0 is

the circumferential coordinate (angle) measured from the direction of appli-

cation for the base motion.

The model of the primary steel tank used in the hydrostatic and hydrodynamic

analyses is shown in Figure 12. The hydrodynamic pressures on the tank com-

puted by the above procedure are given in Table 4 along with the hydrostatic

pressures.

t

- 13 -

03 * #3/IMB LUMEN

4.3.3 Thermal Loads

The liquid contents in the tank will remain at temperatures of around 250'F

over a long period. The steel and concrete tanks are constructed and remain

at normal atmospheric temperatures (assumed to be 70'F) until the introduc-

tion of the hot liquid waste contents. The base plate and most of the cylin-

drical wall region of the primary steel tank that is in direct contact with

the liquid will reach and remain at the same temperature as that of the

liquid. Temperatures in the remainder of the steel tank and those in the

secondary concrete tank were computed by ARHCO using heat transfer analysis.

Concrete is subject to creep under sustained loading, especially under ele-

vated temperature conditions. The thermal-creep analysis of the concrete

tank that was conducted by Dr. Y. R. Rashid used the temperature data devel-

oped by ARHCO. The temperatures were assumed to rise gradually over a

period of 30 days to the design levels and then remain steady. The analysis

was continued to further steps in time well beyond the time necessary to

establish self-limiting cracking and creep deformations. The soil over-

burden load, live load of 40 psf, and internal vapor pressures in the tank

were included in the analysis as initial mechanical loading on the tank.

This detailed report on the thermal-creep analysis is included as Appendix A.

The detached portion of the primary steel tank (Figure 12) was analyzed for

thermal stresses due to temperature change. Simultaneously, concrete tank

displacements at the dome and the base slab regions where the two tanks are

connected were applied to the steel tank. The displacements of the concrete

tank in the dome region were obtained from the results of the thermal creep

analysis. The displacements in the base slab were computed by the formula

8 a·R·A T

where A is the radial displacement at radius R, a is the coefficient of ex-

pansion for concrete (6.38 x 10-6 in./in./'F) and AT is the change in tem-

perature.

- 14 -[Ul [* /IMB L LD M IN

4.3.4 Earthquake Ground Motion

Ground motion at a given point due to an earthquake may be represented by

two horizontal components and one vertical component. The rotational com-

ponents are negligible. The soil-tank structure is assumed to be rigid in

the vertical direction, and the responses due to vertical ground motion are

obtained by scaling the gravity load responses by a factor of 0.167 (the

design SSE maximum vertical ground acceleration specified is 2/3 x maximum

horizontal ground acceleration, 0.25g = 0.167g).

The response of the soil-tank structure to a horizontal component of SSE

input base motion time-history was computed. This input base motion was

determined as described in Section 3. The equations of motion for the soil-

tank model were solved by a step-by-step method, and the entire time-histories

of the responses were computed. Only the maximum values of the response

parameters were recorded (with the time of occurrence), mainly because of the

large number of response parameters of interest. Also, instead of computing

the responses of the system to two independent, mutually perpendicular hor-

izontal components, it was assumed that they cause the same maximum re-

sponses, though they may occur at different times.

4.4 Computer Programs

The main computer program used for the analyses reported herein was AXIDYN,

a computer program for the static and dynamic analysis of axisymmetric struc-

tures by the finite element method. The program, written in Fortran IV, was

developed at the Department of Civil Engineering of the University of

California, Berkeley,9 under the direction of Professor E. Wilson, and was

used in all the finite element analyses reported here.

The structure to be analyzed by AXIDYN can consist of axisymmetric shells,

axisymmetric solids, or a combination of the two. The axisymmetric shells

are represented by conical-frustum-shaped shell elements, whereas the axi-

symmetric solid body is represented by an assemblage of toroids of quadri-

lateral or triangular sections. The two types of elements are shown in

Figure 8 with the degrees of freedom considered in the analysis for such

elements. The nodal points on a vertical section are seen in Figure 8 to

be nodal circles.

- 15 - [Lil M)Mj/IN)LOSMIE

The program will handle static or dynamic forces that are axisymmetric or

are such that they can be developed into Fourier series form along the nodal

circles, i.e., as functions of 0. AXIDYN accepts five types of loading

cases:

0 Dead loads

• Arbitrary static loads

• Arbitrary dynamic loads

0 Horizontal earthquake accelerations

0 Vertical earthquake accelerations

Dead loads, arbitrary static loads, and horizontal earthquake accelerations

are the load cases considered in the present analysis.

The program has the capability of performing dynamic analyses both by the

modal superposition approach and by direct integration of the coupled equa-

tions of motion. The latter approach was used in the current investigation.

A new subroutine, developed for the step-by-step integration of equations

by a procedure12 that is more accurate and stable than the procedure origi-

nally developed for the CDC 6600 computer system, was modified to handle

large finite element models encountered in the present analyses on the CDC

7600 computer system. Such a system at the Lawrence Berkeley Laboratory of

the University of California at Berkeley was used for all computer analyses.

Other computer programs were also used for preparation, checking, and plot-

ting of data, and for the deconvolution analysis described in Section 3.

Among these is a program named MATRAN, which performs matrix operations on

data in matrix form, including structural analyses and time-series analyses.

The latter capability was particularly useful for the deconvolution analysis.

MATRAN is a substantially expanded version of program SMIS. The latter pro-

gram was also developed at the Civil Engineering Department of the University

of California, Berkeley.

Another program, SAP IV, also developed by the Civil Engineering Department

of the University of California at Berkeley,13 was used in the thermal analy-

sis of the primary steel tank. SAP IV is a general three-dimensional struc-

- 16 -[u] M 9#3/IMB L[LD [Rfil IM

tural analysis program and was used instead of AXIDYN because the latter does

not handle thermal loads.

4.5 Load Combinations and Computation of Stresses

As explained in Section 4.2, the tanks were entirely modeled by shell ele-

ments. The computer output of forces on shell elements is in'terms of stress

resultants, longitudinal force and moment, circumferential force and moment,

and in-plane shear force and torsional moment. These stress resultants are

shown in Figure 13 for a vertically oriented shell element, which represents

tank walls. Tensile forces and moments producing tension on the outside face

of a shell element are considered positive. This convention is followed in

the figures and tables of this report. For a horizontally oriented shell

element, representing the base slab of the tank, the stress resultants shown

in Figure 13 are still valid except that the longitudinal forces may be

interpreted as the radial forces. Note that no transverse shear (i.e., shear

across the shell thickness) is output by the computer program; it may be

approximately computed from the longitudinal and circumferential moments.

Stresses from the three sets of stress resultants -- longitudinal force and

moment, circumferential force and moment, and shear and torsional moment --

are computed on appropriate sections of the elements. First, though, the

stress resultants from various loads were combined and the following consid-

erations were taken into account in this combination process.

Among the load cases considered here (Section 4.4), two loads -- hydrodynamic

pressures and horizontal earthquake ground motion -- are nonaxisymmetric.

The hydrodynamic pressures act normal to the container wall, and the magni-

tude varies over the circumference as a cosine function of the angle 0 from

the direction of applied ground motion (see Section 4.3.2). A component of

horizontal earthquake ground motion may be represented by radial and tangen-

tial loads (in the horizontal plane) varying over the circumference as cosineand sine functions, respectively, of the angle 0 measured from the direction

of applied ground motion. For both of these nonaxisymmetric loadings the

longitudinal and circumferential stress resultants vary cosinusoidally,

whereas the in-plane shear and torsion vary sinusoidally, from the direction

of applied ground motion. The other three loads -- gravity load, hydrostatic

- 17 -9 M) e/IMB 0= GL [MI IM

.

pressures, and vertical earthquake ground motion -- are axisymmetric. Stress

resultants on an element due to these loads are constant over the circumfer-

ence, and in particular the in-plane shear and torsion are zero everywhere.

The seismic design criteria specify that the horizontal ground motion shall

be represented by two mutually perpendicular components acting simultane-

ously. The maximum values of a stress resultant in an element due to the two

mutually perpendicular horizontal components will occur at 90' angles

and probably at different times. Let us assume that the magnitudes of a

stress resultant due to the two components are equal. If we combine the

particular response due to the two components by the root mean square method,

it is clear that at no point along the circumference will the combined value

of the response be greater than the response due to one component at a sec-

tion parallel to that component. The same argument holds for hydrodynamic

loads because they are generated by horizontal earthquake ground motion.

Therefore, in obtaining the combined stress resultant from dynamic and static

loads, one needs to consider only one component of the horizontal ground mo-

tion. Furthermore, according to the argument presented in the preceding para-

graph, in combining the stress resultants from axisymmetric and nonaxisymmetric

loads included in the present analysis, the circumferential variation of these

stress resultants need not be considered.

For the static loadings (dead load and hydrostatic pressures) the direction

of the action of stress resultants is known from the computer output. How-

ever, for dynamic loadings (vertical and horizontal earthquake ground motions

and hydrodynamic pressures) only the maximum values of the various stress

resultants are known. These may act in either direction and may occur at

different times during the earthquake. Hence, algebraic summation was used

in combining stress resultants from the static load cases, whereas absolute

summation was conservatively used in combining stress resultants from the

dynamic load cases. However, in combining the total static and the total

dynamic forces and moments, directions (or signs) were assigned to the dynamic

forces and moments independently to produce the worst possible stresses.

In determining the stresses in the primary steel tank, the results of our

analyses considering the various load conditions, namely dead, surcharge,

- 18 -[L:[1 [ e/IM3&[WOMIM

thermal, hydromechanical loads, and earthquake ground motion are considered.

The thermal-creep analysis by Dr. Y. R. Rashid, which used a nonlinear method'

of analysis, included the long-term loads,.consisting of dead, surcharge, and

vapor pressure at the inner surface of the dome, as initial mechanical load-

ing on the tank. The results of this thermal-creep analysis and the results

of our earthquake analysis of the tank as a whole were combined to check the

stresses at the concrete tank. Effects of the hydrodynamic loads (which act

directly on the primary steel tank) on the concrete tank are small and are

not consi dered.

1

- 19 -[U][ #3/IMB LILL[i [1 IM

r

5. RESULTS OF ANALYSIS

5.1 Primary Steel Tank

The primary steel tank was analyzed as a part of the overall soil-tank model

(Figure 9) for gravity loads and earthquake ground motion. It was analyzed

separately for hydrostatic and hydrodynamic loads (Figure 12) as well as

thermal loads.

Internal forces (i;e., both forces and moments) in the primary tank caused

by the hydromechanical loads are plotted in Figures 15 and 16. For conve-

nience in plotting, the top knuckle and roof portion and the base knuckle

and base plate portion have been developed vertically in these figures. The

hydrostatic pressures and corresponding internal forces are constant over

the circumference of the tank. The hydrodynamic pressures, which are caused

by earthquake motion, and the corresponding internal forces vary along the

circumference with the cosine of the angle measured from the direction of

applied motion. The values of hydrodynamic internal forces shown in Figures

15 and 16 are maximum values acting on a section parallel to the applied

motion. The hydrodynamic internal forces are generally much smaller than

the hydrostatic internal forces.

The longitudinal (or meridional) and circumferential (or hoop) moments due

to hydromechanical loads are significant only at and near the top and bottom

knuckles. The longitudinal forces are generally of smaller magnitude in

comparison to circumferential forces. The latter are maximum near the base

of the tank for hydrostatic load and are essentially constant over the cylin-

drical portion of the tank for hydrodynamic load. Note that the hoop forces

caused by hydrostatic pressures are generally tensile, whereas the hoop

forces due to hydrodynamic pressures may act either way.

The internal forces in the primary tank caused by gravity loads and soil-

structure interaction due to earthquake ground motion are general,ly much

smaller than those caused by hydromechanical loads, and are listed in Tables

5 and 6. The moments and forces are of any significance only at and near

the base knuckle and to a lesser extent near the top knuckle. The moments

- 20 -' 06[ e/ 11=11:DIMI IM

are more significant in the longitudinal direction and the forces are more

significant in the circumferential direction. Note that the gravity loads

and corresponding internal forces are constant along the circumference,

whereas the earthquake-caused internal forces vary with the cosine of the

angle measured from the direction of applied motion, and the values given in

Tables 5 and 6 are the maximum values. Also note that the earthquake-induced

internal forces may act in either direction.

Due to the nature of the model and computer program used, only the stresses

on the primary tank for thermal loads were available. The stresses are insig-

nificant everywhere except in and near the base and top knuckles of the tank.

In the upper knuckle, the maximum longitudinal and circumferential stresses

are, respectively, 9.6 ksi (compressive) and 3.9 ksi (tensile). For the bot-

tom knuckle, the corresponding maximum stresses are 4.0 ksi and 1.6 ksi (both

tensile).

Stresses due to gravity and hydromechanical loads and earthquake ground

motion were also computed. The circumferential stress is dominated by hoop

tensile force caused by hydrostatic pressures and is maximum at nodal point

(NP) 235, where the thickness of tank liner plate is 1/2 inch. Under long

term loads (gravity + hydrostatic + thermal) the maximum hoop stress at NP 235

is 15.3 ksi, and addition of seismic load stresses boosts it to 20.1 ksi. The

longitudinal stress under long term loads is maximum at NP 133 (at the base of

the base knuckle, see Figure 12) having a value of 13.1 ksi, which increases

to 19.3 ksi when seismic load stresses are added.

The primary tank steel is specified as ASTM 516 Grade 65. According to ASME

Boiler & Pressure Vessel Code Section III Division I,14 the allowable stress

for such steel at temperatures around 250'F is 21 ksi (and the yield stress

is 31.5 ksi). Thus, the maximum computed stresses in the primary steel tank

are less than this allowable value.

The radial displacements of the primary steel tank under hydromechanical

pressures are shown in Figure 14. Maximum displacements of 0.165 inches and

0.104 inches under hydrostatic and hydrodynamic pressures, respectively,

occur near NP 15.

- 21 - 9 [Rle/IMB LL!] 0 ] IN

5.2 Concrete Tank

The secondary concrete tank was analyzed for gravity loads and soil-structure

interaction (due to earthquake ground motion) as a part of the overall soil-

tank model (Figure 9) using computer program AXIDYN. The dome and cylindri-

cal wall portion of it was separately analyzed for thermal loads and creep

by Dr. Rashid using the computer program SAFE-CRACK (Appendix A). This

thermal-creep analysts considered the nonlinear behavior of concrete, and

therefore the gravity loads (including the active lateral soil pressure on

the tank wall) were included as initial mechanical loading in the thermal-

creep analysts.

Hence, for the concrete tank dome and wall, the SAFE-CRACK analysis results

were considered valid for the effect of long term loads (gravity, thermal,

and creep) and AXIDYN analysis results valid for earthquake ground motionloading. However, for the base slab, only AXIDYN results were available for

all loadings and are used herein. Thermal stresses in the base slab are

expected to be small because the connection between the wall and the slab

is of the sliding type. Furthermore, creep will tend to relieve the thermal

stresses. Thus, the effect of thermal loads and creep on the base slab is

considered negligible and is ignored.

The effect of hydromechanical loads, which act directly only on the primary

steel tank, was found to be negligible on the secondary concrete tank and

was ignored.

The lateral displacements in the tank region of the soil-tank model under

earthquake motion are maximum at approximately the same time, 6.56 to 6.57

seconds after the start of earthquake motion. The maximum lateral displace-

ments at the top and bottom of the concrete tank wall (nodal points 359 and

191, respectively) are 1.121 inches and 0.985 inches, respectively, giving a

relative lateral displacement of 0.136 inches between the top and bottom of

the tank wall.

The maximum lateral accelerations due to the earthquake motions are 0.15g at

the base of the tank, 0.21g at the roof of the tank, and 0.295g at the soil

surface close to the right vertical boundary.

- 22 -U m} 98/M3 0.&DMIM

The longitudinal (or meridional) forces and moments and the circumferential

(or hoop) forces and moments on the concrete tank wall, roof slab, and base

slab from the earthquake analysis are given in Table 7. The corresponding

plots of these forces and moments are shown in Figures 17 and 18. The earth-

quake response plots in these figures are envelopes because maximum responses

at different points in the structure may occur at different times and have

either positive or negative values. The earthquake responses are plotted

for a section parallel to the applied horizontal earthquake motion and are

maximum. They vary circumferentially as the cosine of the angle measured

from the direction of applied motion. The internal forces that develop in

the concrete tank under earthquake loading are generally much smaller than

the corresponding responses under dead load.

The results of thermal-creep analysis, including the effect of gravity loads

of the concrete tank dome and wall, are discussed in Appendix A. The forces

and moments on the base slab due to gravity loads, as obtained from AXIDYN

analysis, are shown in Figure 19. The longitudinal moment, which results

mainly from the vertical point load imposed by the tank wall, is maximum

near the tank wall and is the most significant of all internal slab forces

due to gravity loads.

The results from SAFE-CRACK analysis under initial mechanical loading (i.e.,

gravity and soil pressure) indicate an upward displacement of 0.03 inches at

the dome crown and an inward horizontal motion of 0.12 inches of the base of

the wall. Under thermal loading, just after the temperature of the contents

has reached its maximum value (30 days after heating has started), the dis-

placement at the crown is reversed and is now 0.51 inches downwards; simi-

larly, the displacement at wall base has also reversed and is now 0.41 inchesoutward. Due to long-term creep effects, the displacement at the crown of

the dome stabilizes to 0.23 inches upwards and at the base of slab to 0.34

inches outwards.

The results of SAFE-CRACK analysis indicate that under the gravity loads

(initial mechanical loading), there is no cracking in concrete and the maxi-

mum compressive stress in concrete is less than 1000 psi. Maximum stress in

meridional and hoop steel reinforcement is less than 7 ksi compressive and

- 23 -CLD M) g#j/Im) 0=LD[MIE

1 ksi tensile. During heating, the analysis indicates, cracking in con-

crete begins, and by the time temperatures reach their peaks, radial and

meridional cracking has occurred in regions near the dome crown and haunch.

The maximum compressive stress in concrete is less than 1600 psi, except

in a very localized region at the dome crown soffit, where it is 2600 psi.

Maximum stresses in steel reinforcement are less thad 24.2 ksi compressive

and less than 7 ksi tensile. The analysis further indicates that after long-

term creep, when stable conditions are established, the cracking spreads

somewhat but remains in the same general region. The maximum compressive

stress in concrete is now less than 1000 psi, whereas stresses in steel are

less than 24.2 ksi compressive and 4.0 ksi tensile. The high compressive

stress (24.2 ksi) in reinforcement after heating and long-term creep effects

is confined to a very small area near the dome crown, being less than 13 ksi

elsewhere.

The SAFE-CRACK analysis indicates that principal strains in regions of radial

cracking and meridional cracking near the haunch (where diagonal reinforce-

ment exists) are less than 1 percent, indicating adequate reinforcement.

However, principal strains approach 10 percent in the meridionally cracked

region near the dome crown, where no d.iagonal reinforcement exists, indicat-

ing that these cracks may increase in an unstable manner unless diagonal

reinforcement is provided.

The seismic analysis of the tank by AXIDYN computer program was an elastic

analysis, though regions of cracked concrete were modeled by appropriate

elements with reduced stiffness, as explained in Section 4.2. Thus the

results of seismic analysis cannot be directly combined to those from the

nonlinear SAFE-CRACK analysis for long term loads. However, an indication

of additional stresses due to seismic ground motion may be obtained by com-

puting the stresses due to such loading independently. Such computations

indicate maximum stresses (tensile or compressive) of 5.4 ksi in hoop steel

in the cracked concrete region near the dome haunch. The maximum stresses

in the uncracked region of the dome are less than 120 psi compressive in

concrete and 1.7 ksi tensile or compressive in steel. In the tank wall,

maximum compressive stress in concrete is less than 400 psi and maximum

stress in reinforcement steel is 11.5 ksi (indicating some flexural crack-

ing in concrete at the base of the wall in the longitudinal direction.

- 24 -9 e/IMBL[LD [i il Im

b 1

Stresses in the base slab for long-term and seismic loads were computed from

the AXIDYN analysis results. The, longitudinal stresses in a localized re-gion near the tank wall location under long-term (viz. gravity) loading are

quite high: 35.8 ksi tensile in bottom reinforcement steel (indicating some

flexural cracking at the bottom' face) and 2000 psi compressive in concrete.Addition of seismic stresses bcdosts these values to 42.7 ksi and 2475 psi.,

respectively. Elsewhere in the base slab, the stresses are substantially

smaller.

The specified ultimate compressive strength (f ) of the tank concrete is

4500 psi. The allowable compressive stress in concrete, according to the

old ACI 318-6315 code, are 2025 psi for long term loads and 2700 psi when

seismic loads are also considered. Thus the compressive stresses in concrete

are within allowable values everywhere in the tank except in a very localized

region at the dome crown soffit for a short period during and after heating.

Reinforcement steel is specified as ASTM 615-68 Grade 60 with minimum yield'4»,

strength of 60 ksi and allowable stresses of 24 ksi for long-term loads and

32 ksi when seismic stresses are included. The computed stresses in rein-

forcement steel exceed these allowable values in a couple of localized re-

gions at the dome crown and in base slab near the tank wall, though they are

well within the yield strength of the steel.

In-plane shear stresses caused by seismic ground motion result in high

nominal shear stresses in the tank wall ranging from 252 psi to 395 psi,

the latter occurring near the base of the wall. According to ACI 318-63,

the allowable stress is 446 psi, assuming that longitudinal and circum-

ferential steel reinforcement help resist the in-plane shear.

- 25 -9 [* e/MB LLI] 94 ME

r

6. SUMMARY AND CONCLUSIONS

The underground 241-SY tank structure, which consists of a primary steel

tank and a secondary concrete tank and is proposed to provide leakproof

containment for radioactive waste liquids, has been analyzed for gravity

and thermal loads, as well as for Safe Shutdown Earthquake ground motion.

The secondary concrete tank has also been analyzed for long-term creep

effects.

The tank structure was analyzed by the finite element method using an elas-

tic analysis approach, except for the thermal-creep analysis of concrete

tank which involved a nonlinear approach. The surrounding soil was included

in the model for the seismic analysis.

An evaluation of the results indicates that the stresses in the primary steel

tank are within their allowable values. The stresses in concrete and rein-

forcement steel of the concrete tank are also within their respective allow-

able values with the exception of a few localized areas. The stresses in

concrete and steel reinforcement in a very small region at the dome crown

exceed slightly their allowable values. The stress in bottom steel rein-

forcement in the base slab near its junction with the tank wall also exceeds

the allowable value though it is well within its yield strength.

Cracking in the dome and upper wall regions of the concrete tank is expected

under thermal and creep loads. Satisfactory reinforcement exists to limit

this cracking except for certain regions where meridional cracking may in-

crease in an unstable manner. To limit meridional cracking in the concrete

tank, it is recommended that diagonal reinforcement be extended throughout

the dome region and in the cylindrical wall region up to at least 8 feet

below the dome-to-cylinder junction.

- 26 -

0.0 me 8/IMB L 9 94 E

7. REFERENCES

1. John A. Blume & Associates, Engineers, Seismic Analysis of Under-

ground Waste Storage Tanks 241-AZ-101 and -102 at Hanford, Washington,

Report No. JABE-ARHCO-01, prepared for ARHCO, Richland, Washington,

San Francisco, April 1971.

2. ARHCO Drawings

241-SY: H-2-37701, H-2-37706, H-2-37707, H-2-37708, H-2-37773

241-AZ: H-2-67243, H-2-67317

3. John A. Blume & Associates, Engineers, Investigation to Determine

Dynamic Soil Properties at the 241-SY Tank Site, Report No. ARHCO-

JABE-0, prepared for ARHCO, Richland, Washington, San Francisco,

March 1974.

4. Kintzer, F., Internal Memo to A. B. Cunningham, John A. Blume &

Associates, Engineers, San Francisco, April 2, 1974.

5. Seed, H. Bolton and I. M. Idriss, Soil Moduli and Damping Factors

for Dynamic Response Analysis, EERC 70-10, Earthquake Engineering

Research Center, College of Engineering, University of California,

Berkeley, California, December 1970.

6. Seed, H. Bolton, and I.M. Idriss, Response of Horizontal Soil Layers

During Earthquakes, Research Report, Soil Mechanics and Bituminous

Laboratory, University of California, Berkeley, 1967.

7. Edwards, Norman W., A Procedure for the Dynamic Analysis of Thin

Walled Cylindrical Liquid Storage Tanks Subjected to Lateral Ground

Motions, Ph.D. dissertation, University of Michigan, Ann Arbor,

Michigan, 1969.

- 27 - U N3993/BLI ]MIE

6 »

8. Zienkiewicz, 0. C., The Finite Element Method in Structural and

Continuum Mechanics, McGraw-Hill, London, 1968.

9. Ghosh, Sukmar, and Edward Wilson, Dynamic Stress Analysis of

Axisymmetric Structures Under Arbitrary Loading, EERC 69-10,

Earthquake Engineering Research Center of the College of Engineering,

University of California, Berkeley, California, September 1969.

10. Lysmer, John, and Roger L. Kuhlemeyer, "Finite Dynamic Model For

Infinite Media," Journal of Engineering Mechanics Division, Proceedings

ASCE, Vol. 95, No. EM4, August 1969, pp. 859-877.

11. Nuclear Reactors and Earthquakes, TID 7024, USAEC, Division of Reactor

Development, August 1963.

12. Farhoomand, Iraj, Nonlinear Dynamic Stress Analysis of Two-Dimensional

Solids, unpublished dissertation for the degree of Doctor of Philosophy,

University of California, Berkeley, California, 1970.

13. Bathe, K.-J., Wilson, E. L., and F. E. Peterson, SAP IV, A Structural

Analysts Program for Static and Dynamic Response of Linear Systems,

Report No. EERC 73-11, College of Engineering, University of California,

Berkeley, California, June 1973.

14. ASME Boiler and Pressure Vessel Code Section Ill, Division 1, 1971

Edition, American Society of Mechanical Engineers, New York.

15· Building Code Requirements for Reinforced Concrete (ACI 318-63),

American Concrete Institute, Detroit, 1963.

- 28 -

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TABLE 1

SOIL PROPERTIES BASED ON GEOPHYSICAL DATA

Depth, Layer Density,Shear Poisson's

ft No. pcf ksf pModulus, Ratio,

1 108 1,900 0.235

2 127 2,200 0.1812

3 108 2,800 0.20

4 108 3,500 0.28

5 108 4,100 0.3436

6 127 4,375 0.38

7 127 4,500 0.3949

8 115 4,600 0.41

9 115 4,670 0.4263

10 108 4,740 0.43

11 108 4,760 0.43

12 108 4,875 0.44

13 108 4,920 0.44

14 108 5,060 0.44

15 108 5,125 0.44

16 108 5,240 0.44

17 108 5,300 0.44

18 108 5,450 0.42155

19 134 87,500 0.37165

20 142 90,000 0.37

- 29 -[L:!] [ EMB/I#) L[LD [i¥il IN

TABLE 2

SOIL PROPERTIES USED IN DECONVOLUTION

Layer Damping,Max. Shear Shear

Depth Strain, Modulus, %No.% ksf

1 0.0042 1710 2.8

5 12 0.0159 1650 5.6

123 0.0289 1736 7.0

4 0.0347 2012 7.0

5 0.0392 2194 7.036

6 0.0469 2188 7.0

7 0.0537 2115 7.049

8 0.0636 2024 7.0

9 0.0711 1985 7.063

10 0.0787 1943 7.0

11 0.0885 1809 7.0

12 0.0928 1828 7.0

13 0.0966 1820 7.0

14 0.0965 1877 7.0

15 0.0909 1932 7.0

16 0.0837 2044 7.0

17 0.0703 2279 7.0

155 18 0.0690 2371 7.0

- -30_ [LD[Rle/IM LUMIM

TABLE 3

SOIL-TANK MODEL PROPERTIES

Mass Modulus of Poisson'sMaterial Density, Elasticity, Ratio,

lbs-sec2/ft4 ksf u

Steel 15.217 396.72 x 104 0.300

Concrete 4.658 54.72 x 104 0.150

Insulating Concrete 0.932 2.88 x 104 0.150

Backfill - Layer 1 3.727 4561.0 0.200

Layer 2 3.727 4880.0 0.200

Layer 3 3.727 8527.0 0.200

Layer 4 3.727 12000.0 0.200

Soil - Layer 5 3.540 4755.0 0.230

Layer 6 3.665 5192.0 0.180

Layer 7 3.354 8890.0 0.270

Layer 8 3.944 12510.0 0.390

Layer 9 3.571 13348.0 0.420

Layer 10 3.354 13776.0 0.435

Layer 11 3.354 14976.0 0.440

- 31 -9 MEMB/IMBILIABM IN

TABLE 4

HYDROSTATIC AND HYDRODYNAMIC PRESSURES

Soil-Tank Steel Tank Coordinates, ft Hydrostatic HydrodynamicModel Model Pressure* Pressure

Node No. Node No. R Z ksf ksf

104 1 31.08 617.76 0 02 32.29 617.76 0 0

119 3 33.50 617.76 0 0133 4 36.50 617.76 3.521 0.787147 5 37.00 617.90 3.507 0.808161 6 37.37 618.26 3.468 0.802175 7 37.50 618.76 3.415 0.814190 8 37.50 619.74 3.305 0.813205 9 37.50 620.83 3.195 0.812220 10 37.50 622.83 2.983 0.809

11 37.50 624.58 2.797 0.804235 12 37.50 626.33 2.612 0.798

13 37.50 628.08 2.426 0.791250 14 37.50 629.83 2.240 0.782

15 37.50 631.54 2.059 0.772265 16 37.50 633.25 1.878 0.760

17 37.50 635.25 1.666 0.744280 18 37.50 637.25 1.454 0.726

19 37.50 639.75 1.188 0.699295 20 37.50 642.25 0.923 0.668

21 37.50 644.25 0.711 0.640310 22 37.50 646.25 0.499 0.608

23 37.50 648.01 0.312 0.577325 24 37.50 649.50 0.312 0

25 37.50 650.50 0.312 0340 26 37.50 651.50 0.312 0349 27 37.50 652.60 0.312 0358 28 37.50 653.70 0.312 0366 29 37.40 654.59 0.312 0375 30 37.11 655.43 0.312 0383 31 36.63 656.19 0.312 0391 32 36.00 656.82 0 0

33 35.00 657.50 0 0397 34 34.00 658.11 0 0

* Pressure includes 5-foot water pressure in vapor space

-32 _ 06 FJMS/BLU[IMIR

1 - 1

TABLE 5

LONGITUDINAL INTERNAL FORCES IN PRIMARY TANK

Soil-Tank Coordinates Hydrostatic Hydrodynamic Dead + Live Load EarthquakeModel

R Z Mom. Force Mom. Force Mom. Force Mom. ForceNode No. ft ft kft/ft k/ft kft/ft k/ft kft/ft k/ft kft/ft k/ft

104 31.08 617.76 0.016 4.30 0.000 0.45 -0.014 6.60 0.015 1.65119 33.50 617.76 0.109 4.24 0.001 0.47 0.055 5.48 0.070 1.31119 33.50 617.76 0.098 4.02 0.001 1.61 0.046 2.27 0.058 0.47133 36.50 617.76 -0.597 3.56 -0.003 1.16 -0.530 -0.36 0.653 2.10147 37.00 617.90 -0.489 2.72 -0.260 1.46 0.427 -2.80 0.244 4.12161 37.37 618.26 -0.253 2.85 -0.308 1.45 0.766 -2.22 0.650 3.67175 37.50 618.76 0.156 1.35 -0.125 0.95 0.527 -1.52 0.522 2.12

W 190 37.50 619.80 0.629 5.18 0.188 2.55 -0.032 -2.09 0.055 1.44W 205 37.50 620.83 0.661 5.28 0.224 3.55 -0.113 -3.91 0.064 2.89

'

205 37.50 620.83 0.022 3.58 0.037 1.94 -0.097 -0.11 0.057 0.53220 37.50 622.83 0.343 3.64 0.013 3.04 -0.004 -2.34 0.014 1.71235 37.50 626.33 0.026 1.83 -0.022 3.22 0.004 -1.91 0.005 1.26235 37.50 626.33 -0.021 4.63 0.003 3.80 0.000 -1.90 0.000 1.02250 37.50 629.83 -0.053 3.65 -0.020 4.14 -0.001 -1.87 0.001 0.90265 37.50 633.25 -0.002 3.44 0.000 4.15 0.000 -1.79 0.001 0.78 1280 37.50 637.25 0.007 3.64 0.004 4.11 0.000 -1.71 0.001 0.27295 37.50 642.25 0.000 3.13 0.003 3.54 0.000 -1.61 0.000 0.31310 37.50 646.25 -0.012 2.96 0.033 3.40 0.000 -1.54 0.001 0.58325 37.50 649.50 -0.018 4.20 -0.043 0.66 0.000 -1.50 0.001 0.55325 37.50 649.50 0.012 2.92 -0.020 2.26 0.001 -1.48 0.001 0.74340 37.50 651.50 0.006 3.60 0.004 1.69 -0.002 -1.56 0.001 0.92349 37.50 652.60 0.056 3.67 0.015 1.39 -0.022 -1.53 0.018 1.05

4 358 37.50 653.70 0.025 3.77 -0.004 1.08 -0.004 -0.04 0.007 2.03

9 366 37.40 654.59 -0.024 3.07 -0.016 0.73 0.022 -1.17 0.021 1.56375 37.11 655.43 -0.105 2.54 -0.014 0.62 0.043 -1.12 0.057 1.33

a 383 36.63 656.19 -0.184 3.17 -0.013 0.60 0.045 -1.59 0.056 3.31391 36.00 656.82 0.254 5.44 0.029 0.60 -0.148 -2.79 0.213 2.90r

C liiiil

TABLE 6

CIRCUMFERENTIAL INTERNAL FORCES IN PRIMARY TANK

Soil-Tank Coordinates Hydrostatic Hydrodynamic Dead + Live Load EarthquakeModel Mom. ForceR Z Mom. Force Mom. Force Mom. ForceNode No. ft ft kft/ft k/ft kft/ft k/ft kft/ft k/ft kft/ft k/ft

104 31.08 617.76 0.005 1.29 0.000 0.14 -0.005 5.08 0.005 6.15119 33.50 617.76 0.034 1.55 0.000 - 2.63 0.017 4.85 0.022 6.73119 33.50 617.76 0.035 1.69 0.000 - 4.37 0.016 6.28 0.025 12.31133 36.50 617.76 -0.192 1.80 -0.001 - 7.08 -0.175 5.06 0.212 13.29147 37.00 617.90 -0.164 6.72 -0.080 - 7.18 0.115 9.37 0.058 9.04161 37.37 618.26 -0.088 25.39 -0.095 - 4.71 0.226 19.92 0.189 4.32175 37.50 618.76 0.044 53.23 -0.038 2.35 0.158 24.83 0.156 13.04190 37.50 619.74 0.189 104.22 0.057 21.09 -0.009 15.97 0.017 12.24

r 205 37.50 620.83 0.198 122.11 0.067 31.46 -0.034 4.12 0.019 4.57205 37.50 620.83 0.007 104.41 0.011 26.64 -0.028 4.27 0.017 4.50220 37.50 622.83 0.010 104.25 0.004 30.48 -0.001 0.93 0.003 0.48235 37.50 626.33 -0.008 89.77 0.000 29.25 0.001 0.08 0.002 0.21235 37.50 626.33 0.006 90.61 0.001 29.42 0.000 0.08 0.000 0.27250 37.50 629.83 -0.016 78.58 -0.006 29.57 0.000 0.01 0.000 0.23265 37.50 633.25 -0.001 63.37 0.000 28.04 0.000 0.01 0.000 0.16280 37.50 637.25 0.002 45.83 0.001 26.49 0.000 0.00 0.000 0.20295 37.50 642.25 0.000 25.73 0.001 - 24.00 0.000 0.00 0.000 0.20310 37.50 646.25 -0.004 11.00 0.010 21.26 0.000 - 0.01 0.000 0.18325 37.50 649.50 -0.005 13.74 -0.013 0.39 0.000 0.08 0.000 0.10325 37.50 649.50 0.004 10.25 -0.006 0.82 0.000 - 0.03 0.000 0.16340 37.50 651.50 0.002 12.60 0.001 0.09 0.000 - 0.22 0.000 0.47349 37.50 652.60 0.017 7.64 0.004 - 1.46 -0.007 1.82 0.055 1.23

C 358 37.50 653.70 0.007 - 4.08 -O.001 - 4.89 -O.001 6.96 0.002 5.45 366 37.40 654.59 -0.008 - 22.52 -0.005 - 8.05 0.007 14.32 0.006 11.15# 375 37.11 655.43 -0.032 - 34.20 -0.004 - 8.04 0.013 14.88 0.017 -11.89

-0.053 - 24.18 -0.004 - 5.19 8.40 0.016 2.71 383 36.63 656.19 0.012

391 36.00 656.82 0.078 1.84 0.009 - 1.48 -0.044 0.34 0.064 8.79rC liiiil

TABLE 7

INTERNAL FORCES IN CONCRETE TANK DUE TO EARTHQUAKE

Longitudinal Circumferential

Area Moment Force Moment ForceNodalPoint

kft/ft k/ft kft/ft k/ft

16 0.044 3.72 0.061 0.5030 0.030 4.70 -0.097 3.6845 0.048 5.41 0.322 6.5560 0.096 7.09 0.373 10.1275 0.242 9.22 0.362 13.60

G 90 1.512 11.22 -0.173 19.440 105 1.762 13.11 0.322 29.41

120 3.345 15.54 0.488 40.25134 4.683 17.45 0.794 46.87148 5.444 18.14 1.058 48.47162 6.481 12.50 1.316 50.30177 0.597 7.04 0.357 50.14193 0.005 2.75 0.388 49.29

191 0.043 5.52 0.196 44.73206 4.505 9.68 -0.502 38.78221 4.801 10.95 -0.588 30.36236 5.568 10.46 -0.785 13.43251 5.831 8.51 -0.892 5.73

'... 266 3.151 7.10 -0.533 12.019 281 2.825 5.50 -0.514 18.903 296 2.280 4.09 -0.461 25.31

311 1.290 3.43 -0.342 33.36326 2.352 3.56 -0.516 41.36341 3.262 3.85 -1.047 54.13350 6.303 4.95 -2.231 77.50359 10.600 4.06 -3.755 96.62

359 10.960 6.98 -0.824 16.46367 10.535 6.98 -0.651 15.36376 9.469 6.52 -0.384 13.21384 7.999 6.19 -0.289 14.34391 6.371 6.03 -0.213 15.10397 4.922 4.25 0.105 12.03403 0.951 2.81 0.174 19.91

I

f 408 0.086 2.39 0.456 24.28413 1.011 2.01 0.436 18.52418 0.756 1.93 0.360 14.07423 0.644 1.49 0.314 10.43427 0.547 1.09 0.262 7.18431 0.422 0.56 0.186 4.15435 0.220 0.49 0.065 1.28

- 35 - [LII [ ] e/INLLD MIN

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[LJ][1 e/MBLE:J [IMI [=

APPENDIX A

THERMAL-CREEP ANALYSIS OF

241-SY UNDERGROUND REINFORCED CONCRETE TANK STRUCTURE


by

Y. R. Rashid

APPENDIX A

THERMAL-CREEP ANALYSIS OF

241-SY UNDERGROUND REINFORCED CONCRETE TANK STRUCTURE


PURPOSE AND SCOPE

The 241-SY underground reinforced concrete structure is required to carry

sustained soil pressure and thermal loadings with sufficient margin against

degradation of its structural integrity during its design life. Under simi-

lar time invarient loading conditions, creep and cracking generally develop,

initially in transient modes which tend towards self-limiting processes.

The main objective of the present study is to determine whether the self-

limiting cracking and creep deformations in the tank structure during opera-

tion can be verified by appropriate analyses.

The main structural components of the 241-SY tank are:

a) Concrete, which provides compressive capability and is subject to creep

and cracking.

b) Meridional, hoop, and diagonal reinforcement designed to resist or limit

circumferential, radial, and split cracks, respectively.

c) Secondary steel plate liner, which provides leak-tight seal.

While the steel reinforcement and liner are designed to remain elastic, it

is possible that yielding may occur as a result of excessive deformations

or due to the formation of wide cracks. Similarly, the concrete is designed

to remain stressed well below its ultimate strength, but excessive cracking

or misplacement of reinforcement could result in the compressive failure of

the concrete in some localized regions. These aspects are qualitatively

accounted for in the design; the present analysis, however, provides quanti-

tative assessments of these design considerations.

The analysis is highly dependent on the material properties of the structural

constituents, particularly the creep data of the concrete. Because of therelatively high temperature, 250'F, the concrete undergoes thermally activated

-56- [LON]8/IMBLO=DOMIN

J

creep of much larger magnitude than generally encountered in ordinary concrete

structures. Even highly specialized structures, such as prestressed concrete

pressure vessels for gas-cooled reactors, are designed to operate at lower

tempetatures. Therefore, it was of necessity that detailed time-dependent

analysis be performed to verify the structural integrity under such severe

conditions. Although the operating life of the structure may be several dec-

ades, the analysis time need extend only until self-limiting cracking and

creep deformations are established and the results can be safely extrapolated

to the end of life. In other words, stable deformation and cracking condi- '

tions should prevail after only a few years of tank operations, and the anal-

ysis time may be restricted to a small fraction of the design life. This

premise rests on the assumption that the loadings, which include temperature

and soil pressure, remain constant with time.

COMPUTER PROGRAM AND FINITE ELEMENT GRID I

The computer program, SAFE-CRACK, applied to the analysis of this tank is

based on the finite element method for which the structure is idealized as:

a) Triangular axisymmetric elements for the concrete.

b) Uniaxial tension-compression elements for the reinforcement.

c) Axisymmetric membrane elements for the secondary liner.

The reinforcement is placed along the element edges to ensure bond compatibi-

lity between the concrete and reinforcement. Because of the axisymmetric

idealization, the meridional reinforcement is assumed to be continuous in

the hoop direction but with zero hoop stiffness. Reduction of the elastic

modulus of the reinforcement, to account for the concrete and reinforcement

occupying the same position, is made appropriately.

The finite element grid consists of 402 nodes, 660 concrete elements, 66

liner elements, 153 meridional and diagonal reinforcement elements and 148

hoop reinforcement elements. The basic grid, namely, the triangular elements

are placed five layers (10 elements) across the thickness maintaining an

aspect ratio of 4.3 approximately. Based on experience with this type of

analysis, this.as.pect ratio, although larger than desired, is selected to

provide good accuracy while maintaining reasonable running time.

- 57 - 0=01*e/MB L U[Vil IN

MATERIAL PROPERTIES

The material properties and mechanical behavior of concrete and reinforcement

are described below:

a) The concrete is assumed to be elastic-perfectly plastic in compression

and elastic-cracked in tension with the following material data:

Compressive Strength Cault) = 4500 psi at 28 days

Modulus of Elasticity (E) = 3.8 x 106 ps;

Poisson's Ratio (v) = 0.15

Coeficient of Thermal Expansion (a) = 6.38 x 10-6 in./in./oF

Tensile Strength (a ) = 450 psicrack

b) The liner and reinforcement steels are assumed to be elastic-perfectly

plastic with the following average properties:

Liner

Yield Strength (a ) = 35000 psiyieldModulus Elasticity (E) = 27.7 x 106 psi

Poisson's Ratio (v) = 0.3

Coeficient of Thermal Expansion (a) = 6.38 x 10-6 in./in./0F

Reinforcement

Yield Strength ('yield) = 60000 psi

Modulus of Elasticity (E) = 27.7 x 106 psi

Coeficient of Thermal Expansion (a) = 6.38 x 10-6 in./in./oF

c) Creep data for concrete with properties somewhat different than given

above are built into the SAFE-CRACK program. Multiplication by the ratioE

of the two concrete elastic moduli program concrete is used to adjustEtank concrete

the program creep data for the tank concrete.

The ratio is computed internally by the program as a function of temperature

and age. For the case at hand, this ratio is larger than unity, implying

that the tank concrete is softer than the built-in properties. The creep

data in SAFE-CRACK are somewhat complicated expressions of temperature and

age. To provide useful information in this report the adjusted creep curves,

including the elastic response, for the temperatures of 70'F, 150'F, 200'F,

250'F and 300'F and for the initial age of 60 days are plotted in Figure 1.

- 58 _ Xgle3/®[LUMIE

Creep curves for other temperatures can be obtained from Figure 1 by linear

extrapolation. The computer program, however, describes the creep data as

continuous functions of temperature and age. It should be noted that the

temperatures in the tank assumed for this analysis range from 65'F before

heating to 250°F at the end of a 30 days heating period. The age of the

concrete at the start of the heating period is assumed to be 90 days.

ANALYSIS PROCEDURE

As mentioned earlier, the computer program used is SAFE-CRACK. The basic

triangular finite element grid was first established. The steel reinforce-

ment areas were determined from the structural drawings, lumped into uniaxial

elements, and placed along the triangular element boundaries as close as pos-

sible to their original positions. This ensured full bonding compatibility

between the concrete and reinforcement.

The meridional and diagonal (radial) reinforcement, being discontinuous in

the circumferential direction, were modeled as continuous shells but with

zero hoop stiffness. The hoop reinforcement, being geometrically axisym-

metric, was represented exactly in the grid and placed at the nodes closest

to their original positions.

The liner elements were modeled as axisymmetric membrane shell elements, i.e.

with extensional (no bending) meridional and hoop stiffness. These elements

were placed at the inner surface between each pair of nodes. By virtue of

the no-bending properties of these elements, the liner and concrete elements

remain in intimate contact with each other during deformations, implying

that the liner is anchored continuously to the concrete.

The loading, other than thermal, consisted of:

a) Soil overburden extending 6.5 feet above the crown with unit weight of

120 pcf.

b) Live load of 40 psf.

c) Vapor pressure of -6 inches of water at the top inner surface of the dome.

- 59 -U 1*} e/IMBL ] M IN

The soil was assumed to be fully saturated and therefore the soil overburden

was treated as a hydrostatic load on the outside surface of the tank.

The boundary conditions at the bottom were assumed to be sliding with zero

rotation. This type of boundary condition is specified in the design. As

will be discussed later, the sliding condition showed no harmful effects on

the tank according to analysis results.

In order to simulate the tank structure being heated from 65'F to 250'F for

30 days, the thermal loading was treated as pseudo steady state where the

temperature at any time after heating began were obtained by linear extrapo-

lation between the initial (65'F) temperatures and the final temperatures.

This was considered a close approximation to the true transient temperature

field since the heating rate is quite slow.

The time history of the analysis consisted of 30 time steps. The first step

at zero time (corresponding to the age of 90 days) considered only the mech-

anical loads. Time steps 2 through 11 considered the thermal loading as 10%

increments each 3 days. The rest of the time steps covered a period of

approximately 5.5 years and extended the analysis much beyond the time nec-

essary to establish that stable conditions will prevail in the tank struc-

ture during operation.

The output of the computer program consists of:

a) Input data printed for reference

b) The concrete relaxation moduli

c) The element temperature histories

d) The finite element grid description

e) Nodal displacements at each step

f) Element stresses and strains at each step

The last three items are used to study the response of the tank and are

transmitted along with the other output data as a supplement to this report.

-60-[LJ] Mj /IMB LUMM

DISCUSSION OF THE ANALYSIS RESULTS

Figure 2 shows a plot of the axial displacement at the crown as a function

of time. As can be noticed, the initial value, i.e. due to soil pressure

alone is (small) positive in spite of the top overburden. Evidently the

lateral hydrostatic soil pressure over a projected depth of 55 feet is the

cause for net upward displacement at the crown. As heating begins, a nega-

tive crown displacement results because the upward and outward displacement

due to the free thermal expansion is counteracted by a negative thermal

moment. It should be stated that during heating, cracking develops, and

part of the thermal forces are therefore dissipated. At the end of 30 days

all loadings had reached constant values, and the displacement at the crown

followed a rapid transient creep process in the direction of free thermal

expansion, i.e., towards the positive direction. This is in agreement with

the expected behavior of thermal creep problems where the steady state re-

sponse of the structure, after thermal stresses relax out, is primarily con-

trolled by the free thermal expansion.

This general behavior is more evident in Figure 3 where the deformed outer

surface is plotted at 30 days and 2000 days. As mentioned above, the 30-day

deformations show clearly the influence of the thermal moment on the dome.

As the thermal moment relaxes out the deformations tend towards the free

thermal expansion shape as shown by the 2000-day deformed shape. In contrast

with the behavior of the dome, the cylindrical portion of the structure pre-

dictably deformed uniformly outwards due to the thermal loading followed by

a uniform inward deformation under creep.

The cracking behavior of the structure is presented in Figures 4 through 8.

Figures 5 and 6 show the extent of the radial cracks which are caused by the

hoop stresses and Figures 7 and 8 show the extent of the meridional cracks

which are caused by the maximum principal stresses in the R-Z plane. These

figures also show that the majority of the cracks occurred during heating.

With the exception of the haunch region, the cylindrical portion of the

structure is free of cracking.

The most significant fact which needs to be pointed out is that the meridional

cracks are primarily of the split type, i.e., the crack surfaces are in the

- 61 -9 M} Mj/IMB L &0 11 IN

general direction·of the middle surface of the shell. This type of crackcan be controlled by diagonal reinforcement which runs perpendicular to the

middle surface of the structure. The original design provides for such re-

inforcement in the haunch ar4a only. It appears from Figure 5 that the

diagonal reinforcement is required throughout the dome and to a distance

of at least 8 ft. below the outer dome-to-cylinder junction.

By examining the output, in particular the hoop and the principal strains

in the cracked elements, one can easily see that the magnitudes of the hoop

strains are quite small, indicating that the circumferential reinforcement

adequately provides for limiting the radial cracks. Similarly the principal

strains in meridionally cracked elements in the haunch area, where diagonal

reinforcement exists, are also limited to about 1%. This is considered

small and hence stable. In contrast, however, the principal strains approach

10% in the crown, where meridional cracks dominate and where there are no

diagonal reinforcements. Without diagonal reinforcement to limit these cracks,

they might increase in an unstable manner.

The stresses in the liner and reinforcement remain well below the yield

stresses of the materials. This reinforces the other findings of this anal-

ysis that no structural instability is evident.

CONCLUSIONS AND RECOMMENDATIONS

The present analysis indicates the following:

1) The structure is stable under the loading conditions given.

2) Sliding boundary condition at the base, as provided for in the design,

is adequate.

3) The liner and reinforcement remain elastic and hence no unbounded de-

formations occurred. See Stress Table (Table 1).

4) The radial crack sizes, i.e., hoop strains in the cracked elements,

are quite small indicating adequate hoop reinforcement.

5) The meridional crack sizes, i.e., principal strains in the crackedelements, range from about 1% in the haunch area where diagonal re-

inforcement exists to about 8% in the crown area where diagonal re-

inforcement is absent. It is recommended, therefore, that diagonal

- 62 - [1=0 [e #3/IMB & 0.0 WA M

reinforcement be extended throughout the dome and to a depth of at least

8 feet below the dome-to-cylinder junction (at elevation 654.84ft.)

6) The analysis of the primary steel tank and the weld junction connect-

ing the primary tank to the secondary liner was not within the scope

of this analysis. Therefore, no evaluation of the particular area

of structure can be given in this report.

- 63 - [1 [Re/ [L[!J 1] ] IR

TABLE I

HIGHEST STRESSES IN THE STRUCTURE

TimeStructural Stress* Stress Occurred,Component Location psi type Days

Concrete Crown -3000 radial 30

(Principal)

Liner Crown 26000 radial and hoop 30Dome -13000 meridional 30

Reinforcement Crown -25000 hoop 2000 daysHaunch 7000 meridional 2000 days

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[L ] MB#3/IMBO=WOMIM

INVESTIGATION TO DETERMINE

DYNAMIC SOIL PROPERTIES

AT THE

241-SY TANK SITE

-1



AT THE

241-SY TANK SITE

prepared for

ATLANTIC RICHFIELD HANFORD COMPANY

October 1974

by

URS/John A. Blume & Associates, Engineers

Sheraton-Palace Hotel

130 Jessie Street

San Francisco, California 94105



AT THE

241-SY TANK SITE

CONTENTS

.2295.

INTRODUCTION .................... ... 1

FIELD INVESTIGATIONS .................... .

Drilling ................................................. .... 1

Geophysical Measurements ............................................ 3

DYNAMIC SOIL PROPERTIES .................................. 3

Design Modulus Values .........................,........... 10

REFERENCES ............................................... 11

FIGURES

1 Drill Hole 1 and Seismic Refraction Lines 1 and 2, SitePlan 241-SY Waste Storage Tanks ...........................:...... 2

2 Seismic Refraction Line 1, 241-SY Waste Storage Tanks ............. 4

3 Seismic Refraction Line 2, 241-SY Waste Storage Tanks ............. 5

4 Drill Hole 1: Shear (Vs) and Compressional (V ) Velocities, 241-SYWaste Storage Tanks ............................................... 6

5 Maximum Elastic Moduli of Foundation Materials, 241-SYTank Site ...................................····················.. 8

6 Design Elastic Moduli as a Function of Strain, 241-SYTank Site .......................................... ............... 9

APPENDIX A Driller's Log ............... . ... A.1-A.2

Grain Size Classification ..... ... A.3-A. 7

- ii -9 [FR #3/IM SLD [R:AIN



AT THE

241-SY TANK SITE

INTRODUCTION

This report describes results of a subsurface geophysical investigation

carried out at the 241-SY waste storage tank site located in the 200 West

area of the Hanford Atomic Energy Commission Reservation near Richland, Wash-

ington. The work was conducted by URS/John A. Blume & Associates, Engineers,

for Atlantic Richfield Hanford Company (ARHCO) of Richland, Washington. The

investigation consisted of drilling and logging one drill hole to a depth of

150 feet and measuring shear and compressional wave velocities in this drill

hole. Seismic velocities were also measured by refraction techniques across

the ground surface. Dynamic soil properties to be used in seismic analysis

of the tanks were derived from geophysical measurements.

The drilling was completed in late February 1974, and geophysical measure-

ments were carried out in early March. The investigation was directed by

Andrew Cunningham, who also prepared this report with the assistance of

Fred Kintzer.

FIELD INVESTIGATIONS

Drilling

Exploratory drilling at the site was carried out by Hatch Drilling Company

of Richland, Washington, who also compiled the driller's log (shown inAppendix A). Drilling was done using cable tool equipment, and samples were

collected at 5-foot intervals. Steel casing with an approximate diameter of

6 inches was installed in the hole as the drilling proceeded. Representa-

tive soil samples were selected and delivered to a soils laboratory for test-

ing to classify and identify the soils according to ASTM procedures. The

location of drill hole 1 at the 241-SY tank site is shown in Figure 1.

-1- 06 m3 #3/IMB 0= CWWAIN

X 408 SCALE : 1" • 100'

<PUTURE -rANKS .\

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N 86388 1

td< CO.0.

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FUTURE TAN 19,-X

'241- SY TANK FARM

DRILL HOLE / ANS SEIS/V\1CREFRACTION LINES Z AN'·D·2SITE PLAN

24 1-SY TAN/< S/TE FIGURE 1

-2-

9 R) #3/ [L OSM IM

Geophysical Measurements

Geophysical measurements at the site consisted of uphole determinations of

shear and compressional wave velocities and measurements of velocities of

horizontally propagated shear and compressional waves on the ground surface

by seismic refraction techniques. The seismic refraction data confirm that

the velocities measured in the drill hole were comparable to those measured

by refraction techniques around the peri.phery of the drill hole and that the

moduli data, derived from drill-hole measurements, can be extrapolated for

the area surrounding the drill hole.

Uphole velocity measurements were performed in drill hole 1 at the 241-SY

tank site using a triaxial uphole seismometer probe to record the seismic

waves produced by an 8-pound sledge hammer at the ground surface. Electric

signals from the velocity-sensitive geophones were transmitted to the sur-

face via a multiconductor cable. At the surface, the signals were amplified

and recorded on a 6-channel oscillograph recorder. Seismic-wave velocities

were measured at 10-foot intervals as the probe was pulled up from the bot-

tom of the drill hole.

Seismic refraction measurements at the ground surface were made using a

Bison portable seismograph, model 15708, and a 6-channel oscillograph

recorder in conjunction with a triaxial seismometer array. An 8-pound

sledge hammer was again used as the energy source for the surface measure-

ments. Locations of the seismic refraction lines are shown in Figure 1.

Seismic refraction line 1 extends 200 feet to the northeast from drill hole

1, and seismic refraction line 2 extends 200 feet in a southeasterly direc-

tion. Time-distance plots for the seismic refraction lines are shown in

Figures 2 and 3, and a time-depth plot of uphole seismic measurements is

shown in Figure 4.

Time-distance and time-depth graphs are constructed by plotting travel time

against impact distance. Travel time is the time required for the seismic

wave to travel from the energy source, in this case the sledgehammer impact,

to the detector. The impact distance along a surface refraction line is the

distance along the ground between the detector and the point of impact.

-3-

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-6- U [ ]e/IML[!=0 [1 0 IN

Impact distance on a time-depth graph is the vertical distance between the

energy source at the ground surface and the detector, which was positioned at

10-foot intervals down the drill hole. The slope of a line connecting a series

of points on these graphs is equal to the velocity of the wave passing through

the ground. The depths to various soil layers beneath the ground surface can

be derived from the surface refraction measurements using known principles of

wave propagation and refraction. Depths to soil layers having different seis-

mic velocities can be observed directly on the time-depth graphs.


Dynamic soil properties were derived for the 241-SY tank site from on-site

seismic measurements of shear and compressional wave velocities of verti-

cally propagated seismic waves. Laboratory measurements of moduli on

selected samples obtained in drilling were not undertaken because of special

problems with soils of the Hanford Reservation: because the soils are unce-

mented, it is not possible to keep samples in an undisturbed condition

throughout the sampling and testing procedures, and the relatively high con-

tent of gravels makes it impossible to test much of the material.

Calculated values of shear modulus for comparison were obtained by convert-

ing blow counts recorded during drilling into estimated soil densities using

Gibbs and Holtz's criteria (1957). Using these densities, shear-wave veloc-

ities were calculated by means of formulae derived by Hardin and Richart

(1963). Values of shear modulus at various depths were then derived from

these calculated velocities. Although the reliability of density measure-

ments based on blow counts has been questioned and the data of Hardin and

Richart were extrapolated in these calculations, reasonable similarity was

observed in the two sets of data. Shear moduli derived from measured shear-

wave velocities at the tank site were lower.

The shear modulus for low strain levels, G , calculated from shear-wavemax

velocities, is shown in Figure 5 as a function of depth below ground surface.

Shear modulus is shown in Figure 6 as a decreasing function of strain level.

The moduli are expressed as ratios of the maximum values shown in Figure 5.

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Z[kQ-

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0

100 1

/500 /0 20 30 40

MAXIMUM SHEAR Al°OULUS (KS')

MAAXZMUM 5 LASTX C M°/'PULI °PFOUNOATZON MATERJALS

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SMEAR STRAIN e)

DESIGN ELASTIC MODUL/ ASA F u N C TION OF STR,Al N< AFTER SEED AN/> 18)RISS, /970)

2 4 1 -SY TAN,'< SIT E FtGURE Co

-9- 0=0 M #j/IMB [L[LO M IN

Design Modulus Values

The design curves in Figures 5 and 6 are recommended for the 241-SY wastestorage tanks. For any depth and shear strain, the appropriate modulus canreadily be computed from Figures 5 and 6. For example, the shear moduluscorresponding to a shear strain of 2 x 10-2% at a depth of 50 feet can beevaluated as follows: from Figure 5, G = 31 ksi; the modulus ratio cor-maxresponding to the strain is found from Figure 6 to be 0.65; the desired shear

modulus, G, is then 0.65(31 ksi) = 20.4 ksi.

- 10 -9 [ 8/IMB [L [LS [MI E

=,

REFERENCES.-1

Bechtel Corporation, October 1971, Final Soil Investigation Report for

the Fast Flux Test Facility, Richland, Washington.

Gibbs, H. J., and W. G. Holtz, 1957, "Research on Determining the Densityof Sand by Spoon Penetration Test," Proceedings, Fourth International

Conference on Soil Mechanics and Foundations Engineering, v. 1, pp. 35-39.

Hardin, B. 0., and F. E. Richart, February 1963, "Elastic Wave Velocities

in Granular Soils," Journal of Soil Mechanics and Foundations Division,

ASCE, v. 89, no. SM1, pp. 33-65.

John A. Blume & Associates, Engineers, April 1971, Seismic Analysis of

Underground Waste Storage Tanks 241-AZ-101 and 102 at Hanford, Washington,

JABE-ARHCO-01.

Seed, H. B., and I. M. Idriss, 1970, '"Soil Moduli and Damping Factors for..'

Dynamic Response Analysis," Report No. EERC 70-10, Earthquake Engineering

Research Center, University of California, Berkeley.

Shannon and Wilson, Inc., June 30, 1972, Supplementary Soils Investiga-

tion, Washington Public Power Supply System, Hanford No. 2 Nuclear Power

Plant.

.....

- 11 -06/#3/05&8=0[ 1

r.

-

APPENDIX A

DRILLER'S LOG

DEPTH SAMPLE BLOWCOUNTDESCRIPTION

(ft) Depth Type (blows/inches)

Medium, brown, silty, fine- 0 3.0 D*to-medium sand withoccasional fine-to-coarsegravel and roots 5.0

Dense, gray, fine sandy, 7.0 Dfine-to-coarse gravel 10with some silt

12.0

Very dense alternate layers 14.0 D 31/12"of gray fine-to-medium 17.0 N** 50/5"sand and gray-brown 20 19.0 D 26/12"silty fine sand with 22.0 N 50/5"occasional 2"-lenses 25.0 N 50/6"of hard, sandy silt 30 31.0 N 50/6"

36.0 50/2"35.0 N

Very dense gray-brown,slightly silty to silty, 40medium-to-coarse sand 41.0 D 41/12"

and fine-to-coarse

gravel (42' to 49',very gravelly) 49.0

Very dense, light brown, 50 50.0 N 50/3"slightly silty to silty,

55.0 D 17/6"fine sand with somefine-to-coarse gravel 59.0 N 50/3"60and medium-to-coarsesand 63.0

Very dense, light brown, 65.0 N 50/5"silty, fine-to-mediumsand with occasional 70 70.0 N 50/4"1/2"-lenses of sandy 75.0 N 50/4"Silt 79.0 N 50/5"

80

85.0 D 16/6"

89.5 D 24/6"90 90.0 N 50/5"

95.0 D 18/6"

- A. 1 -ag Ipmj/IMBLUJIB:f[' E

APPENDIX A

DRILLER'S LOG

(cont.)

DEPTH SAMPLE BLOWCOUNTDESCRIPTION

(ft) Depth Type (blows/inches)

Very dense, light brown, 100 100.0 D 22/6"silty, fine-to-medium 100.5 N 50/5"sand with occasional 105.0 D 21/6"1/2"-lenses of sandySilt 109.5 D 22/6"

110 110.0 N 50/4"

115.0 D 21/6"

119.5 D 21/6"120 120.0 N 50/4"

124.5 D 18/6"127.0

129.5 D 24/6"Alternate lenses of silt 130 130.0 N 50/3"

and silty fine-to-mediumsand 135.0 D 21/6"

140 140.0 D 17/6"140.5 N 50/5-1/2"145.0 D 18/6"

149.5 D 17/6"150.0 150 150.0 N 50/5"

Bottom of boring

* D denotes 5"-diameter sampler using 1400 1b hammer, 30" drop

** N denotes standard penetration resistance

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«te 50:»,«i, .ซปซ1' 3 i,» «flt, ' . , 1 f - International Nuclear ...

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