Structural Evaluation Report€¦ · 140-pound hammer with a free fall of 30 inches, is the...

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520 S. Main Street, Suite 2531 ● Akron, Ohio 44311 ● Tel: 330-572-2100 ● Fax: 330-572-2101 www.GPDGroup.com GPD Engineering And Architecture Professional Corporation GEOTECHNICAL REPORT Site Number: PA-9876 Site Name: Bradys Run Site Data: 4270 Dutch Ridge Road Beaver (Beaver County), Pennsylvania 15009 Latitude 40° 42' 32.72'' N, Longitude 80° 22' 33.77'' W Proposed 190-ft Monopole GPD is pleased to submit this Geotechnical Report for the aforementioned tower. The purpose of the following report is to summarize the soil/rock conditions encountered during the subsurface exploration at this site and provide geotechnical engineering parameters for the proposed tower foundation system. Recommendations for site preparation, construction procedures and quality control were beyond the scope of this study, but can be provided upon request. We at GPD appreciate the opportunity to provide continuing professional services to you. Please feel free to contact us with any questions or if you need additional assistance. Respectfully Submitted, Dustin Vincent, E.I.T. Chip Wilkinson, P.E. Geotechnical Specialist Practice Leader Pennsylvania P.E. License #PE076229 Attachments: Site Location Map Satellite Photograph Topographic Map Boring Location Plan Boring Logs Unified Soil Classification System General Notes GPD# 2015706.03 June 4, 2015

Transcript of Structural Evaluation Report€¦ · 140-pound hammer with a free fall of 30 inches, is the...

Page 1: Structural Evaluation Report€¦ · 140-pound hammer with a free fall of 30 inches, is the standard penetration resistance value (N). Sampling depths and penetration distance, plus

520 S. Main Street, Suite 2531 ● Akron, Ohio 44311 ● Tel: 330-572-2100 ● Fax: 330-572-2101 www.GPDGroup.com

GPD Engineering And Architecture Professional Corporation

GEOTECHNICAL REPORT

Site Number: PA-9876 Site Name: Bradys Run

Site Data: 4270 Dutch Ridge Road Beaver (Beaver County), Pennsylvania 15009

Latitude 40° 42' 32.72'' N, Longitude 80° 22' 33.77'' W

Proposed 190-ft Monopole

GPD is pleased to submit this Geotechnical Report for the aforementioned tower. The purpose of the following

report is to summarize the soil/rock conditions encountered during the subsurface exploration at this site and provide geotechnical engineering parameters for the proposed tower foundation system. Recommendations for

site preparation, construction procedures and quality control were beyond the scope of this study, but can be

provided upon request.

We at GPD appreciate the opportunity to provide continuing professional services to you. Please feel free to contact us with any questions or if you need additional assistance.

Respectfully Submitted,

Dustin Vincent, E.I.T. Chip Wilkinson, P.E.

Geotechnical Specialist Practice Leader

Pennsylvania P.E. License #PE076229 Attachments: Site Location Map

Satellite Photograph Topographic Map

Boring Location Plan Boring Logs

Unified Soil Classification System General Notes

GPD# 2015706.03

June 4, 2015

Page 2: Structural Evaluation Report€¦ · 140-pound hammer with a free fall of 30 inches, is the standard penetration resistance value (N). Sampling depths and penetration distance, plus

Proposed 190-ft Monopole Site Number: PA-9876

6/4/2015 Page 2

GEOTECHNICAL RECOMMENDATIONS

Based on the results of this study, it is our opinion that either a cast-in-place concrete pier (caisson) or a shallow

foundation system would be appropriate for support of a monopole at this site. The following net design

parameters may be used to design the proposed foundation system. A factor of safety of 3 should be applied to the

ultimate bearing pressure values provided below. The cohesion, internal angle of friction and unit weight parameters

along with the passive earth pressure coefficient (KP), vertical modulus of subgrade reaction (pci) and sliding friction

coefficient values given in the following tables are based on the results of the sample borings, published values and

our past experience with similar soil/rock types. These values should, therefore, be considered approximate.

Monopole – Drilled Pier – Ultimate Design Parameters

Depth (feet)

Soil/Rock Description

Unit

Weight (pcf)

Passive Earth

Pressure Coefficient

Ultimate Bearing Pressure

(psf)

Internal Angle of Friction

(Degrees)

Cohesive Strength

(psf)

0 – 3.5* Topsoil and medium dense silty fine to coarse

sand with gravel and cobbles 115 - Ignore - -

3.5 – 6 Medium dense silty fine to coarse sand with

gravel and cobbles 115 KP = 3.25 4,500 32 0

6 – 15 Highly weathered shale 140 KP = 5.0 21,000 42 0

15 – 29 Highly weathered shale 140 KP = 5.0 30,000 42 0

29 – 34 Hard slightly to moderately weathered shale 145 - 40,000 0 9,000

*The first 3.5 feet should be ignored due to potential frost effects and construction disturbance considerations.

Monopole – Shallow Foundation System – Ultimate Design Parameters

Depth (feet)

Soil/Rock Description

Unit

Weight (pcf)

Ultimate Bearing Pressure

(psf)

Sliding Friction

Coefficient @ Base

Vertical Modulus of Subgrade Reaction

(pci)

Internal Angle of Friction

(Degrees)

Cohesion (psf)

0 – 3.5* Topsoil and medium dense silty fine to coarse sand with gravel and cobbles

115 Ignore - - - -

3.5 – 6 Medium dense silty fine to coarse sand

with gravel and cobbles 115 4,500 0.35 75 32 0

6 – 15 Highly weathered shale 135 21,000 0.45 350 42 0

*The first 3.5 feet should be ignored due to potential frost effects and construction disturbance considerations.

The above parameters are provided for the design of a cast-in-place concrete pier (caisson) or a shallow foundation

system. In the event that a different foundation type is chosen, these parameters are not considered valid and GPD

should be notified immediately to provide appropriate design parameters, as warranted.

Page 3: Structural Evaluation Report€¦ · 140-pound hammer with a free fall of 30 inches, is the standard penetration resistance value (N). Sampling depths and penetration distance, plus

Proposed 190-ft Monopole Site Number: PA-9876

6/4/2015 Page 3

GEOTECHNICAL EXPLORATION

Drilling and soil sampling was performed by GPD using a truck-mounted SIMCO 2400 SK-1 drill rig with hollow-stem

augers and a manual SPT hammer. Two (2) sample borings were drilled near the proposed tower foundation.

Representative samples were obtained by the split-barrel sampling procedure in general accordance with

appropriate ASTM standards. In the split-barrel sampling procedure, the number of blows required to advance a

standard 2-inch O.D. split-barrel sampler the last 12 inches of the typical total 18-inch penetration by means of a

140-pound hammer with a free fall of 30 inches, is the standard penetration resistance value (N). Sampling depths

and penetration distance, plus the standard penetration resistance values, are shown on the attached boring logs.

The samples were sealed and mailed to our laboratory for soil classification in general accordance with appropriate

ASTM standards.

The subsurface conditions encountered at the boring location are indicated on the attached boring logs. The

stratification boundaries on the boring logs represent the approximate location of changes in soil/rock types;

in-situ, the transition between materials may be gradual. The boring log includes visual classifications of the

materials encountered during drilling as well as the driller’s interpretation of the subsurface conditions between

samples.

LABORATORY TESTING

The samples were classified in the laboratory based on visual observation, texture and plasticity. The descriptions

of the soils indicated on the boring log are in accordance with the enclosed General Notes and the Unified Soil

Classification System. Estimated group symbols according to the Unified Soil Classification System are given on the

boring logs. A brief description of this classification system is attached to this report.

The laboratory testing program consisted of performing the following tests:

Natural water content tests (ASTM D-2216)

Soil Resistivity (ASTM G-187-12A)

Soil pH Test (ASTM D-4972)

Information from these tests was used in conjunction with field penetration test data to evaluate soil strength in-

situ, volume change potential, and soil classification. Results of these tests are attached and provided on the

boring logs.

SOIL CORROSIVITY

Ground resistivity and soil pH testing were performed as a part of the geotechnical investigation at this site. A

representative soil sample was obtained within the upper 10-ft of soil for laboratory testing. Laboratory resistivity

measurements were obtained using a MILLER-400A implementing the 2-electrode method in conjunction with an

electrolyte box. Based on the laboratory test results, the soil is rated “mildly corrosive” with resistivity

measurements of about 18,000 ohm-cm (refer to Table below) and has a pH of about 5.6 at about 23°C.

Soil Resistivity

Resistivity (Ohm-cm) Soil Type Corrosion Rating

0 to 1,000 Moist Clay Extremely Corrosive 1,000 to 3,000 Moist Clay Highly Corrosive 3,000 to 5,000 Clay Corrosive 5,000 to 10,000 Silty Clay/Clayey Silt Moderately Corrosive 10,000 to 20,000 Sandy Silt Mildly Corrosive

>20,000 Sand/Gravel/Rock Non-Corrosive

Page 4: Structural Evaluation Report€¦ · 140-pound hammer with a free fall of 30 inches, is the standard penetration resistance value (N). Sampling depths and penetration distance, plus

Proposed 190-ft Monopole Site Number: PA-9876

6/4/2015 Page 4

SOIL CLASSIFICATION

The soil samples were classified in general accordance with appropriate ASTM standards based on visual

observation, texture, testing and plasticity. Descriptions of the soils indicated on the boring log are in accordance

with the enclosed General Notes and the Unified Soil Classification System. A brief description of this classification

system is attached to this report.

GROUNDWATER

Groundwater was not encountered during drilling operations as noted on the attached boring log. It should be

noted that fluctuations in the groundwater level can occur and perched water can develop over low permeability

soil or rock strata following periods of heavy or prolonged precipitation. Long term monitoring in cased holes or

piezometers would be necessary to accurately evaluate the potential range of groundwater conditions on the site.

ROCK EXPLORATION

The boring was advanced into the rock using core drilling procedures in general accordance with the appropriate

ASTM standard. The rock was classified in the field and the “percent recovery” and rock quality designation (RQD)

values were determined.

The “percent recovery” is the ratio of the sample length retrieved to the drilled length, expressed as a percent. An

indication of the actual in-situ rock quality is provided by calculating the sample’s RQD. The RQD is the percentage

of the length of broken cores retrieved which have core segments at least 4 inches in length compared to each

drilled length. The percent recovery and RQD are related to rock soundness and quality as illustrated below:

ROCK QUALITY DESIGNATION (RQD)

Relation of RQD and In-situ Rock Quality

RQD (%) Rock Quality

90 – 100 Excellent

75 – 90 Good

50 – 75 Fair

25 – 50 Poor

0 -25 Very Poor

Classification and descriptions of rock core samples are based on visual and tactile observations. Petrographic

analysis of thin sections may indicate other rock types. Percent recovery and rock quality designation (RQD) were

calculated for these samples and are noted at their depths of occurrence on the boring logs.

Page 5: Structural Evaluation Report€¦ · 140-pound hammer with a free fall of 30 inches, is the standard penetration resistance value (N). Sampling depths and penetration distance, plus

Proposed 190-ft Monopole Site Number: PA-9876

6/4/2015 Page 5

QUALIFICATIONS

The analysis and recommendations presented in this report are based upon the data obtained from the borings

performed at this site and from other information discussed in this report. This report does not reflect variations

that may occur across the site or due to the modifying effects of weather.

This report has been prepared for the exclusive use of Elevated Properties LLC for specific application to the

project discussed herein and has been prepared in accordance with generally accepted geotechnical engineering

practices. No warranties, either expressed or implied, are intended or made. In the event that changes in the

nature or design as outlined in this report are planned, the conclusions and recommendations contained in this

report shall not be considered valid unless GPD reviews the changes and either verifies or modifies the conclusions

of this report in writing.

The scope of services for this project does not include either specifically or by implication, any environmental

assessment of the site or identification of contaminated or hazardous materials or conditions. If the owner is

concerned about the potential for such contamination, other studies should be undertaken.

Page 6: Structural Evaluation Report€¦ · 140-pound hammer with a free fall of 30 inches, is the standard penetration resistance value (N). Sampling depths and penetration distance, plus

GPD Job Number: 2015706.03

Date: June 2015

SITE LOCATION MAP Site Name: Bradys Run

Site Number: PA-9876

Page 7: Structural Evaluation Report€¦ · 140-pound hammer with a free fall of 30 inches, is the standard penetration resistance value (N). Sampling depths and penetration distance, plus

GPD Job Number: 2015706.03

Date: June 2015

SATELLITE PHOTOGRAPH Site Name: Bradys Run

Site Number: PA-9876

Page 8: Structural Evaluation Report€¦ · 140-pound hammer with a free fall of 30 inches, is the standard penetration resistance value (N). Sampling depths and penetration distance, plus

GPD Job Number: 2015706.03

Date: June 2015

TOPOGRAPHIC MAP Site Name: Bradys Run

Site Number: PA-9876

Page 9: Structural Evaluation Report€¦ · 140-pound hammer with a free fall of 30 inches, is the standard penetration resistance value (N). Sampling depths and penetration distance, plus

GPD Job Number: 2015706.03

Date: June 2015

BORING LOCATION PLAN Site Name: Bradys Run

Site Number: PA-9876

B-1 B-2

N

Page 10: Structural Evaluation Report€¦ · 140-pound hammer with a free fall of 30 inches, is the standard penetration resistance value (N). Sampling depths and penetration distance, plus

12

10

0

100

100

100

100

100

0

100(43)

Topsoil, 2 inches

Medium Dense brown fine to coarse Silty Sand (SM) with gravel andcobbles and trace weathered rock fragments

*Driller drove rock at 1-ft

Tannish gray highly weathered Shale

Gray below 16 feet

Hard dark gray slightly to moderately weathered Shale with some sand

Boring terminated at 34.0 feet

50/2"

7-8-20(28)

35-50/5"

25-50/5"

50/4"

50/4"

50/3"

SS1

SS2

SS3

SS4

SS5

SS6

SS7

RC8

AT TIME OF DRILLING --- DRY

LOGGED BY Dustin Vincent

DRILLING METHOD Hollow Stem Auger - 3 1/4" ID

CHECKED BY Nicholas Zadd

GROUND ELEVATION

GROUND WATER LEVELS:

DATE STARTED May 29, 2015 COMPLETED May 29, 2015

DRILLING CONTRACTOR GPD

HOLE SIZE 7.5 in

AT END OF DRILLING ---

NOTES SIMCO SK-1 drill rig with manual SPT hammer

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CLIENT Elevated Properties LLC

PROJECT NUMBER 2015706.03

PROJECT NAME Bradys Run

PROJECT LOCATION Beaver, Pennsylvania

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Page 11: Structural Evaluation Report€¦ · 140-pound hammer with a free fall of 30 inches, is the standard penetration resistance value (N). Sampling depths and penetration distance, plus

Topsoil, 2 inches

Brown fine to coarse Silty Sand (SM) with gravel and cobbles andtrace weathered rock fragments

Tannish gray highly weathered Shale

Gray below 17 feet

Auger Refusal at 27.0 feet

AT TIME OF DRILLING --- DRY

LOGGED BY Dustin Vincent

DRILLING METHOD Hollow Stem Auger - 3 1/4" ID

CHECKED BY Nicholas Zadd

GROUND ELEVATION

GROUND WATER LEVELS:

DATE STARTED May 29, 2015 COMPLETED May 29, 2015

DRILLING CONTRACTOR GPD

HOLE SIZE 7.5 in

AT END OF DRILLING --- DRY

NOTES SIMCO SK-1 drill rig with manual SPT hammer

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Boring Number: B-2

CLIENT Elevated Properties LLC

PROJECT NUMBER 2015706.03

PROJECT NAME Bradys Run

PROJECT LOCATION Beaver, Pennsylvania

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Page 12: Structural Evaluation Report€¦ · 140-pound hammer with a free fall of 30 inches, is the standard penetration resistance value (N). Sampling depths and penetration distance, plus

Letter Symbol

GW

GP

GM

GC

SW

SP

SM

SC

ML

CL

OL

MH

CH

OH

PT

Organic clays of medium to high plasticity.

Peat, muck, and other highly organic soils.

Well-graded sands and gravelly sands, little or no

fines.Poorly-graded sands and gravelly sands, little or no

fines.

Silty sands, sand-silt mixtures

Inorganic clays of low to medium plasticity, gravelly

clays, sandy clays, silty clays, lean clays.

Unified Soil Classification System

Clayey sands, sandy-clay mixtures.

Organic clays of medium to high plasticity.

Inorganic silts, micaceous or diatomaceous fines

sands or silts, elastic silts.

Description

Silts and Clays

Liquid Limit greater than

50%

Gravels

With Fines

Clean Sands

Major Divisions

Clean

GravelsS

an

ds

Mo

re t

han

½ p

assi

ng

thro

ugh t

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No

. 2

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siev

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Inorganic silts, very fine sands, rock flour, silty or

clayey fine sands.

Gra

vel

s

Mo

re t

han

½ c

oar

se

frac

tio

n r

etai

ned

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Inorganic clays of high plasticity, fat clays.

Consistency Classification

Highly Organic Soils

Co

ars

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s

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Sands With

Fines

Silts and Clays

Liquid Limit less than

50%

Well-graded gravels and gravel-sand mixtures,

little or no fines. Poorly-graded gravels and gravel-sand mixtures, little

or no fines.

Silty gravels, gravel-sand-silt mixtures.

Clayey gravels, gravel-sand-clay mixtures.

Cohesive SoilsGranular Soils

Description - Blows Per Foot (Corrected) Description - Blows Per Foot (Corrected)

MCS

<5

5 ¯ 15

16 ¯ 40

41 ¯ 65

>65

SPT

<4

4 ¯ 10

11 ¯ 30

31 ¯ 50

>50

Very loose

Loose

Medium dense

Dense

Very dense

Very soft

Soft

Firm

Stiff

Very Stiff

Hard

MCS

<3

3 ¯ 5

6 ¯ 10

11 ¯ 20

21 ¯ 40

>40

SPT

<2

2 ¯ 4

5 ¯ 8

9 ¯ 15

16 ¯ 30

>30

MCS = Modified California Sampler SPT = Standard Penetration Test Sampler

Page 13: Structural Evaluation Report€¦ · 140-pound hammer with a free fall of 30 inches, is the standard penetration resistance value (N). Sampling depths and penetration distance, plus

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5 " 5 p 6 :5 p 6 : " 5 p : 55 p : 5 " 9 p 5 59 p 5 5 " 6 p 5 56 p 5 5 " 7 p 5 57 p 5 5 " 8 p 5 58 p 5 5 <q X U Z T r P Q s X Y \ U T U X Y \ Q Z s P U W T U X Y

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! " # $ % � � . G 2 E 2 ( 4 $ ) - .O 2 G 4 $ ) - .$ ) - .o 2 I 1 F E � L G Io ) I 2 G L . 2 ( 4 � L G I� L G IO 2 G 4 � L G IZ s S R Q X [ P Q R S T U V Q P X s � � S P \ Y Q Z Z P X s � � Q \ \ U Y ] T � U s � Y Q Z Z Q Z/ ) 0 + 1 + . 2 0 3 4

= > ? @ A > ? BC ( . 2 G 0 L . 1 0 � ( L 4 2 G + ) - N L G 4 1 0 � E L . 2 G 1 L ( ) G 3 ) ( ) G * 1 . J( L 4 2 G + L . ( 2 L + . � " 1 0 3 J � � E E � . J 1 3 �C ( . 2 G 0 L . 1 0 � ( L 4 2 G + ) - N L G 4 1 0 � E L . 2 G 1 L ( ) G 3 ) ( ) G * 1 . J( L 4 2 G + ( 2 + + . J L 0 � " 1 0 3 J � � E E � . J 1 3 �' G 2 L � + L ( ) 0 � I 2 - 1 0 1 . 2 M ( L 0 2 + ) - - G L 3 . F G 2 * 1 . J ( 1 . . ( 2G 2 + 1 + . L 0 3 2 . ) - G L 3 . F G 1 0 �% G L 3 . F G 2 M ( L 0 2 + L M M 2 L G M ) ( 1 + J 2 I ) G � ( ) + + 4 H+ ) E 2 . 1 E 2 + + . G 1 L . 2 I = > ? @ A > ? B� G 2 L . 2 G . J L 0 ; " - ) ) . � f 9 p 5 E �9 " - ) ) . . ) ; " - ) ) . � 5 p ; E . ) 9 p 5 E �7 " 1 0 3 J . ) 9 " - ) ) . � 5 p 9 E . ) 5 p ; E �9 � " 1 0 3 J . ) 7 " 1 0 3 J � ; 5 E E . ) 9 5 5 E E �� " 1 0 3 J . ) 9 � " 1 0 3 J � 9 5 E E . ) ; 5 E E �9 , 8 " 1 0 3 J . ) � " 1 0 3 J � ; E E . ) 9 5 E E �9 , 8 " 1 0 3 J ) G ( 2 + + � M L M 2 G . J 1 0 � � d ; E E �

_ A g h > ? i @ ? } ~K G 4 mo ) 1 + . mn 2 . m

_ A g h > ? i @ ? } ~O 2 G 4 # J 1 3 � ' 2 I I 2 I# J 1 3 � ' 2 I I 2 Io 2 I 1 F E ' 2 I I 2 I# J 1 0 ' 2 I I 2 IO 2 G 4 # J 1 0 ' 2 I I 2 I# J 1 3 � ( 4 � L E 1 0 L . 2 I# J 1 0 ( 4 � L E 1 0 L . 2 I6 p : " 9 59 5 " : 5: 5 " 6 : 56 : 5 " : 6 :: 6 : " 9 H 5 : 59 H 5 : 5 " 6 H � 5 5f 6 H � 5 5

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= } l i } ~ A ~ @O 2 G 4 / ) L G + 2 � G L 1 0 2 I/ ) L G + 2 � G L 1 0 2 Io 2 I 1 F E � G L 1 0 2 I% 1 0 2 � G L 1 0 2 IO 2 G 4 % 1 0 2 � G L 1 0 2 I] P S U Y | Z U � Q \ T Q P q U Y X R X ] {� � � � � � �     � ¡ ¢ £ � ¤ ¢ ¥ ¦ � § � ¨ © � ª «P X s � V X U \ Z¬ } ? ­ g� 1 .O F �/ L N 1 . 4/ L N 2 ¬ } ? ­ _ ? B l A @ A >d � E E � d 5 p 6 : 1 0 �� E E . ) : 5 E E � 5 p 6 : 1 0 . ) 6 1 0 �: 5 E E . ) � 5 5 E E � 6 1 0 . ) 6 7 1 0 �f � 5 5 E E � f 6 7 1 0 �P X s � ® r S R U T { \ Q Z s P U W T U X Y¯ ° _ ¬ B ± ² A³ 5 " 9 5 5´ : " ³ 5: 5 " ´ :6 : " : 5� 2 + + . J L 0 6 :

µ ? ¶ A ¯ B ~ b Af 7 p ´ � E E6 p 5 E E " 7 p ´ � E E5 p 7 6 E E " 6 p 5 E E5 p 5 ´ : E E " 5 p 7 6 E Ed 5 p 5 ´ : E E· ) 3 � � 2 0 2 G L ( ( 4 - G 2 + J H ¸ ) 1 0 . + + . L 1 0 2 I L 0 I I 1 + 3 ) ( ) G L . 1 ) 02 � . 2 0 I + 1 0 . ) G ) 3 � F M . ) 6 : E E � 9 1 0 � H ) M 2 0 ¸ ) 1 0 . + E L 43 ) 0 . L 1 0 3 ( L 4 H 3 ) G 2 G 1 0 � + F 0 I 2 G J L E E 2 G 1 E M L 3 . p· ) 3 � E L + + 1 + I 2 3 ) E M ) + 2 I : 5 e ) G ( 2 + + H + 1 � 0 1 - 1 3 L 0 .M ) G . 1 ) 0 + ) - . J 2 G ) 3 � + J ) * I 1 + 3 ) ( ) G L . 1 ) 0 L 0 I* 2 L . J 2 G 1 0 � 2 - - 2 3 . + H 3 ) G 2 + 3 L 0 0 ) . D 2 D G ) � 2 0 D 4 J L 0 I) G + 3 G L M 2 I D 4 � 0 1 - 2 p· ) 3 � E L + + 1 + E ) G 2 . J L 0 : 5 e I 2 3 ) E M ) + 2 I H 3 ) E M ( 2 . 2I 1 + 3 ) ( ) G L . 1 ) 0 ) - G ) 3 � - L D G 1 3 H 3 ) G 2 E L 4 D 2 2 � . G 2 E 2 ( 4D G ) � 2 0 L 0 I � 1 N 2 + 3 ( F 0 � + ) F 0 I * J 2 0 + . G F 3 � D 4J L E E 2 G H E L 4 D 2 + J L N 2 I * 1 . J L � 0 1 - 2 p¯ } h ¹ º B g g _ A g h > ? i @ ? } ~� � 3 2 ( ( 2 0 .� ) ) I% L 1 G� ) ) GO 2 G 4 � ) ) G

\ Q ] P Q Q X [ » Q S T � Q P U Y ]$ ( 1 � J . ( 4 n 2 L . J 2 G 2 I mn 2 L . J 2 G 2 I m� 1 � J ( 4 n 2 L . J 2 G 2 I m

= > ? @ A > ? B/ ) J 2 + 1 N 2 + ) 1 ( . J L . 3 L 0 D 2 D G ) � 2 0 I ) * 0 1 0 . ) + E L ( (L 0 � F ( L G ( F E M + * J 1 3 J G 2 + 1 + . - F G . J 2 G D G 2 L � I ) * 0¼ 0 3 ( F + 1 ) 0 ) - + E L ( ( M ) 3 � 2 . + ) - I 1 - - 2 G 2 0 . + ) 1 ( +¼ 0 3 ( F + 1 ) 0 � G 2 L . 2 G . J L 0 ; 1 0 3 J 2 + . J 1 3 � � ´ : E E �¼ 0 3 ( F + 1 ) 0 9 , 8 " 1 0 3 J . ) ; 1 0 3 J 2 + � ; . ) ´ : E E � . J 1 3 �2 � . 2 0 I 1 0 � . J G ) F � J . J 2 + L E M ( 2¼ 0 3 ( F + 1 ) 0 ( 2 + + . J L 0 9 , 8 " 1 0 3 J � ; E E � . J 1 3 �

O 2 G 4 $ ) - .$ ) - .% 1 G E � o 2 I 1 F E $ . 1 - - �$ . 1 - -O 2 G 4 $ . 1 - -� L G IO 2 G 4 � L G I

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