ebmud digester seismic assessment - draft 8-5-14 · references american concrete institute (aci)...

Technical Memorandum

Limitations: This is a draft memorandum and is not intended to be a final representation of the work done or recommendations made by Brown and Caldwell. It should not be relied upon; consult the final report.

201 N Civic Drive, Suite 115 Walnut Creek, CA 94596 T: 925.937.9010 F: 925.937.9026

Prepared for: East Bay Municipal Utility District

Project Title: Digester Upgrades Planning

Project No.: 137180

Subject: Digesters 2, 3 and 4 Preliminary Seismic Evaluation

Date: August 5, 2014

To: Alicia Chakrabarti

From: Adam Ross

Copy to: File

Prepared by:

Eric Wilkins, Project Engineer California License C 78683

Reviewed by:

Edgardo Quiroz, Managing Structural Engineer California License S 4906

Technical Memorandum Digesters 2-4 Preliminary Seismic Evaluation

ii

DRAFT for review purposes only. Use of contents on this sheet is subject to the limitations specified at the beginning of this document.

Table of Contents Introduction ............................................................................................................................................................... 1

Section 1: Scope of Work ......................................................................................................................................... 1 1.1 Reference Materials ........................................................................................................................................ 1 1.2 Preliminary Seismic Evaluation Goals ............................................................................................................ 2 1.3 Assumptions and Limitations ......................................................................................................................... 2

Section 2: Findings and Recommendations of Previous Seismic Evaluations ..................................................... 2

Section 3: Preliminary Seismic Evaluation and Methodology ............................................................................... 3 3.1 Description of Structures ................................................................................................................................ 3 3.2 Methodology .................................................................................................................................................... 4 3.3 Preliminary Seismic Evaluation Results ......................................................................................................... 4 3.4 Recommendations .......................................................................................................................................... 5

Attachment A: Preliminary Seismic Evaluation Calculations .................................................................................. A

Attachment B: Internal Curb Detail ......................................................................................................................... B


1

DRAFT for review purposes only. Use of contents on this sheet is subject to the limitations specified at the beginning of this document. \\bcwckfp01\projects\137000\137180 - EBMUD Digester P2 Constr. Period\Phase 3 Planning\EBMUD Digester Seismic Assessment - DRAFT 8-5-14.docx

Introduction This Technical Memorandum (TM) discusses the results of the Preliminary Seismic Evaluation (PSE) of Digesters 2, 3 and 4 at the East Bay Municipal Utility District Main Wastewater Treatment Plant (EBMUD/District), presents the findings of previous seismic evaluation reports, and provides recommendations for mitigating structural deficiencies to minimize digester failure during the design seismic event. For this evaluation the main structural performance level required is “Life Safety”; however, to achieve this seismic performance level the digesters have to meet the “Collapse Prevention” performance level since the digesters are non-occupied but digester failure can be a life-threatening event. Digester failure is defined as the inability of the digesters to retain digester sludge during the design seismic event. The design seismic event as defined in the current California Building Code, 2013 edition, is the earthquake effects that are two-thirds of the corresponding Maximum Considered Earthquake (MCE) effects. The MCE is defined as the ground motion values from the USGS that have a 2 percent probability of being exceeded in 50 years, with a recurrence period of 2,500 years.

EBMUD requested Brown and Caldwell (BC) to review previous seismic evaluations reports for the digester complex and to perform an independent preliminary seismic evaluation, based on current seismic codes, to answer the following questions:

Do Digesters 2, 3 and 4 present a life safety issue during a design seismic event? What are the failure modes and the results of these failures?

Will the digesters fail during the design seismic event if they are empty or abandoned? What are the failure modes and the results of these failures?

What are the easiest and/or least expensive mitigation methods to fix the structural deficiencies?

Can the digesters accommodate new covers and what type?

The previous seismic evaluation reports have identified that Digesters 2, 3 and 4 are deficient in resisting seismic loads in their current operating condition. One of the objectives of this PSE is to identify the failure mechanisms and to evaluate the possibility for mitigating the structural deficiencies to minimize life-threatening risk.

Section 1: Scope of Work The PSE of EBMUD Digesters 2, 3 and 4 involves reviewing existing design drawings and previous seismic evaluation reports, and performing preliminary seismic calculations to identify potential failure mechanisms and provide conceptual-level rehabilitation techniques that would minimize digester failure. The findings of the existing document review, results of the PSE, and recommendations for mitigating seismic deficiencies, including conceptual level cost estimates, are presented in this TM.

1.1 Reference Materials The following documents were available for the PSE:

Contract Drawings for the Construction of Sludge Digestion Tanks and Control Building and Installation of Equipment, Project SD 50, dated 1950.

Contract Drawings for the Construction of Sludge Digestion Tank No. 4, Project SD 96, dated 1957.

Repair of Digesters 1, 2, 3 & 4, Project SD 180, dated 1988, prepared by John Carollo Engineers.

Technical Memorandum Digesters 2, 3 and 4 Preliminary Seismic Evaluation

2


Seismic Evaluation of Selected East Bay Municipal Utility District Wastewater Facilities, By EQE Engineering, dated July 1991.

Technical memorandum 1, Structural Evaluation of Digesters, by CH2MHill, dated December 2001.

1.2 Preliminary Seismic Evaluation Goals Based on the results of previous seismic evaluation done on Digesters 2, 3 and 4, the digesters present structural deficiencies to resist seismic loads. The main goals of the PSE are to identify the failure mechanisms during the design seismic event and to evaluate possible rehabilitation techniques for minimizing life-threatening risk.

1.3 Assumptions and Limitations The seismic evaluation is based on existing design documents and conservative estimates for material properties. The digesters are assumed to be in good condition. A structural evaluation of the digesters walls and existing pile foundation were not part of this scope and these structural elements are assumed to provide adequate performance for the Collapse Prevention performance level. These structural elements should be verified during the final seismic evaluation.

Section 2: Findings and Recommendations of Previous Seismic Evaluations EQE Engineering and CH2MHill have previously conducted seismic evaluations of the digesters and the following are their findings and recommendations:

EQE Engineering (July 1991)

Findings: Concrete curb at the base is inadequate to resist sliding during a seismic event. The base of the tank wall is inadequate to resist shearing. Uplift is possible during a seismic event. Recommendations: Provide a pile supported concrete collar around the perimeter of the tank and tied into the existing

foundation to resist sliding. Seismic cables can be attached to the wall and the new concrete collar to resist uplift. Attaching cables

to existing foundation is not recommended. If the concrete collar is too expensive, further analysis can be done with reduced fluid height or the

installation of a baffle system to reduce sloshing effects on the walls.

CH2MHill (December 2001)

Findings: Concrete piles are battered and will attract large forces during a seismic event. A seismic event could

likely damage the piles and the foundation. Concrete piles not detailed for ductility and will likely become damaged during a seismic event. Corbels have inadequate horizontal reinforcement to resist large vertical forces during a seismic event if

they are supporting the cover.


3


Covers are restrained from rotating with relatively weak guides. During a seismic event the guides will likely fail and the covers could rotate causing damage to the attached piping.

Sliding or rocking at the base is likely due to the minimal concrete curb.

Recommendations: Do nothing (structural deficiencies remain). Strengthen foundation with a pile supported concrete skirt; however this approach is prohibitively

expensive. Does not resolve issues with the corbels and covers. Take tanks out of service (similar to digester 1 which was converted to secondary containment for

chemical storage). Will require slight modification of base (new curb on inside) to restrain against sliding.

Section 3: Preliminary Seismic Evaluation and Methodology

3.1 Description of Structures Digesters 1 through 4 surround the Digester Control Building. Digesters 1, 2 and 3, and the Digester Control Building were built in 1950, while Digester 4, located on the north-east corner of the cluster, was built in 1957. The numbering system of the first four digesters changed to accommodate future digesters numbers with the pattern of having all odd number digesters on the south side of the complex and the even number digesters on the north end. The numbering is incremental from east to west. Therefore, the original Digester 1 became Digester 3, original Digester 2 became Digester 1, original Digester 3 became Digester 4, and original Digester 4 is currently Digester 2. This important to note since (current) Digester 2 was constructed with a slightly different design. Digester 1 was decommissioned, the cover removed, and the tank space converted into a chemical storage area. From this point on all references to digester numbers are based on the current numbering system.

The digesters’ foundation consists of a 1’-9” thick mat foundation supported by concrete piles. The mat foundation is sloped down to the center of the digester to form a cone. Digester 2 is supported by a total of 267 piles, with the 76 perimeter piles battered at a 3:1 angle. Digesters 3 and 4 are supported by a total of 245 piles – the perimeter piles are not battered.

Each digester is 95 feet in diameter (internal) and approximately 28 feet tall (sidewall). The digesters are partially buried and are approximately 9 feet below grade. The digester walls are made of reinforced concrete and are pre-stressed with post-tensioning rods. The rods are protected with a layer of shotcrete 2 inches thick. The lower 16 feet of the Digester 2 wall has a 12-3/4-inch core while the upper wall has an 11-1/4-inch core. The lower 16 feet of the walls for Digesters 3 and 4 have a 12-inch core while the upper wall has a 10-inch core. The digester walls rest on top of the mat foundation and are unanchored. There is an internal, unreinforced concrete wedge built into the mat foundation that partially restrains the digester walls.

The original digesters had 7/8-inch diameter post-tensioning rods. In 1988, John Carollo Engineers rehabilitated the existing digesters and replaced the above-grade post-tensioned rods on all four digesters, and the below-grade rods on Digesters 2 and 4 as well. The new post-tensioning rods have a diameter of 1-3/8-inches. Note that the existing rods below grade on Digester 3 remained in place.

Digesters 3 and 4 have floating steel covers from original construction. Digester 2 has a dual-membrane gas holder cover.


4


3.2 Methodology Based on the review of the design documents and previous seismic evaluations, BC identified the potential seismic deficiencies of Digesters 2, 3 and 4 that could cause life-threatening conditions. These deficiencies are:

1. The lack of uplift restraint of the digesters walls; and,

2. The inadequate shear/sliding resistance at the base of the wall provided by the unreinforced concrete curb on the mat foundation.

These deficiencies were further evaluated based on the California Building Code 2013 (CBC) which references American Concrete Institute (ACI) 350-06 Code Requirements for Environmental Engineering Concrete Structures and Commentary, ACI 350.3-06 Seismic Design of Liquid-Containing Concrete Structures and Commentary and the American Society of Civil Engineers (ASCE) 7-10 Minimum Design Loads for Buildings and Other Structures. Since the seismic performance level is the Life Safety, a Risk Category III with an Importance Factor I=1.25 was used. Note that this Risk Category is recommended by the CBC for wastewater facilities.

Once the failure modes were assessed, potential rehabilitation techniques were evaluated to provide a Life Safety Performance level (by preventing digester failure) during the design seismic event.

Since the existing floating covers on Digesters 3 and 4 are much heavier than the current steel fixed-dome covers installed during the Digester Upgrades Phases I and II – 900 kips for the existing floating cover compared to the 280 kips for the new steel fixed cover – the analysis was done using the lighter fixed-dome cover. If the seismic deficiencies persisted with this approach, a lower digester sludge level was considered to reduce the seismic demand.

3.3 Preliminary Seismic Evaluation Results The following are the results of the PSE:

Digesters 3 and 4 with the lighter, fixed-dome cover and operating at the current liquid level do not have adequate capacity to resist sliding or overturning (rocking of digester wall causing sludge leakage).

o By inference, these digesters do not have adequate capacity with the heavier, existing floating covers.

Digesters 3 and 4 with the lighter, fixed-dome cover, and no sludge contents (empty), do not have adequate capacity to resist sliding. Overturning resistance is adequate.

Digester 2 with current gas membrane cover and operating at the current liquid level does not have adequate capacity to resist sliding or overturning (rocking of digester wall causing sludge leakage).

Digester 2 with current gas membrane cover and no sludge contents (empty) does not have adequate capacity to resist sliding. Overturning resistance is adequate.

Digesters 3 and 4 with the lighter, fixed-dome cover and a reduced liquid level of approximately 9 feet below the top of the digester wall will have adequate capacity to resist overturning.

Digester 2 with current gas membrane cover and a reduced liquid level of approximately 9 feet below the top of the digester wall will have adequate capacity to resist overturning.

All three digesters will require a new interior concrete curb to resist sliding.

These results are summarized in Table 1.


5


Table 1. Preliminary Seismic Evaluation Results

Cover Liquid Level Overturning Condition Sliding Condition

Existing Floating Cover Any Fail Fail

New Cover (Fixed-dome or Dual-Membrane)

Empty Pass Fail


Full / current overflow level

Fail Fail


9’ below top of wall

Pass Fail

3.4 Recommendations To decrease the likelihood of the digesters losing their contents during a seismic event, Brown and Caldwell recommends the following:

Replace the existing floating covers on Digesters 3 and 4 with steel, fixed-dome covers or dual-membrane covers, which are significantly lighter than floating covers thereby reducing the seismic weight of the structure.

Build a new concrete curb inside the digesters to prevent sliding during a seismic event.

Reduce the liquid level of the digesters to a maximum elevation of 9 feet below the top of the digester wall to prevent rocking.

These recommendations are for seismic stability only and are preliminary. More rigorous calculations are required to provide a beyond-conceptual level of confidence. Further investigation must be conducted to determine the ability of the digester walls and foundation to resist the forces during the design seismic event.


A


Attachment A: Preliminary Seismic Evaluation Calculations

Design Maps Summary Report

Report Title

Building Code Reference Document

Site Coordinates

Site Soil Classification

Risk Category

User–Specified Input

EBMUD Digesters 2�4

Tue July 8, 2014 17:21:56 UTC

ASCE 7�10 Standard

(which utilizes USGS hazard data available in 2008)

37.8252°N, 122.296°W

Site Class E – “Soft Clay Soil”

I/II/III

USGS–Provided Output

SS = 1.636 g S

MS = 1.472 g S

DS = 0.982 g

S1 = 0.643 g S

M1 = 1.543 g S

D1 = 1.029 g

For information on how the SS and S1 values above have been calculated from probabilistic (risk�targeted) and

deterministic ground motions in the direction of maximum horizontal response, please return to the application and

select the “2009 NEHRP” building code reference document.

Design Maps Summary Report http://ehp2�earthquake.wr.usgs.gov/designmaps/us/summary.php?templa...

1 of 2 7/8/2014 10:22 AM

For PGAM, T

L, C

RS, and C

R1 values, please view the detailed report.

Although this information is a product of the U.S. Geological Survey, we provide no warranty, expressed or implied, as to the accuracy of

the data contained therein. This tool is not a substitute for technical subject�matter knowledge.

Design Maps Summary Report http://ehp2�earthquake.wr.usgs.gov/designmaps/us/summary.php?templa...

2 of 2 7/8/2014 10:22 AM

Design Maps Summary Report

Report Title

Building Code Reference Document

Site Coordinates

Site Soil Classification

Risk Category

User–Specified Input

EBMUD Digesters 2�4

Tue July 8, 2014 17:20:59 UTC

ASCE 7�10 Standard

(which utilizes USGS hazard data available in 2008)

37.8252°N, 122.296°W

Site Class D – “Stiff Soil”

I/II/III

USGS–Provided Output

SS = 1.636 g S

MS = 1.636 g S

DS = 1.091 g

S1 = 0.643 g S

M1 = 0.964 g S

D1 = 0.643 g

For information on how the SS and S1 values above have been calculated from probabilistic (risk�targeted) and

deterministic ground motions in the direction of maximum horizontal response, please return to the application and

select the “2009 NEHRP” building code reference document.

Design Maps Summary Report http://ehp1�earthquake.cr.usgs.gov/designmaps/us/summary.php?templa...

1 of 2 7/8/2014 10:21 AM

For PGAM, T

L, C

RS, and C

R1 values, please view the detailed report.

Although this information is a product of the U.S. Geological Survey, we provide no warranty, expressed or implied, as to the accuracy of

the data contained therein. This tool is not a substitute for technical subject�matter knowledge.

Design Maps Summary Report http://ehp1�earthquake.cr.usgs.gov/designmaps/us/summary.php?templa...

2 of 2 7/8/2014 10:21 AM

WESTECH

Tank Geometry and Inputs:

Dr:= 95·ft

Wall:= 12in

TWE := 139.0ft

MLE := 136.5ft

BWE:= 91.3ft

GLE:= 109ft

hD:= 8.5in

gap := 3·in

SS:= 10ft + 2.5in

Ywp := 36.85in

Yd:= 41.5in

Ibp:=62.4-

ft3

Cover Applied Loads:

Wc := 169796·ibf

Wss := 601201bf

Wp:= 6615·lbf

WM:= 34275·lbf

IbfLive:= 50·-

ft2

IbfInsulation := 0.583-

f?

EBMUD Phase 2Oakland, CA

Job: 20761 B page 195' Fixed Digester Cover (DCB1)

Nominal tank diameter

Assumed thickness of tank wall

Top of wall elevation from contract documents

Max liquid level from contract documents

Bottom of wall elevation on inside of tank

at the tank wall.

Ground level elevation (Assume 30 feet

below TWE if not known.)

Height of side sheet above tank wall from

AutoCAD layout

Gap between concrete tank and side sheet

Side sheet height measured from layout

Center of projected wind area on cover

(measured from AutoCAD)

Center of mass of the dome section

(from AutoCAD)

Density of liquid in the digester

Weight of steel from parts list

Weight of side sheets from parts list

Calculated weight cover mounted equipment

Combined weight of four mixers

Uniform live, and vacuum, load

Weight of insulation assumed from phase

one of project.

Gas:= 8·inH20 Specified normal operating gas pressure

NOTE: Per CBC-2007, the iive load is increased by a factor of 1.6. Since 18 inH20 is the maximum required design

pressure, increasing it by another 1.6 effectively designs the tank to 28.8 inH20. Since this is not what is

required, a design of 12 inH20 shall be used. Increasing that by 1.6 effectively designs the cover to 19 inH20

exceeding the required design pressure of 18 inH20.

Gaswc:= 12·inH20

Calculation run on 8/31/2009 by M.A

Specified maximum internal gas pressure

Checked by:..sR!1- ｾ｟Ｓ｟｟Ｏ

EWilkins

Cloud

EWilkins

Text Box

=270 kips, 3" of concrete has weight of 150 pcf (0.25')*(3.14*(97')^2/4) = 277 kips, use 3" concrete roof for Westech Cover

Title:

Existing Digester Analysis with Seismic Site Class D

Circular Tank � Hydrodynamic Slosh per ACI 350.3�06 and ASCE 7�10REV 1 , 2/4/2014

INPUT: NOTE � ALL REFERENCES ARE TO ACI 350.3�06 UNLESS NOTED OTHERWISE

SHEET MODIFIED PER ASCE 7�10 SECTION 15.7.7.3

TYPE 3:= TANK TYPE (USE 2 FOR NONFLEXIBLE CONNECTION AND 3 FOR FLEXIBLE)

PER ACI 350.3 FIGURE R2.1.1

HL 33ft:= DESIGNED DEPTH OF STORED LIQUID

HW 38ft:= WALL HEIGHT

D 95ft:= INSIDE DIAMETER OF CIRCULAR TANK

tw 13.84in:= AVERAGE WALL THICKNESS

tr 3in:= AVERAGE ROOF THICKNESS

γL 62.4lbf

ft3

:= SPECIFIC WEIGHT OF CONTAINED LIQUID

γC 150lbf

ft3

:= SPECIFIC WEIGHT OF CONCRETE

f'c 3500psi:= CONCRETE COMPRESSIVE STRENGTH

Ie 1.25:= IMPORTANCE FACTOR ASCE 7�10 15.7.7.3 and 15.4.1.1

SDS 1.091:= BASED ON THE GEOTECHNICAL REPORT

SD1 0.643:= BASED ON THE GEOTECHNICAL REPORT

Ri 1.5:= NOTE: THIS VALUE GIVES ULTIMATE LOAD ASCE 7�10 Table 15.4�2

Rc 1:= NOTE: THIS VALUE GIVES ULTIMATE LOAD Table 4.1.1(b)

TL 8 sec⋅:= LONG�PERIOD TRANSITION PERIOD ASCE 7�10 Figure 22�12 thru 22�16

Client: EBMUDClient Number:Task Number:

Date Started: 7/17/2014Last Modified: Calc. By:Checked:

P:\EWilkins\EBMUD\Digester Analysis\

Page: 1 of 10

Title:



THE FOLLOWING INPUT IS NOT REQUIRED UNLESS YOU ARE DOING A FLEXIBLE BASE

CONNECTION PER ACI 350.3. TYPICALLY WILL ONLY BE USED BY DENVER OFFICE

CROSS SECTIONAL AREA OF REINFORCEMENTAs .5in

2:=

Es 29000000psi:= MODULUS OF ELASTICITY OF REINFORCEMENT

Lc 18in:= EFFECTIVE LENGTH OF BASE CABLE OR STRAND

Sc 24in:= CENTER TO CENTER SPACING BETWEEN INDIVIDUAL CABLE LOOPS

α 45:= ANGLE OF BASE CABLE OR STRAND WITH HORIZONTAL, DEGREE

Gp 500psi:= SHEAR MODULUS OF BEARING PAD (ONLY APPPLIES FOR TYPE 3

BASES

wp 18in:= WIDTH OF ELASTOMERIC BEARING PAD

Lp 36in:= LENGTH OF INDIVIDUAL BEARING PADS

tp .25in:= THICKNESS OF ELASTOMERIC BEARING PAD

Sp 36in:= CENTER TO CENTER SPACING BETWEEN INDIVIDUAL BEARING PADS

CALCULATIONS

1. CALCULATE THE TOTAL WALL AND ROOF WEIGHT : APPENDIX A � STEP 5

WW π D tw+( )⋅ HW⋅ tw⋅ γC⋅:=WW 1.99 10

3× kip⋅=

Wr

π

4D 2 tw⋅+( )2⋅ tr⋅ γC⋅:=

Wr 278.87 kip⋅=

WL

π

4D

2⋅ HL⋅ γL⋅:= WL 1.46 104× kip⋅= TOTAL MASS OF STORED LIQUID,

Determine effective mass coefficient SECTION 9.6.2

ε min 1 0.0151D

HL

2

⋅ 0.1908D

HL

⋅− 1.021+,

:=ε 0.6= EQ (9�45)




Page: 2 of 10

Title:



2. CALCULATE THE EQUIVALENT MASS OF THE IMPULSIVE (Wi) AND CONVECTIVE (Wc)

COMPONENT OF THE STORED LIQUID : APPENDIX A � STEP 6

REFERENCE SECTION 9.3.1

W i

tanh 0.866D

HL

⋅

0.866D

HL

⋅WL⋅:= W i 5.78 10

3× kip⋅= EQ (9�15)

Wc 0.230D

HL

⋅ tanh 3.68HL

D

⋅

⋅ WL⋅:= Wc 8.27 103× kip⋅= EQ (9�16)

3. COMPUTE HEIGHTS TO CENTER OF GRAVITY: APPENDIX A � STEP 7

EXCLUDING BASE PRESSURE (EBP) REFERENCE SECTION 9.3.2

hw

HW

2:=

hw 19 ft⋅=

hr HW

tr

2+:=

hr 38.13 ft⋅=

EQ (9�17)hi 0.5 0.09375

D

HL

⋅

−

HL⋅D

HL

1.333<if

0.375 HL⋅ otherwise

:=hi 12.38 ft⋅=

EQ (9�18)

hc 1

cosh 3.68HL

D⋅

1−

3.68HL

D⋅ sinh 3.68

HL

D⋅

⋅

−

HL⋅:=EQ (9�19)

hc 18.43 ft⋅=

INCLUDING BASE PRESSURE (IBP) REFERENCE SECTION 9.3.3

h'i 0.45 HL⋅D

HL

0.75<if

0.866D

HL

⋅

2 tanh 0.866D

HL

⋅

⋅

1

8−

HL⋅ otherwise

:= EQ (9�20)

EQ (9�21)

h'i 37.58 ft⋅=




Page: 3 of 10

Title:



EQ (9�22)h'c 1

cosh 3.68HL

D⋅

2.01−

3.68HL

D⋅ sinh 3.68

HL

D⋅

⋅

−

HL⋅:=

h'c 34.18 ft⋅=

4. CALCULATE COMBINED NATURAL FREQUENCY OF VIBRATION (ωωωωi) : APPENDIX A � STEP 8


CW 0.09375 0.2039HL

D

⋅+ 0.1034HL

D

2

⋅− 0.1253HL

D

3

⋅− 0.1267HL

D

4

⋅+ 0.03186HL

D

5

⋅−:=

CW 0.15= Figure 9.3.4(a)

CI CW 10⋅tw

D

2

⋅:= CI 0.23= EQ (9�24)

Ec 57000lbf

0.5

inf'c⋅:= Ec 3.37 10

6× psi⋅= ACI 318 Section 8.5.1

ωi CI

1

HL

⋅Ec

γC

g

⋅:=ωi 71.58

1

sec⋅=

EQ (9�23)

5. CALCULATE COMBINED NATURAL FREQUENCY OF VIBRATION (ωωωωc) : APPENDIX A � STEP 9


λ 3.68 g⋅ tanh 3.68HL

D

⋅

⋅:= λ 10.07ft

0.5

sec⋅= EQ (9�29)

ωc

λ

D:=

ωc 1.031

sec⋅=

EQ (9�28)

6. CALCULATE COMBINED NATURAL PERIODS OF VIBRATION (Ti AND Tc):

REFERENCE SECTION 9.3.4 APPENDIX A � STEP 10

ka

As Es⋅ cos α( )2⋅

Lc Sc⋅

2 Gp⋅ wp⋅ Lp⋅

tp Sp⋅

+:= ka 1.17 104×

kip

ft2

⋅= EQ (9�27)




Page: 4 of 10

Title:



Ti

1.25sec8 π⋅ WW Wr+ W i+( )⋅

g D⋅ ka⋅1.25sec>if

8 π⋅ WW Wr+ W i+( )⋅

g D⋅ ka⋅otherwise

TYPE 3=if

2 π⋅ωi

otherwise

:=

EQ (9�26)

EQ (9�25)Ti 0.08 sec⋅=

Tc

2π

ωc

:=Tc 6.08 sec⋅= EQ (9�30)

7. CALCULATE THE SEISMIC RESPONSE COEFFICIENTS (Ci AND Cc): APPENDIX A � STEP 11

REFERENCE SECTION 9.4.1 AND 15.7.7.3 IN ASCE 7�10

TS

SD1

SDS

sec⋅:=TS 0.59 sec⋅= EQ (9�34)

Ci SDS Ti TS≤if

minSD1 sec⋅

Ti

SDS,

otherwise

:=EQ (9�32)

Ci 1.09= EQ (9�33)

Cc min1.5SD1 sec⋅

Tc

1.5 SDS⋅,

Tc TL≤if

1.5SD1 TL⋅ sec⋅

Tc2

otherwise

:= ASCE 7�10 15.7.7.3(a)

and EQ 15.7�10

Cc 0.16= EQ (9�38)

8. CALCULATE THE WAVE DEPTH : APPENDIX A � STEP 12

REFERENCE SECTION 7.1

dmax

D

2

Cc⋅ Ie⋅:= dmax 9.41 ft⋅= EQ (7�2)

CALCULATE THE FREEBOARD:

HF HW HL−:= HF 5 ft⋅=

HFcheck if dmax HF> " CONFIRM LIQUID SPILLS ARE OK", "FREEBOARD IS OK", ( ):=

NOTE: REFER TO ASCE 7'10 SECTION 15.7.6.1.2AND TABLE 15.7'3 FOR MINIMUM FREEBOARDREQUIREMENTS

HFcheck " CONFIRM LIQUID SPILLS ARE OK"=




Page: 5 of 10

Title:



APPENDIX A � STEP 139. COMPUTE DYNAMIC LATERAL FORCES:


PW Ci Ie⋅ε WW⋅

Ri

⋅:= PW 1.08 103× kip⋅= EQ (4�1)

Pr Ci Ie⋅Wr

Ri

⋅:= Pr 253.54 kip⋅= EQ (4�2)

Pi Ci Ie⋅W i

Ri

⋅:=Pi 5.25 10

3× kip⋅=EQ (4�3)

Pc Cc Ie⋅Wc

Rc

⋅:= Pc 1.64 103× kip⋅=

EQ (4�4)

DETERMINE BASE SHEAR (Vb) NOTE: DYNAMIC EARTH PRESSURES NOT INCLUDED.

PRESSURE CAN BE COMBINED BY SRSS PER EQUATION (4'5)

Vb Pi PW+ Pr+( )2 Pc2+:= Vb 6.78 10

3× kip⋅= EQ (4�5)

10. COMPUTE BENDING AND OVERTURNING MOMENTS: APPENDIX A � STEP 14


MW PW hw⋅:= MW 2.05 104× ft kip⋅⋅= EQ (4�6)

Mr Pr hr⋅:= Mr( ) 9.67 103× ft kip⋅⋅= EQ (4�7)

Mi Pi hi⋅:= Mi 6.5 104× ft kip⋅⋅=

EQ (4�8)

Mc Pc hc⋅:=Mc 3.02 10

4× ft kip⋅⋅= EQ (4�9)

DETERMINE MOMENT EXCLUDING BASE PRESSURE (EBP)

Mb Mi MW+ Mr+( )2 Mc2+:=

Mb 9.98 104× ft kip⋅⋅= EQ (4�10)

DETERMINE OVERTURNING MOMENT AT BASE INCLUDING BASE PRESSURE (IBP)

M'i Pi h'i⋅:= M'i 1.97 105× ft kip⋅⋅= EQ (4�11)

M'c Pc h'c⋅:=M'c 5.6 10

4× ft kip⋅⋅= EQ (4�12)

Mo M'i MW+ Mr+( )2 M'c2+:= Mo 2.34 10

5× ft kip⋅⋅= EQ (4�13)




Page: 6 of 10

Title:



11. COMPUTE VERTICAL AMPLIFICATION FACTOR: APPENDIX A � STEP 15

REFERENCE SECTION ASCE 7�10

15.7.7.3(b) and 15.7.2(c)

Ct 0.2SDS:= Ct 0.22=

12. COMPUTE HYDRODYNAMIC PRESSURE: APPENDIX A � STEP 16


EQ (4�15) with I, Ri and b taken

as 1.0 per ASCE 7�10 15.7.7.3(b)uv min Ct 0.2 SDS⋅, ( ):= uv 0.22= i 0 10..:=

yi 1 .1 i⋅−( ) HL⋅:= qhyi

γL HL yi−( )⋅:= phyi

uv qhyi

⋅:= EQ (4�14)

Height qhy (ksf) phy (ksf)

33.00 0.00 0.00

29.70 0.21 0.04

26.40 0.41 0.09

23.10 0.62 0.13

19.80 0.82 0.18

16.50 1.03 0.22

13.20 1.24 0.27

9.90 1.44 0.31

6.60 1.65 0.36

3.30 1.85 0.40

0.00 2.06 0.45

y

ft

qhy

ksf

phy

ksf

Top

Bottom

13. COMPUTE VERTICAL DISTRIBUTION OF PRESSURES: APPENDIX A � STEP 17

REFERENCE SECTION 5.3.3. AND R5.3.3

Pwy

PW

2HW

:=Pwy 14.18

kip

ft⋅=

pwy

Pwy

πD

2⋅

:= pwy 0.095 ksf⋅=




Page: 7 of 10

Title:



COMPUTE THE IMPULSIVE WATER PRESSURE (piy):

Piyi

Pi

24 HL⋅ 6 hi⋅− 6HL 12 hi⋅−( )

yi

HL

⋅−

⋅

HL2

:= piyi

2 Piyi

⋅( ) cos 0( )⋅

πD

2⋅

:=

Height Piy (kip/ft) piy (ksf)

33.00 19.89 0.27

29.70 31.82 0.43

26.40 43.76 0.59

23.10 55.69 0.75

19.80 67.62 0.91

16.50 79.56 1.07

13.20 91.49 1.23

9.90 103.42 1.39

6.60 115.36 1.55

3.30 127.29 1.71

0.00 139.22 1.87

y

ft

Piy

kip

ft

piy

ksf

0 50 100 1500

10

20

30

40

Hei

ght

Above

Bas

e (f

t)

y

ft

Piy

kip

ft

Top

Bottom




Page: 8 of 10

Title:



COMPUTE THE CONVECTIVE WATER PRESSURE (pcy):

Pcyi

Pc

24 HL⋅ 6 hc⋅− 6HL 12 hc⋅−( )

yi

HL

⋅−

⋅

HL2

:= pcyi

16 Pcyi

⋅( ) cos 0( )⋅

9πD

2⋅

:=

Height Pcy (kip/ft) pcy (ksf)

33.00 33.57 0.40

29.70 31.82 0.38

26.40 30.08 0.36

23.10 28.33 0.34

19.80 26.59 0.32

16.50 24.84 0.30

13.20 23.10 0.28

9.90 21.35 0.25

6.60 19.61 0.23

3.30 17.86 0.21

0.00 16.12 0.19

y

ft

Pcy

kip

ft

pcy

ksf

15 20 25 30 350

10

20

30

40

Hei

ght

Above

Bas

e (f

t)

y

ft

Pcy

kip

ft

Top

Bottom




Page: 9 of 10

Title:



14. CALCULATE THE HOOP FORCES: APPENDIX A � STEP 18


Nyi

piyi

D

2⋅ pwy

D

2⋅+

2

pcyi

D

2⋅

2

+ phyi

D

2⋅

2

+:= σyi

Nyi

tw:=

Ultimate Hoop Force Ultimate Hoop Stress EQ (6�2)EQ (6�1)

20 40 60 80 1000

10

20

30

40

Hei

ght

Above

Bas

e (f

t)

y

ft

Ny

kip

ft

Height Ny (kip/ft) σy (psi)

33.00 25.61 154.20

29.70 30.70 184.86

26.40 36.82 221.70

23.10 43.54 262.14

19.80 50.61 304.74

16.50 57.92 348.72

13.20 65.37 393.61

9.90 72.93 439.13

6.60 80.57 485.11

3.30 88.26 531.43

0.00 95.99 578.00

y

ft

Ny

kip

ft

σy

psi

Top

Bottom

NOTE ABOVE FORCES ARE FOR A FREE BASE AND SHOULD BE ADJUSTED TOACCOUNT FOR BASE RESTRAINT PER SECTION R6.2.

NOTE: DYNAMIC EARTH PRESSURES NOT INCLUDED. PRESSURE CAN BE

COMBINED BY SRSS PER EQUATION (4'5)

ADDITIONAL DESIGN OUTPUT

Vb 6.78 103× kip⋅= BASE SHEAR

Mb 9.98 104× ft kip⋅⋅=

OTM EXCLUDING BASE PRESSURE

Mo 2.34 105× ft kip⋅⋅= OTM INCLUDING BASE PRESSURE





Page: 10 of 10

Title:

Existing Digester Analysis with Seismic Site Class E











γL 62.4lbf

ft3


γC 150lbf

ft3












Page: 1 of 10

Title:






2:=






BASES





CALCULATIONS


WW π D tw+( )⋅ HW⋅ tw⋅ γC⋅:=WW 1.99 10

3× kip⋅=

Wr

π

4D 2 tw⋅+( )2⋅ tr⋅ γC⋅:=

Wr 278.87 kip⋅=

WL

π

4D



ε min 1 0.0151D

HL

2

⋅ 0.1908D

HL

⋅− 1.021+,

:=ε 0.6= EQ (9�45)




Page: 2 of 10

Title:






W i

tanh 0.866D

HL

⋅

0.866D

HL

⋅WL⋅:= W i 5.78 10

3× kip⋅= EQ (9�15)

Wc 0.230D

HL

⋅ tanh 3.68HL

D

⋅

⋅ WL⋅:= Wc 8.27 103× kip⋅= EQ (9�16)



hw

HW

2:=

hw 19 ft⋅=

hr HW

tr

2+:=

hr 38.13 ft⋅=

EQ (9�17)hi 0.5 0.09375

D

HL

⋅

−

HL⋅D

HL

1.333<if


:=hi 12.38 ft⋅=

EQ (9�18)

hc 1

cosh 3.68HL

D⋅

1−

3.68HL

D⋅ sinh 3.68

HL

D⋅

⋅

−

HL⋅:=EQ (9�19)

hc 18.43 ft⋅=


h'i 0.45 HL⋅D

HL

0.75<if

0.866D

HL

⋅

2 tanh 0.866D

HL

⋅

⋅

1

8−

HL⋅ otherwise

:= EQ (9�20)

EQ (9�21)

h'i 37.58 ft⋅=




Page: 3 of 10

Title:



EQ (9�22)h'c 1

cosh 3.68HL

D⋅

2.01−

3.68HL

D⋅ sinh 3.68

HL

D⋅

⋅

−

HL⋅:=

h'c 34.18 ft⋅=



CW 0.09375 0.2039HL

D

⋅+ 0.1034HL

D

2

⋅− 0.1253HL

D

3

⋅− 0.1267HL

D

4

⋅+ 0.03186HL

D

5

⋅−:=

CW 0.15= Figure 9.3.4(a)

CI CW 10⋅tw

D

2

⋅:= CI 0.23= EQ (9�24)

Ec 57000lbf

0.5

inf'c⋅:= Ec 3.37 10


ωi CI

1

HL

⋅Ec

γC

g

⋅:=ωi 71.58

1

sec⋅=

EQ (9�23)



λ 3.68 g⋅ tanh 3.68HL

D

⋅

⋅:= λ 10.07ft

0.5

sec⋅= EQ (9�29)

ωc

λ

D:=

ωc 1.031

sec⋅=

EQ (9�28)



ka


Lc Sc⋅

2 Gp⋅ wp⋅ Lp⋅

tp Sp⋅

+:= ka 1.17 104×

kip

ft2

⋅= EQ (9�27)




Page: 4 of 10

Title:



Ti

1.25sec8 π⋅ WW Wr+ W i+( )⋅


8 π⋅ WW Wr+ W i+( )⋅


TYPE 3=if

2 π⋅ωi

otherwise

:=

EQ (9�26)

EQ (9�25)Ti 0.08 sec⋅=

Tc

2π

ωc

:=Tc 6.08 sec⋅= EQ (9�30)



TS

SD1

SDS

sec⋅:=TS 1.05 sec⋅= EQ (9�34)

Ci SDS Ti TS≤if

minSD1 sec⋅

Ti

SDS,

otherwise

:=EQ (9�32)

Ci 0.98= EQ (9�33)

Cc min1.5SD1 sec⋅

Tc

1.5 SDS⋅,

Tc TL≤if

1.5SD1 TL⋅ sec⋅

Tc2

otherwise

:= ASCE 7�10 15.7.7.3(a)

and EQ 15.7�10

Cc 0.25= EQ (9�38)



dmax

D

2

Cc⋅ Ie⋅:= dmax 15.07 ft⋅= EQ (7�2)









Page: 5 of 10

Title:





PW Ci Ie⋅ε WW⋅

Ri

⋅:= PW 969.96 kip⋅= EQ (4�1)

Pr Ci Ie⋅Wr

Ri

⋅:= Pr 228.21 kip⋅= EQ (4�2)

Pi Ci Ie⋅W i

Ri

⋅:=Pi 4.73 10

3× kip⋅=EQ (4�3)

Pc Cc Ie⋅Wc

Rc

⋅:= Pc 2.62 103× kip⋅=

EQ (4�4)



Vb Pi PW+ Pr+( )2 Pc2+:= Vb 6.48 10

3× kip⋅= EQ (4�5)





Mi Pi hi⋅:= Mi 5.85 104× ft kip⋅⋅=

EQ (4�8)

Mc Pc hc⋅:=Mc 4.84 10

4× ft kip⋅⋅= EQ (4�9)



Mb 9.83 104× ft kip⋅⋅= EQ (4�10)



M'c Pc h'c⋅:=M'c 8.97 10

4× ft kip⋅⋅= EQ (4�12)

Mo M'i MW+ Mr+( )2 M'c2+:= Mo 2.23 10

5× ft kip⋅⋅= EQ (4�13)




Page: 6 of 10

Title:





15.7.7.3(b) and 15.7.2(c)

Ct 0.2SDS:= Ct 0.2=





yi 1 .1 i⋅−( ) HL⋅:= qhyi


uv qhyi

⋅:= EQ (4�14)


33.00 0.00 0.00

29.70 0.21 0.04

26.40 0.41 0.08

23.10 0.62 0.12

19.80 0.82 0.16

16.50 1.03 0.20

13.20 1.24 0.24

9.90 1.44 0.28

6.60 1.65 0.32

3.30 1.85 0.36

0.00 2.06 0.40

y

ft

qhy

ksf

phy

ksf

Top

Bottom



Pwy

PW

2HW

:=Pwy 12.76

kip

ft⋅=

pwy

Pwy

πD

2⋅

:= pwy 0.086 ksf⋅=




Page: 7 of 10

Title:




Piyi

Pi

24 HL⋅ 6 hi⋅− 6HL 12 hi⋅−( )

yi

HL

⋅−

⋅

HL2

:= piyi

2 Piyi

⋅( ) cos 0( )⋅

πD

2⋅

:=


33.00 17.90 0.24

29.70 28.64 0.38

26.40 39.38 0.53

23.10 50.13 0.67

19.80 60.87 0.82

16.50 71.61 0.96

13.20 82.35 1.10

9.90 93.09 1.25

6.60 103.83 1.39

3.30 114.57 1.54

0.00 125.31 1.68

y

ft

Piy

kip

ft

piy

ksf

0 50 100 1500

10

20

30

40

Hei

ght

Above

Bas

e (f

t)

y

ft

Piy

kip

ft

Top

Bottom




Page: 8 of 10

Title:




Pcyi

Pc

24 HL⋅ 6 hc⋅− 6HL 12 hc⋅−( )

yi

HL

⋅−

⋅

HL2

:= pcyi

16 Pcyi

⋅( ) cos 0( )⋅

9πD

2⋅

:=


33.00 53.72 0.64

29.70 50.93 0.61

26.40 48.14 0.57

23.10 45.34 0.54

19.80 42.55 0.51

16.50 39.76 0.47

13.20 36.96 0.44

9.90 34.17 0.41

6.60 31.38 0.37

3.30 28.59 0.34

0.00 25.79 0.31

y

ft

Pcy

kip

ft

pcy

ksf

20 30 40 50 600

10

20

30

40

Hei

ght

Above

Bas

e (f

t)

y

ft

Pcy

kip

ft

Top

Bottom




Page: 9 of 10

Title:





Nyi

piyi

D

2⋅ pwy

D

2⋅+

2

pcyi

D

2⋅

2

+ phyi

D

2⋅

2

+:= σyi

Nyi

tw:=


20 40 60 80 1000

10

20

30

40

Hei

ght

Above

Bas

e (f

t)

y

ft

Ny

kip

ft


33.00 34.11 205.35

29.70 36.49 219.71

26.40 40.07 241.27

23.10 44.56 268.31

19.80 49.72 299.35

16.50 55.35 333.27

13.20 61.33 369.27

9.90 67.56 406.81

6.60 73.99 445.50

3.30 80.56 485.06

0.00 87.24 525.30

y

ft

Ny

kip

ft

σy

psi

Top

Bottom






Mb 9.83 104× ft kip⋅⋅=







Page: 10 of 10

Title:

Digester Analysis with Westech Cover and Reduced Liquid Level











γL 62.4lbf

ft3


γC 150lbf

ft3












Page: 1 of 10

Title:






2:=






BASES





CALCULATIONS


WW π D tw+( )⋅ HW⋅ tw⋅ γC⋅:=WW 1.99 10

3× kip⋅=

Wr

π

4D 2 tw⋅+( )2⋅ tr⋅ γC⋅:=

Wr 278.87 kip⋅=

WL

π

4D



ε min 1 0.0151D

HL

2

⋅ 0.1908D

HL

⋅− 1.021+,

:=ε 0.57= EQ (9�45)




Page: 2 of 10

Title:






W i

tanh 0.866D

HL

⋅

0.866D

HL

⋅WL⋅:= W i 4.8 10

3× kip⋅= EQ (9�15)

Wc 0.230D

HL

⋅ tanh 3.68HL

D

⋅

⋅ WL⋅:= Wc 7.94 103× kip⋅= EQ (9�16)



hw

HW

2:=

hw 19 ft⋅=

hr HW

tr

2+:=

hr 38.13 ft⋅=

EQ (9�17)hi 0.5 0.09375

D

HL

⋅

−

HL⋅D

HL

1.333<if


:=hi 11.25 ft⋅=

EQ (9�18)

hc 1

cosh 3.68HL

D⋅

1−

3.68HL

D⋅ sinh 3.68

HL

D⋅

⋅

−

HL⋅:=EQ (9�19)

hc 16.49 ft⋅=


h'i 0.45 HL⋅D

HL

0.75<if

0.866D

HL

⋅

2 tanh 0.866D

HL

⋅

⋅

1

8−

HL⋅ otherwise

:= EQ (9�20)

EQ (9�21)

h'i 37.73 ft⋅=




Page: 3 of 10

Title:



EQ (9�22)h'c 1

cosh 3.68HL

D⋅

2.01−

3.68HL

D⋅ sinh 3.68

HL

D⋅

⋅

−

HL⋅:=

h'c 34.57 ft⋅=



CW 0.09375 0.2039HL

D

⋅+ 0.1034HL

D

2

⋅− 0.1253HL

D

3

⋅− 0.1267HL

D

4

⋅+ 0.03186HL

D

5

⋅−:=

CW 0.15= Figure 9.3.4(a)

CI CW 10⋅tw

D

2

⋅:= CI 0.23= EQ (9�24)

Ec 57000lbf

0.5

inf'c⋅:= Ec 3.37 10


ωi CI

1

HL

⋅Ec

γC

g

⋅:=ωi 76.89

1

sec⋅=

EQ (9�23)



λ 3.68 g⋅ tanh 3.68HL

D

⋅

⋅:= λ 9.86ft

0.5

sec⋅= EQ (9�29)

ωc

λ

D:=

ωc 1.011

sec⋅=

EQ (9�28)



ka


Lc Sc⋅

2 Gp⋅ wp⋅ Lp⋅

tp Sp⋅

+:= ka 1.17 104×

kip

ft2

⋅= EQ (9�27)




Page: 4 of 10

Title:



Ti

1.25sec8 π⋅ WW Wr+ W i+( )⋅


8 π⋅ WW Wr+ W i+( )⋅


TYPE 3=if

2 π⋅ωi

otherwise

:=

EQ (9�26)

EQ (9�25)Ti 0.07 sec⋅=

Tc

2π

ωc

:=Tc 6.21 sec⋅= EQ (9�30)



TS

SD1

SDS

sec⋅:=TS 0.59 sec⋅= EQ (9�34)

Ci SDS Ti TS≤if

minSD1 sec⋅

Ti

SDS,

otherwise

:=EQ (9�32)

Ci 1.09= EQ (9�33)

Cc min1.5SD1 sec⋅

Tc

1.5 SDS⋅,

Tc TL≤if

1.5SD1 TL⋅ sec⋅

Tc2

otherwise

:= ASCE 7�10 15.7.7.3(a)

and EQ 15.7�10

Cc 0.16= EQ (9�38)



dmax

D

2

Cc⋅ Ie⋅:= dmax 9.22 ft⋅= EQ (7�2)









Page: 5 of 10

Title:





PW Ci Ie⋅ε WW⋅

Ri

⋅:= PW 1.03 103× kip⋅= EQ (4�1)

Pr Ci Ie⋅Wr

Ri

⋅:= Pr 253.54 kip⋅= EQ (4�2)

Pi Ci Ie⋅W i

Ri

⋅:=Pi 4.36 10

3× kip⋅=EQ (4�3)

Pc Cc Ie⋅Wc

Rc

⋅:= Pc 1.54 103× kip⋅=

EQ (4�4)



Vb Pi PW+ Pr+( )2 Pc2+:= Vb 5.85 10

3× kip⋅= EQ (4�5)





Mi Pi hi⋅:= Mi 4.91 104× ft kip⋅⋅=

EQ (4�8)

Mc Pc hc⋅:=Mc 2.54 10

4× ft kip⋅⋅= EQ (4�9)



Mb 8.23 104× ft kip⋅⋅= EQ (4�10)



M'c Pc h'c⋅:=M'c 5.33 10

4× ft kip⋅⋅= EQ (4�12)

Mo M'i MW+ Mr+( )2 M'c2+:= Mo 2.01 10

5× ft kip⋅⋅= EQ (4�13)




Page: 6 of 10

Title:





15.7.7.3(b) and 15.7.2(c)

Ct 0.2SDS:= Ct 0.22=





yi 1 .1 i⋅−( ) HL⋅:= qhyi


uv qhyi

⋅:= EQ (4�14)


30.00 0.00 0.00

27.00 0.19 0.04

24.00 0.37 0.08

21.00 0.56 0.12

18.00 0.75 0.16

15.00 0.94 0.20

12.00 1.12 0.25

9.00 1.31 0.29

6.00 1.50 0.33

3.00 1.68 0.37

0.00 1.87 0.41

y

ft

qhy

ksf

phy

ksf

Top

Bottom



Pwy

PW

2HW

:=Pwy 13.5

kip

ft⋅=

pwy

Pwy

πD

2⋅

:= pwy 0.09 ksf⋅=




Page: 7 of 10

Title:




Piyi

Pi

24 HL⋅ 6 hi⋅− 6HL 12 hi⋅−( )

yi

HL

⋅−

⋅

HL2

:= piyi

2 Piyi

⋅( ) cos 0( )⋅

πD

2⋅

:=


30.00 18.18 0.24

27.00 29.09 0.39

24.00 39.99 0.54

21.00 50.90 0.68

18.00 61.81 0.83

15.00 72.71 0.97

12.00 83.62 1.12

9.00 94.53 1.27

6.00 105.43 1.41

3.00 116.34 1.56

0.00 127.25 1.71

y

ft

Piy

kip

ft

piy

ksf

0 50 100 1500

10

20

30

Hei

ght

Above

Bas

e (f

t)

y

ft

Piy

kip

ft

Top

Bottom




Page: 8 of 10

Title:




Pcyi

Pc

24 HL⋅ 6 hc⋅− 6HL 12 hc⋅−( )

yi

HL

⋅−

⋅

HL2

:= pcyi

16 Pcyi

⋅( ) cos 0( )⋅

9πD

2⋅

:=


30.00 33.35 0.40

27.00 31.82 0.38

24.00 30.29 0.36

21.00 28.76 0.34

18.00 27.23 0.32

15.00 25.70 0.31

12.00 24.17 0.29

9.00 22.64 0.27

6.00 21.11 0.25

3.00 19.58 0.23

0.00 18.06 0.22

y

ft

Pcy

kip

ft

pcy

ksf

15 20 25 30 350

10

20

30

Hei

ght

Above

Bas

e (f

t)

y

ft

Pcy

kip

ft

Top

Bottom




Page: 9 of 10

Title:





Nyi

piyi

D

2⋅ pwy

D

2⋅+

2

pcyi

D

2⋅

2

+ phyi

D

2⋅

2

+:= σyi

Nyi

tw:=


20 40 60 80 1000

10

20

30

Hei

ght

Above

Bas

e (f

t)

y

ft

Ny

kip

ft


30.00 24.66 148.46

27.00 29.13 175.38

24.00 34.56 208.08

21.00 40.57 244.26

18.00 46.93 282.58

15.00 53.52 322.27

12.00 60.27 362.89

9.00 67.12 404.16

6.00 74.06 445.90

3.00 81.04 487.99

0.00 88.08 530.34

y

ft

Ny

kip

ft

σy

psi

Top

Bottom






Mb 8.23 104× ft kip⋅⋅=







Page: 10 of 10

Title:

Digester Analysis with Dystor Cover and Reduced Liquid Level










tr 1.5in:= AVERAGE ROOF THICKNESS

γL 62.4lbf

ft3


γC 150lbf

ft3












Page: 1 of 10

Title:






2:=






BASES





CALCULATIONS


WW π D tw+( )⋅ HW⋅ tw⋅ γC⋅:=WW 1.99 10

3× kip⋅=

Wr

π

4D 2 tw⋅+( )2⋅ tr⋅ γC⋅:=

Wr 139.44 kip⋅=

WL

π

4D



ε min 1 0.0151D

HL

2

⋅ 0.1908D

HL

⋅− 1.021+,

:=ε 0.57= EQ (9�45)




Page: 2 of 10

Title:






W i

tanh 0.866D

HL

⋅

0.866D

HL

⋅WL⋅:= W i 4.8 10

3× kip⋅= EQ (9�15)

Wc 0.230D

HL

⋅ tanh 3.68HL

D

⋅

⋅ WL⋅:= Wc 7.94 103× kip⋅= EQ (9�16)



hw

HW

2:=

hw 19 ft⋅=

hr HW

tr

2+:=

hr 38.06 ft⋅=

EQ (9�17)hi 0.5 0.09375

D

HL

⋅

−

HL⋅D

HL

1.333<if


:=hi 11.25 ft⋅=

EQ (9�18)

hc 1

cosh 3.68HL

D⋅

1−

3.68HL

D⋅ sinh 3.68

HL

D⋅

⋅

−

HL⋅:=EQ (9�19)

hc 16.49 ft⋅=


h'i 0.45 HL⋅D

HL

0.75<if

0.866D

HL

⋅

2 tanh 0.866D

HL

⋅

⋅

1

8−

HL⋅ otherwise

:= EQ (9�20)

EQ (9�21)

h'i 37.73 ft⋅=




Page: 3 of 10

Title:



EQ (9�22)h'c 1

cosh 3.68HL

D⋅

2.01−

3.68HL

D⋅ sinh 3.68

HL

D⋅

⋅

−

HL⋅:=

h'c 34.57 ft⋅=



CW 0.09375 0.2039HL

D

⋅+ 0.1034HL

D

2

⋅− 0.1253HL

D

3

⋅− 0.1267HL

D

4

⋅+ 0.03186HL

D

5

⋅−:=

CW 0.15= Figure 9.3.4(a)

CI CW 10⋅tw

D

2

⋅:= CI 0.23= EQ (9�24)

Ec 57000lbf

0.5

inf'c⋅:= Ec 3.37 10


ωi CI

1

HL

⋅Ec

γC

g

⋅:=ωi 76.89

1

sec⋅=

EQ (9�23)



λ 3.68 g⋅ tanh 3.68HL

D

⋅

⋅:= λ 9.86ft

0.5

sec⋅= EQ (9�29)

ωc

λ

D:=

ωc 1.011

sec⋅=

EQ (9�28)



ka


Lc Sc⋅

2 Gp⋅ wp⋅ Lp⋅

tp Sp⋅

+:= ka 1.17 104×

kip

ft2

⋅= EQ (9�27)




Page: 4 of 10

Title:



Ti

1.25sec8 π⋅ WW Wr+ W i+( )⋅


8 π⋅ WW Wr+ W i+( )⋅


TYPE 3=if

2 π⋅ωi

otherwise

:=

EQ (9�26)

EQ (9�25)Ti 0.07 sec⋅=

Tc

2π

ωc

:=Tc 6.21 sec⋅= EQ (9�30)



TS

SD1

SDS

sec⋅:=TS 0.59 sec⋅= EQ (9�34)

Ci SDS Ti TS≤if

minSD1 sec⋅

Ti

SDS,

otherwise

:=EQ (9�32)

Ci 1.09= EQ (9�33)

Cc min1.5SD1 sec⋅

Tc

1.5 SDS⋅,

Tc TL≤if

1.5SD1 TL⋅ sec⋅

Tc2

otherwise

:= ASCE 7�10 15.7.7.3(a)

and EQ 15.7�10

Cc 0.16= EQ (9�38)



dmax

D

2

Cc⋅ Ie⋅:= dmax 9.22 ft⋅= EQ (7�2)









Page: 5 of 10

Title:





PW Ci Ie⋅ε WW⋅

Ri

⋅:= PW 1.03 103× kip⋅= EQ (4�1)

Pr Ci Ie⋅Wr

Ri

⋅:= Pr 126.77 kip⋅= EQ (4�2)

Pi Ci Ie⋅W i

Ri

⋅:=Pi 4.36 10

3× kip⋅=EQ (4�3)

Pc Cc Ie⋅Wc

Rc

⋅:= Pc 1.54 103× kip⋅=

EQ (4�4)



Vb Pi PW+ Pr+( )2 Pc2+:= Vb 5.73 10

3× kip⋅= EQ (4�5)





Mi Pi hi⋅:= Mi 4.91 104× ft kip⋅⋅=

EQ (4�8)

Mc Pc hc⋅:=Mc 2.54 10

4× ft kip⋅⋅= EQ (4�9)



Mb 7.77 104× ft kip⋅⋅= EQ (4�10)



M'c Pc h'c⋅:=M'c 5.33 10

4× ft kip⋅⋅= EQ (4�12)

Mo M'i MW+ Mr+( )2 M'c2+:= Mo 1.96 10

5× ft kip⋅⋅= EQ (4�13)




Page: 6 of 10

Title:





15.7.7.3(b) and 15.7.2(c)

Ct 0.2SDS:= Ct 0.22=





yi 1 .1 i⋅−( ) HL⋅:= qhyi


uv qhyi

⋅:= EQ (4�14)


30.00 0.00 0.00

27.00 0.19 0.04

24.00 0.37 0.08

21.00 0.56 0.12

18.00 0.75 0.16

15.00 0.94 0.20

12.00 1.12 0.25

9.00 1.31 0.29

6.00 1.50 0.33

3.00 1.68 0.37

0.00 1.87 0.41

y

ft

qhy

ksf

phy

ksf

Top

Bottom



Pwy

PW

2HW

:=Pwy 13.5

kip

ft⋅=

pwy

Pwy

πD

2⋅

:= pwy 0.09 ksf⋅=




Page: 7 of 10

Title:




Piyi

Pi

24 HL⋅ 6 hi⋅− 6HL 12 hi⋅−( )

yi

HL

⋅−

⋅

HL2

:= piyi

2 Piyi

⋅( ) cos 0( )⋅

πD

2⋅

:=


30.00 18.18 0.24

27.00 29.09 0.39

24.00 39.99 0.54

21.00 50.90 0.68

18.00 61.81 0.83

15.00 72.71 0.97

12.00 83.62 1.12

9.00 94.53 1.27

6.00 105.43 1.41

3.00 116.34 1.56

0.00 127.25 1.71

y

ft

Piy

kip

ft

piy

ksf

0 50 100 1500

10

20

30

Hei

ght

Above

Bas

e (f

t)

y

ft

Piy

kip

ft

Top

Bottom




Page: 8 of 10

Title:




Pcyi

Pc

24 HL⋅ 6 hc⋅− 6HL 12 hc⋅−( )

yi

HL

⋅−

⋅

HL2

:= pcyi

16 Pcyi

⋅( ) cos 0( )⋅

9πD

2⋅

:=


30.00 33.35 0.40

27.00 31.82 0.38

24.00 30.29 0.36

21.00 28.76 0.34

18.00 27.23 0.32

15.00 25.70 0.31

12.00 24.17 0.29

9.00 22.64 0.27

6.00 21.11 0.25

3.00 19.58 0.23

0.00 18.06 0.22

y

ft

Pcy

kip

ft

pcy

ksf

15 20 25 30 350

10

20

30

Hei

ght

Above

Bas

e (f

t)

y

ft

Pcy

kip

ft

Top

Bottom




Page: 9 of 10

Title:





Nyi

piyi

D

2⋅ pwy

D

2⋅+

2

pcyi

D

2⋅

2

+ phyi

D

2⋅

2

+:= σyi

Nyi

tw:=


20 40 60 80 1000

10

20

30

Hei

ght

Above

Bas

e (f

t)

y

ft

Ny

kip

ft


30.00 24.66 148.46

27.00 29.13 175.38

24.00 34.56 208.08

21.00 40.57 244.26

18.00 46.93 282.58

15.00 53.52 322.27

12.00 60.27 362.89

9.00 67.12 404.16

6.00 74.06 445.90

3.00 81.04 487.99

0.00 88.08 530.34

y

ft

Ny

kip

ft

σy

psi

Top

Bottom






Mb 7.77 104× ft kip⋅⋅=







Page: 10 of 10

2020 Wake Avenue July 3, 2008 Oakland, California Project No. 401360001

401360001 R Geo Eval 25

ported on mat foundation may include subsidence of the structure due to foundation

failure or uplifting of the structure to the ground surface due to the development of large

excess pore pressure during an extended period of ground shaking. Similar liquefaction-

related damages to underground structures were observed in the recent major earth-

quake events worldwide (1995, Kobe, Japan; 1999, Ji Ji, Taiwan).

A precise estimation of dynamic uplift pressure for an underground structure is difficult.

However, for preliminary design purposes, it may be assumed to be the effective over-

burden pressure acting at the foundation level of the tank. Considering an

approximately 18-foot embedment of the proposed FOG Tanks below the finished grade

and the historic high groundwater level during the earthquake event, an uplift pressure

on the order of 1,100 psf may be used in design.

9.2. Spread Footings

Relatively shallow, spread footings may be used for supporting light-weight at-grade struc-

tures, including retaining walls. Isolated or continuous spread footings founded on

compacted reworked fill may be designed using an allowable bearing capacity of 1,500 psf.

Spread footings should be founded at a depth 18 inches or more below the lowest adjacent

grade. Continuous and isolated footings should be 18 and 24 inches wide, respectively. The

allowable bearing capacity recommended here may be increased by one-third when consid-

ering loads of short duration such as wind or seismic forces. The spread footings should be

reinforced in accordance with the recommendations of the project structural engineer.

Spread footings may be founded on 24 inches of compacted reworked fill. Earthwork and

compaction requirements are discussed in Section 9.8.1.

9.2.1. Lateral Resistance

For resistance of structural footings and buried structures to lateral loads, we recommend an

allowable passive pressure of 250 psf per foot of depth be used with a value of up to

2,500 psf. This value assumes that the ground is horizontal for a distance of 10 feet, or three

times the height generating the passive pressure, whichever is greater. We recommend that

2020 Wake Avenue July 3, 2008 Oakland, California Project No. 401360001

401360001 R Geo Eval 26

the upper 1 foot of soil not protected by pavement or a concrete slab be neglected when cal-

culating passive resistance.

For frictional resistance to lateral loads, we recommend a coefficient of friction of 0.35

be used between soil and concrete. The allowable lateral resistance can be taken as the

sum of the frictional resistance and passive resistance provided the passive resistance

does not exceed one-half of the total allowable resistance. The passive resistance values

may be increased by one-third when considering loads of short duration such as wind or

seismic forces.

9.2.2. Static Settlement

We estimate that the structures supported on spread footings, designed and constructed

as recommended herein, will undergo total settlement on the order of 1 inch.

Differential settlement on the order of ½ inch over a horizontal span of 40 feet should

be anticipated.

9.3. Slab-on-Grade

We understand that the Odor Control Equipment is planned to be supported on a 35 feet by

14 feet slab-on-grade foundation. The location of the Odor Control Equipment between the

Blend Tanks and the Electrical Building. We anticipate the soft Bay Mud in this area to be

close to the ground surface (appropriately 4 feet below existing grade). Furthermore, there is

potential for liquefaction as discussed in Section 7.1.3. EBMUD should be prepared to pro-

vide repair and maintenance from static settlement of the Bay Mud and movements

associated with a seismic event. This may entail temporarily shutting down the Odor Control

Equipment for several weeks. If this is not acceptable, the Odor Control Equipment should

be supported on pile foundations.

We recommend that conventional, slab-on-grade floors, underlain by compacted fill materi-

als of generally very low to low expansion potential, be at least 5 inches in thickness and be

reinforced with No. 4 reinforcing bars spaced 18 inches on-center each way. The reinforcing

EWilkins

Highlight

EWilkins

Highlight

EWilkins

Highlight

www.hilti.us Profis Anchor 2.4.8

Input data and results must be checked for agreement with the existing conditions and for plausibility!PROFIS Anchor ( c ) 2003-2009 Hilti AG, FL-9494 Schaan Hilti is a registered Trademark of Hilti AG, Schaan

Company:Specifier:Address:Phone I Fax:E-Mail:

Brown and CaldwellEric Wilkins

|

Page:Project:Sub-Project I Pos. No.:Date:

1EBMUD Digesters 2-4

7/16/2014

Specifier's comments: Dowels for new interior curb

1 Input dataAnchor type and diameter: HIT-RE 500-SD + Rebar A 615 Gr.60 #5

Effective embedment depth: hef,act = 8.000 in. (hef,limit = - in.)

Material: ASTM A 615 Gr.60

Evaluation Service Report: ESR-2322

Issued I Valid: 2/1/2014 | 4/1/2016

Proof: design method ACI 318 / AC308

Stand-off installation: - (Recommended plate thickness: not calculated)

Profile: no profile

Base material: cracked concrete, , fc' = 3500 psi; h = 18.000 in., Temp. short/long: 32/32 °F

Installation: hammer drilled hole, installation condition: dry

Reinforcement: tension: condition B, shear: condition B; no supplemental splitting reinforcement present

edge reinforcement: none or < No. 4 barSeismic loads (cat. C, D, E, or F) no

Geometry [in.] & Loading [lb, in.lb]

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|



7/16/2014

2 Load case/Resulting anchor forcesLoad case: Design loads

Anchor reactions [lb]Tension force: (+Tension, -Compression)

Anchor Tension force Shear force Shear force x Shear force y1 0 1 0 1

max. concrete compressive strain: - [‰]max. concrete compressive stress: - [psi]resulting tension force in (x/y)=(0.000/0.000): 0 [lb]resulting compression force in (x/y)=(0.000/0.000): 0 [lb]

3 Tension load Load Nua [lb] Capacity ffffNn [lb] Utilization bbbbN = Nua/ffffNn Status Steel Strength* N/A N/A N/A N/A

Bond Strength** N/A N/A N/A N/A

Concrete Breakout Strength** N/A N/A N/A N/A

* anchor having the highest loading **anchor group (anchors in tension)

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7/16/2014

4 Shear load Load Vua [lb] Capacity ffffVn [lb] Utilization bbbbV = Vua/ffffVn Status Steel Strength* 1 10044 1 OK

Steel failure (with lever arm)* N/A N/A N/A N/A

Pryout Strength (Bond Strength controls)** 1 22981 1 OK

Concrete edge failure in direction y+** 1 39709 1 OK

* anchor having the highest loading **anchor group (relevant anchors)

4.1 Steel Strength

Vsa = (n 0.6 Ase,V futa) refer to ICC-ES ESR-2322f Vsteel ≥ Vua ACI 318-08 Eq. (D-2)

Variables n Ase,V [in.2] futa [psi] (n 0.6 Ase,V futa) [lb] 1 0.31 90000 16740

Calculations Vsa [lb]

16740

Results Vsa [lb] fsteel f Vsa [lb] Vua [lb]

16740 0.600 10044 1

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|



7/16/2014

4.2 Pryout Strength (Bond Strength controls)

Vcp =kcp[(ANaANa0

) yed,Na yp,Na Na0] ACI 318-08 Eq. (D-30)

f Vcp ≥ Vua ACI 318-08 Eq. (D-1)ANa see ICC-ES AC308, Part D.5.3.7 ANa0 = s2

cr,Na ICC-ES AC308 Eq. (D-16c)

scr,Na = 20 d √tk,uncr1450 ≤ 3 hef ICC-ES AC308 Eq. (D-16d)

ccr,Na = scr,Na2 ICC-ES AC308 Eq. (D-16e)

yed,Na = 0.7 + 0.3 (ca,minccr,Na

) ≤ 1.0 ICC-ES AC308 Eq. (D-16m)

yg,Na = yg,Na0 + [( savgscr,Na

)0.5

· (1 - yg,Na0)] ≥ 1.0 ICC-ES AC308 Eq. (D-16g)

yg,Na0 = √n - [(√n - 1) · ( tk,c

tk,max,c)1.5]≥ 1.0 ICC-ES AC308 Eq. (D-16h)

tk,max,c = kc

p · d √hef · f'c ICC-ES AC308 Eq. (D-16i)

yec,Na = ( 1

1 + 2'e,N

scr,Na) ≤ 1.0 ICC-ES AC308 Eq. (D-16j)

yp,Na = MAX(ca,mincac

, ccr,Nacac

) ≤ 1.0 ICC-ES AC308 Eq. (D-16p)

Na0 = tk,c · kbond · p · d · hef ICC-ES AC308 Eq. (D-16f)

Variables kcp tk,c,uncr [psi] tk,c [psi] danchor [in.] hef [in.] savg [in.] n 2.000 2145 1045 0.625 8.000 - 1

kc f'c [psi] ec1,N [in.] ec2,N [in.] ca,min [in.] cac [in.] kbond 17 3500 0.000 0.000 33.000 15.307 1.00

Calculations scr,Na [in.] ccr,Na [in.] ANa [in.2] ANa0 [in.2] yed,N tk,max [psi]

15.203 7.602 231.14 231.14 1.000 1449

yg,Na0 yg,Na yec1,N yec2,N yp,Na Na0 [lb] 1.000 1.000 1.000 1.000 1.000 16415

Results Vcp [lb] fconcrete f Vcp [lb] Vua [lb]

32830 0.700 22981 1

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7/16/2014

4.3 Concrete edge failure in direction y+

Vcb = (AVcAVc0

) yed,V yc,V yh,V yparallel,V Vb ACI 318-08 Eq. (D-21)

f Vcb ≥ Vua ACI 318-08 Eq. (D-2)AVc see ACI 318-08, Part D.6.2.1, Fig. RD.6.2.1(b) AVc0 = 4.5 c2

a1 ACI 318-08 Eq. (D-23)

yec,V = ( 1

1 + 2e'v

3ca1) ≤ 1.0 ACI 318-08 Eq. (D-26)

yed,V = 0.7 + 0.3( ca21.5ca1

) ≤ 1.0 ACI 318-08 Eq. (D-28)

yh,V = √1.5ca1ha

≥ 1.0 ACI 318-08 Eq. (D-29)

Vb = (7 ( leda)0.2

√da) l √f'c c1.5a1 ACI 318-08 Eq. (D-24)

Variables ca1 [in.] ca2 [in.] ecV [in.] yc,V ha [in.] 33.000 - 0.000 1.000 18.000

le [in.] l da [in.] f'c [psi] yparallel,V 5.000 1.000 0.625 3500 1.000

Calculations AVc [in.2] AVc0 [in.2] yec,V yed,V yh,V Vb [lb] 1782.00 4900.50 1.000 1.000 1.658 94072

Results Vcb [lb] fconcrete f Vcb [lb] Vua [lb]

56728 0.700 39709 1

5 Warnings• Load re-distributions on the anchors due to elastic deformations of the anchor plate are not considered. The anchor plate is assumed to be

sufficiently stiff, in order not to be deformed when subjected to the loading!

• Condition A applies when supplementary reinforcement is used. The Φ factor is increased for non-steel Design Strengths except Pullout Strength and Pryout strength. Condition B applies when supplementary reinforcement is not used and for Pullout Strength and Pryout Strength. Refer to your local standard.

• Design Strengths of adhesive anchor systems are influenced by the cleaning method. Refer to the INSTRUCTIONS FOR USE given in the Evaluation Service Report for cleaning and installation instructions

• The ACI 318-08 version of the software does not account for adhesive anchor special design provisions corresponding to overhead applications.

• Checking the transfer of loads into the base material and the shear resistance are required in accordance with ACI 318 or the relevant standard!

Fastening meets the design criteria!

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7/16/2014

6 Installation dataAnchor plate, steel: - Anchor type and diameter: HIT-RE 500-SD + Rebar A 615 Gr.60 #5Profile: - Installation torque: -0.009 in.lbHole diameter in the fixture: - Hole diameter in the base material: 0.750 in.Plate thickness (input): - Hole depth in the base material: 8.000 in.Recommended plate thickness: - Minimum thickness of the base material: 9.500 in.Cleaning: Premium cleaning of the drilled hole is required

Coordinates Anchor in.

Anchor x y c-x c+x c-y c+y1 0.000 0.000 - - - 33.000

7 Remarks; Your Cooperation Duties• Any and all information and data contained in the Software concern solely the use of Hilti products and are based on the principles, formulas and

security regulations in accordance with Hilti's technical directions and operating, mounting and assembly instructions, etc., that must be strictly complied with by the user. All figures contained therein are average figures, and therefore use-specific tests are to be conducted prior to using the relevant Hilti product. The results of the calculations carried out by means of the Software are based essentially on the data you put in. Therefore, you bear the sole responsibility for the absence of errors, the completeness and the relevance of the data to be put in by you. Moreover, you bear sole responsibility for having the results of the calculation checked and cleared by an expert, particularly with regard to compliance with applicable norms and permits, prior to using them for your specific facility. The Software serves only as an aid to interpret norms and permits without any guarantee as to the absence of errors, the correctness and the relevance of the results or suitability for a specific application.

• You must take all necessary and reasonable steps to prevent or limit damage caused by the Software. In particular, you must arrange for the regular backup of programs and data and, if applicable, carry out the updates of the Software offered by Hilti on a regular basis. If you do not use the AutoUpdate function of the Software, you must ensure that you are using the current and thus up-to-date version of the Software in each case by carrying out manual updates via the Hilti Website. Hilti will not be liable for consequences, such as the recovery of lost or damaged data or programs, arising from a culpable breach of duty by you.

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B


Attachment B: Internal Curb Detail

ebmud digester seismic assessment - draft 8-5-14 · references american concrete institute (aci)...

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