Specifications Part 4 of 4.pdf

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Earth Mechanics, Inc.

Geotechnical & Earthquake Engineering

FIGURE 2-1: MAJOR FAULT SYSTEM IN SAN FRANCISCO BAY AREA

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FIGURE 2-2: IDEALIZED SOIL PROFILE ALONG ANTIOCH BRIDGE

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FIGURE 2-2: IDEALIZED SOIL PROFILE ALONG ANTIOCH BRIDGE (Cont.)

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3.0 GROUND MOTIONS

This section presents a brief summary of ground motion study work. Details can be found in a separate ground motion report entitled “Ground Motion Study for Antioch Bridge Seismic Retrofit Project,” which has been prepared for documenting probabilistic and deterministic seismic hazard study, spectrum-compatible earthquake time histories, site response analysis, and soil-structure interaction analysis in depth with supporting tables and illustrations.

3.1 Seismic Hazard Study

The analytical technique adopted for the probabilistic seismic hazard analysis (PSHA) follows the original work developed by Cornell (1968), except with the extension considering both the aleatory variability and the epistemic uncertainty of ground motion prediction. The site relative to the major faults in the region is shown in Figure 3-1, and the local seismic sources in the delta area are shown in Figure 3-2. The bridge is located about 74 km east of the San Andreas fault, 16 km east of the Greenville fault, and 15 km east of the Pittsburg/Kirby Hills fault. The Midland fault dips toward the site, with the shortest distance to the site at 11 km. For the delta region, the source characterization developed by URS (2007) for the Delta Risk Management Study was adopted, while for the other major faults, the seismic source characterization was based on the 2003 USGS Working Group on Earthquake Probabilities in Northern California (WG 2003).

For the magnitude density function describing how the fault slip-rate is distributed in different size earthquakes, the characteristic model (Youngs and Coppersmith 1995) was used for major faults, and Y&C model with a weight of 0.7 and a normal distribution with a weight of 0.3 was adopted for the faults in the delta region. The rupture dimension model is based on the relations for fault area and fault width (Wells and Coppersmith 1994) for all source types. Five attenuation relationships developed as part of PEER Next Generation Attenuation (NGA) program were used in the probabilistic seismic hazard analysis. These attenuation relations were made for a spectral damping of 5% and adjusted to account for near-fault directivity effects. The near-fault directivity effects were based on a modified form of the Somerville et al. (1997) fault-rupture directivity model (as described in Abrahamson, 2000), comprising two period-dependent scaling factors: one dealing with the increase in shaking intensity in the average horizontal component and another reflecting the directional nature of the shaking intensity.

Uniform hazard spectra (UHS) at six return periods (100-, 300-, 475-, 1,000-, 1,500- and 2,000-years) were then computed, including the fault normal (FN) and fault parallel (FP). Figure 3-3 shows a series of uniform hazard spectra for the FN component, as well as the result of deterministic analyses conducted for the Southern Midland fault using 50th percentile (mean) and 84th percentile (mean plus one standard deviation). Vertical spectrum was developed from a V/H ratio applied to the average of the fault normal and fault parallel components.

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Geotechnical & Earthquake Engineering

From several discussions with Caltrans and the Seismic Peer Review Panel for the toll bridges, the 1,000-year return period ground motion was considered appropriate and selected as the Safety Evaluation Earthquake (SEE) for seismic retrofit evaluation of the Antioch Bridge. Figure 3-4 presents the reference rock spectra for the SEE scenario showing the fault normal (FN), fault parallel (FP), and vertical components.

3.2 Spectrum Compatible Time Histories

Seven sets of spectrum compatible time histories were developed by modifying seed motions (usually actual earthquake records) so that their spectra are similar to the SEE reference rock spectra. Various methods have been developed to perform the spectrum matching. A commonly used method adjusts the Fourier amplitude spectrum based on the ratio of the target response spectrum to the time history response spectrum while keeping the Fourier phase of the reference history fixed. An alternative approach adjusts the time history in the time domain by adding wavelets to the reference time history which used in this project.

As part of the spectral matching procedure, a baseline correction was also applied to the ground motions in acceleration, velocity, and displacement. The baseline is computed by fitting the displacement time history to a high order polynomial (order 4 to 7) and excluding the constant and linear terms. The second derivative of this displacement baseline is computed and it is subtracted from the acceleration ground motion.

The following are a summary of seven seed motions that have been used to generate spectrum-compatible time histories:

● Set 1: 1989 Loma Prieta Earthquake (M=6.9), Saratoga – Aloha Ave at 13.0 km

● Set 2: 1987 Superstition Hill Earthquake (M=6.3), Wildlife Liquefaction Array at 24.7 km

● Set 3: 1987 Whittier Earthquake (M=6.0), Northridge-Saticoy St. at 39.8 km

● Set 4: 1979 Imperial Valley Earthquake (M=6.5), EC CO Center FF at 7.6 km

● Set 5: 1979 Imperial Valley Earthquake (M=6.5), Calexico Fire Station at 10.6 km

● Set 6: 1994 Northridge Earthquake (M=6.7), Century City, LACC at 25.7 km

● Set 7: 1981 Taiwan Earthquake (M=6.3), SMART1 M07 at 21.0 km

3.3 Seismic Response and Kinematic SSI Analysis

For the development of ARS design criteria, six representative piers were selected to conduct site response and kinematic soil-pile interaction analyses. The six selected piers are: South Approach Piers 03 and 12 (20"×20" square concrete piles, the former with a buried pile cap and the latter with a cantilevered one); Main Channel Piers 19 and 21 (54-inch diameter concrete hollow piles with a long cantilever pile length above mud-line); North Approach Piers 30 (20"×20" square concrete

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Geotechnical & Earthquake Engineering piles with a buried pile cap) and Pier 39 (30-inch steel pipe piles with a cantilevered portion above mud-line). The exterior piles for each of the six selected piers are highly battered outward.

Small-strain shear modulus Gmax is best estimated from shear wave velocity values that are measured in the field and by using the relationship of Gmax = ρVs

2, where ρ is mass density and Vs is shear wave velocity. Soil dynamic properties in terms of normalized shear modulus and damping curves have been studied by many researchers. For the site response analyses, we adopted the Seed et al. (1986) relationship for sand and the Vucetic and Dobry (1991) relationship for clays. To deal with potential variations in the determination of in situ soil properties, the following parametric studies were considered: 1) the best-estimate case established from the down-hole shear wave velocity measurements; 2) a lower bound case; and 3) an upper bound case. Scaling factors of 0.75 and 1.25 were used as multiplication factors on the best-estimate shear-wave velocity for lower and upper bound scenarios.

Site response analyses were conducted using the computer program SHAKE91 (Idriss and Sun, 1992), an equivalent linear analysis. The program SHAKE91 has been used for solving one-dimensional shear wave propagation problems for three decades. Engineers have accumulated knowledge from the performance of SHAKE in predicting ground response during earthquakes. To avoid an unrealistic prediction of free-field motion for a long soil column, a relatively short soil column was used for our site response analyses. A transmitting boundary was selected near Elevation (El.) -200 feet where an average shear wave velocity of 1200 feet per second (366 m/sec) is anticipated, which was a controlling parameter in the NGA attenuation models.

To rigorously develop the design response spectra for the pile-supported structure, soil-pile interaction was considered. The method is based on a linear theory making use of the sub-structuring procedure (see Section 5 for detail). The first step involved linearization of p-y curves by performing a lateral pushover analysis of a single pile to a representative displacement level expected during the earthquake. A pile foundation model was then created in which each pile was supported on elastic soil springs that were excited by depth-varying, free-field motions computed from the site response analyses. Sub-structuring was performed to compute resultant forces acting at the pile-cap level. The resultant forces were divided by the foundation stiffness to result in so-called kinematic motions. The kinematic motions formed the basis for development of ARS design curves for the bridge structure. The kinematic motion is calculated at the pile cap level and implicitly contains the statically condensed forces transmitted from the ground to the superstructure along the entire embedded pile length. Therefore, the effects of the depth-varying shaking intensity in the soil column, the depth-varying soil stiffnesses, and the pile properties are included in the solution. The following pile properties were used in conducting kinematic soil-pile interaction analyses (also see Section 5.3):

• 54-inch diameter concrete piles (Main Channel Piers 17 ~ 21)

Effective pile EI = 8.47×1011 lb-in2.

(Infilled section)

Effective pile EI = 6.44×1011 lb-in2.

(Hollow section)

• 30-inch diameter steel pipe piles (Piers 39,40) Effective pile EI = 2.35×1011 lb-in2.

• 14-inch square concrete piles (Abutment 1 and Pier 41) Effective pile EI = 6.95×109 lb-in2.

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Geotechnical & Earthquake Engineering

• 24-inch square concrete piles (the rest of bridge piers) Effective pile EI = 6.07×1010 lb-in2.

• 12-inch square concrete piles (slab bridge piers) Effective pile EI = 3.11×109 lb-in2.

A fixed pile head condition was assumed in all the cases. The analyses were conducted with the in-house computer program KIPS, which is dedicated to performing kinematic soil-pile interaction analyses (Earth Mechanics, Inc., 1999). Considering seven motion sets and three levels of shear wave velocity, 21 kinematic spectra (spectral accelerations and displacements) for each selected pier were computed, from which their mean and mean plus one standard deviation spectra were then obtained.

3.4 ARS Design Curves

The shape of response spectra as obtained from the kinematic soil-pile interaction analyses sometimes contains multiple peaks and valleys. For practical use and simplicity for the design process, it was decided that the final ARS recommendations should be constrained by a well-behaved ARS curve shape for both spectral acceleration and displacement (i.e., the final ARS curves should be smoothed-out). Discussions with the structural designers led to a decision to keep a minimum number of ARS design curves for the response spectrum analyses. From a review of the kinematic spectra from the six piers, it appears that three sets of ARS curves would be adequate to cover horizontal seismic loading for the entire bridge:

• ARS Curve 1: Recommended for design of the South Approach piers (1~16), or the entire Antioch Bridge at all piers as the most simplified but the most conservative design basis

• ARS Curve 2: Recommended for designing the Main Channel piers (17~21), representing 54-inch diameter concrete hollow piles with a long cantilever pile extending above mud-line

• ARS Curve 3: Recommended for designing the North Approach piers (22~41) founded on smaller piles driven through the very soft peat layer

For the vertical spectrum, we recommend using the reference vertical motion spectrum from PSHA without further site response analysis. The recommended SEE design spectra for 5 percent damping are presented on Figure 3-5.

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FIGURE 3-1: FAULT MAP AROUND PROJECT SITE (RED STARS FOR THE SITE)

F

F

F

F

F

F

F

F

F 36.75

37.25

37.75

38.25

-123 -122.5 -122 -121.5 -121

SGN

SGS

NCS

PN

SCZ

CC

NC

SC

MTD

SG

NG

HS

HN

RC NGV

SGV

CON

Southern Midland

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FIGURE 3-2: SEISMIC SOURCES IN THE DELTA REGION (RED FAULTS-WG03; OTHERS- URS,2007)

F

F

37.5

38.5

-122.25 -121.75 -121.25

Southern Midland

HS

NC

Marsh Creek Greenville

Verona

Las Positas

Northern Midland Zone

Thornton Arch Zone

Montezuma Hills Zone

Briones Zone

West Tracy

Vernalis

Midway/Black Butte

Orestimba

CON

MTD

SGV

NGV

Wragg Cyn

PittsBurg- Kirby Hills

Potrero Hills

Cull Cyn

Las Trampas

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FIGURE 3-3: UNIFORM HAZARD SPECTRA AND MCE SPECTRA (SPECTRAL ACCELERATION)

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

0.01 0.1 1 10

S pe ct ra l A cc el er at io n (g

Period (sec)

100 Year

300 Year

475 Year

1,000 Year

1,500 Year

2,000 Year

S. Midland (M6.6) Median

S. Midland (M6.6) 84th

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FIGURE 3-4: REFERENCE ROCK SPECTRA FOR THE SAFETY EVALUATION EARTHQUAKE

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FIGURE 3-5: ARS DESIGN CURVES FOR SAFETY EVALUATION EARTHQUAKE (SEE)

0.2

0.4

0.6

0.8

1.2

1.4

0 1 2 3 4 5 6

Period (second)

P S

A (g

ARS Curve 1 (Pier 1-16) ARS Curve 2 (Pier 17-21) ARS Curve 3 (Pier 22-41) Reference Rock Spectrum

0 1 2 3 4 5 6

Period (second)

R el at iv e D is pl ac em en t ( in ch

ARS Curve 1 (Pier 1-16) ARS Curve 2 (Pier 17-21) ARS Curve 3 (Pier 22-41) Reference Rock Spectrum

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4.0 FOUNDATION EVALUATION

This section presents the description of foundations along the bridge, and the important issues on evaluation of these foundations in terms of axial loading conditions and lateral loading conditions.

Liquefaction potential and associated settlement is evaluated at potentially susceptible locations. In addition, soil support characteristics depicting p-y, t-z, and q-u curves for individual pile are tabulated which can be used for pushover analyses and estimating pile capacities. To assist modeling of the foundations in the global bridge models for seismic response evaluation, foundation stiffness, mass, and damping matrices are provided in Section 5.3.

4.1 Foundation Description

The entire existing bridge is composed of Main Channel, South and North Approaches, and a slab structure in the north end; all supported on pile foundations (see Figure 4-1). Tables 4-1 and 4-2 summarize the number of piles per bent, pile top and pile tip elevations, pile group layout, pile type and size, and design load of the pile for Antioch Bridge and slab bridge piers.

The South Approach consists of Abutment 1 and Pier 2 through Pier 16, with Abutment 1 founded on 14-inch square concrete piles and Piers 2 to 16 on 24-inch square concrete piles. Abutment 1 and Pier 2 through Pier 6 have buried pile caps and the remaining piers have pile caps cantilevered above the mud-line with cantilever height varying from 15 to 28 ft. The Main Channel span contains Piers 17 to 21, each supported on 54-inch diameter concrete hollow piles with a pile cap cantilevered 27 to 52 ft above the mud-line. The North Approach consists of Piers 22 through 41, with Pier 22 through Pier 38 supported on 24-inch square concrete piles, Piers 39 and 40 on 30-inch diameter steel pipe piles in-filled with concrete, and Pier 41 founded on 14-inch square concrete piles. Piers 39 and 40 have pile caps cantilevered 10 to 20 ft above the mud-line, and the remaining piers have embedded pile caps. The design load of a single 54-inch diameter concrete hollow pile is 500 tons. The design load of a single 24-inch square or 30-inch diameter pile is 250 tons, and that of a single 14-inch square pile is 100 tons.

All the pile caps of Antioch Bridge piers are rectangular-shaped on a plan view. The cap width varies from 24 to 48 feet, the cap length varies from 39 to 56 feet, and the cap thickness is between and 7 and 11 feet. Pier 19 in the middle of main crossing channel has the largest cap dimension.

The number of piles per pier varies from 12 to 30. The exterior piles for each Antioch Bridge pier (except Abutment 1 and Pier 41) are highly battered outward with angle 1 (horizontal) to 3 (vertical), for providing higher lateral resistance. The elevation of pile top is between -21 and +5 feet, while that of pile tip is between -112 and -40 feet. The elevation of mud-line varies from -46 to 10 feet, with the lowest value near Pier 20.

The slab structure at the end of the North Approach is composed of 30 piers (Pier 42 through Pier 70 and Abutment 71), each supported on extensions of four 12-inch square concrete vertical piles

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Geotechnical & Earthquake Engineering with a slender cap-beam near the mud-line elevation. The design load of a single 12-inch square pile is 70 tons. The pile layout for each pier can be also found in Appendix A.

4.2 Liquefaction Assessment

The adopted procedure of quantitative liquefaction evaluation is mainly based on the collaborative work of Youd and others (2001), which provides the state-of-the-art summary of consensus recommendations on the extensive developments, after the “simplified procedure” for evaluating soil liquefaction resistance pioneered by Seed and Idriss in 1964. The following briefly describes the definition of safety factor and the criteria based on standard penetration and cone penetration tests. Further details can be found in their original paper.

The factor of safety against liquefaction of a soil sub-layer (FS) is defined by the ratio of soil cyclic resistance ratio (CRR) to soil cyclic stress ratio (CSR), as follows:

CSR

KKMSFCRR

CSR

CRRFS ασ ⋅⋅⋅

== 5.7 in which CRR7.5 is the cyclic resistance ratio for magnitude 7.5 earthquake, MSF is the magnitude scaling factor, Kσ is the correction factor for high overburden pressure, Kα is the correction factor for sloping ground, and CSR can be expressed by the ratio of average shear stress (τav) to effective overburden pressure (σ'v0), as follows:

d v v v av r σ' σ g a σ' τ

CSR ⋅⋅⋅==

0max in which amax is the peak horizontal acceleration at ground surface, σv0 is the total overburden pressure, and rd is the stress reduction coefficient, as function of depth.

For the standard penetration tests (SPT), CRR7.5 can be statistically approximated by

( ) 120

45)(10

)(34

5.7 − cs cs cs N N

N

CRR

in which (N1)60cs is the clean-sand SPT blow count normalized to an overburden pressure of 100kPa (1tsf) and a hammer energy ratio of 60%, and equals to:

SRBENmcs CCCCCNNN ⋅⋅⋅⋅⋅⋅+=+= βαβα 601601 )()( where α and β are correction coefficients for fine content, Nm is the measured SPT blow count and CN, CE, CB, CR and CS are SPT correction coefficients for overburden pressure, energy ratio, borehole diameter, rod length and sampling method, respectively.

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For the cone penetration tests (CPT), CRR7.5 can be approximated by

08.0

93160)(50

05.0

833.050)(

5.71

5.71 csNc csNc csNc csNc q CRRq q CRRq in which (qc1N)cs is the clean-sand cone penetration resistance normalized to an overburden pressure of 100kPa, and equals to:

a c QcNcccsNc p q CKqKq ⋅⋅=⋅= )()( 11 where Kc is the correction factor for grain characteristics, CQ is a normalizing factor, qc is the field cone penetration resistance at tip, and pa is 1atm of pressure.

The results of liquefaction assessment conducted on Abutment 1 through Pier 19 at the southern segments of the bridge and 4 selected piers near the northern half of the slab bridge span are summarized in Table 4-3. The SPT or CPT soundings nearest to each of these piers were chosen for performing analysis, providing the representative results to these pier locations. The peak ground acceleration (amax) of each pier location was computed from the SHAKE runs of the seven input motion sets. A moment magnitude of 6.6 was adopted for the site. When a soil layer has a FS less than unity, it is classified as liquefiable; several successive liquefiable layers make up a potential liquefaction zone. Individual liquefiable layers are identified in Table 4-3. From evaluation of these results, the following observations and recommendations can be made:

• The soil strata at the southern end of the bridge span (from Abutment 1 to Pier 4) are generally non-liquefiable, because none or only few thin liquefiable zones exists for these pier locations;

• On the other hand, the subsoil at the remaining portion of south bridge span and the northern half of the slab bridge span contains liquefiable zone(s) with total thickness varying from 20 to 45 feet; these liquefiable zones might be continuous or localized along these regions;

• The influence of these liquefiable zones on foundation performance is examined in Section 4.6.

4.3 Axial Loading Conditions

Vertical loads on the foundation are resisted by the underlying piles which are axially loaded. The pile resistance is developed when there is relative movement between the pile and the surrounding soil. The load-displacement relation between the pile shaft and soil is characterized by the so-called t-z curve, while that between the pile tip and soil represents the q-u curve. For a well-designed pile, the soil adjacent to the pile should provide a sufficient capacity to withstand the applied load

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Geotechnical & Earthquake Engineering without bearing failure so that the pile does not undergo exceeding settlement under the working load condition. In this section, the t-z and q-u curves of all Antioch Bridge and slab bridge piers are presented, their axial load-deformation (Q-δ) curves in terms of pile head load versus pile head displacement relationship are developed, and their ultimate bearing capacity values computed using CPT data are compared with the capacity estimated from the conventional pile capacity calculations.

4.3.1 t-z and q-u Curves

Determination of the ultimate skin friction resistance (tmax) and end bearing capacity (qmax) as well as development of the t-z and q-u curves are described in this section. The developed t-z and q-u curves are used in the following section for generating Q-δ curves (pile head load vs. pile head deformation), in the soil-structure interaction analysis for forming 6×6 condensed matrices and kinematic motions (see Section 5-3), and in the finite element analysis of the bridge model for simulating the nonlinear soil springs distributed along the piles.

The ultimate skin friction resistance (tmax) in the t-z curve can be obtained by multiplying a unit skin friction of soil (fs) with the pile circumference, and therefore the t-z curves are developed per a linear pile length basis. The general formula for soil unit skin friction (fs) is given in the following equation, depending upon the soil type:

cfclay Kfsand s vs tan':

α δσ where K is the lateral earth pressure coefficient whose value depends on the pile installation method, σv' is the effective overburden pressure, δ is the friction angle between the pile material and the soil as function of soil internal friction angle (φ'), c is the undrained shear strength, and α is the adjustment factor depending on (c, σv'). In the project, K=1.0 and δ=0.75φ' were adopted for sand layers, and α varying from 0.8 to 1.0 was used for clays. The real shape of in-situ t-z curves is affected by the pile installation method, the roughness of pile surface, soil type and depth. The t-z curve adopted in the project is based on the work developed by Vijayvergiya in 1977, as shown in the following equation in a normalized form:

cc z zB z zA t t max where t is the actual skin resistance, (A0, B0) are empirical coefficients, z is the actual relative displacement between the pile surface and soil, and zc is the ultimate relative displacement between the pile surface and soil. It is noted that the skin friction behavior becomes purely plastic when z exceeds zc. In the project, we adopted A0=2 and B0=1 for both sand and clay, zc=0.2 inch for sand and zc=0.01D (where D is pile diameter) for clay. Accordingly, the normalized t-z curves for both sand and clay can be approximated by the following table and plotted in Figure 4-2:

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Geotechnical & Earthquake Engineering t/tmax z/zc

0.000 0.000

0.397 0.050

0.532 0.100

0.694 0.200

0.795 0.300

0.865 0.400

0.949 0.600

1.000 1.000

1.000 ∞

The ultimate end bearing force (qmax) in the q-u curve can be obtained by multiplying a unit end bearing capacity at the pile tip (qt) with the pile-tip area (A). The general formula for soil end bearing capacity (qt) is presented in the following equation, also depending upon the soil type:

cNqclay Nqsand ct vqt

= σ where (Nq, Nc) are bearing capacity factors depending on φ', failure mode and pile geometry, σv' is the effective overburden pressure at tip, and c is the average undrained shear strength beneath the tip. Figure 4-3 depicts several bearing capacity factor Nq versus internal friction angle relationships (Fang, 1991). It can be seen that there are appreciable variations among different theories in determining the end bearing capacity factors. The uncertainty is compounded by different pile installation methods. In the project, Nq varying from 25 to 105 was adopted for sand layers and Nc=9 was used for clays. The shape of in-situ q-u curves is affected by the pile installation method, the pile tip geometry, soil type and depth. The q-u curve adopted in the project is also based on the work developed by Vijayvergiya in 1977, as shown in the following equation:

c c

C c uu uu u u q q max where q is the actual end bearing resistance, C0 is an empirical coefficient, u is the actual end settlement at the tip, and uc is the ultimate end settlement. It is also observed that the end bearing behavior becomes purely plastic when u exceeds uc. In the project, we adopted C0=1/3 and uc=0.1D for both sand and clay. Note that since the displacement for mobilizing full end bearing is relatively large compared to skin friction, the contribution of end bearing resistance will be small during load transfer analyses. The normalized q-u curves for both sand and clay can be approximated by the following table and also plotted in Figure 4-2:

4-6 q/qmax u/uc

0.00 0.00

0.45 0.10

0.63 0.25

0.79 0.50

1.00 1.00

1.00 ∞

In order to compute the t-z curves along an in-situ pile and q-u curve at its tip, the following parameters are required, namely, pile diameter D, pile circumference and tip area, a series of selected depth values from pile top to tip, (γ, c) of soft clay, and (γ, φ') of sand. All these values can be found in Table 2-1 and in the generalized soil profiles provided in Appendix A. The coordinates of t-z and q-u curves of all Antioch Bridge and slab bridge piers developed using these parameters are listed in Appendix B. These t-z and q-u curves are applicable for both the vertical pile and battered pile as long as they are aligned along the pile axis. Also, the presented data are for loading in compression only, whereas a scale factor of 0.75 can be applied on soil skin resistance (t) for tensile loading and there is no end bearing resistance in tension.

4.3.2 Axial Load versus Deformation Analysis

From the complete axial pile-head load versus pile-head deformation (Q-δ) curve of a pile, one can readily find the pile head settlement for any axial load being applied at the pile top, and vice versa.

Once the t-z and q-u curves of a pile are developed and its cross-section area (A) and Young's modulus (E) are given, the Q-δ curve of the soil-pile system can be generated. Figure 4-4a shows a schematic of an embedded pile, and the pile top is subjected to a boundary condition of prescribed load or displacement (Q1 or δ1). Figure 4-4b depicts that this soil-pile system is modeled as a series of nodes (from 1 to N) connected by N-1 sets of elastic axial springs (stiffness=EA/∆li), with N sets of t-z soil springs attached at the pile nodes and one q-u soil spring at the tip node. Because of the nonlinear nature of t-z and q-u curves, iterative solution schemes are usually adopted. This kind of boundary value problem can be readily solved using most modern computer codes.

In this project, the BMCOL program developed by Matlock et al. (1981) in the axial mode was used to compute the Q-δ curves of the piles of Antioch Bridge and slab bridge piers. The input data required include: the pile geometry and deformability, a series of t-z curves along the pile, one q-u curve at the tip, and a series of desired prescribed settlements δ's at pile top. For all piles investigated, the prescribed δ's are -3, -2, -1, -0.5, -0.25, -0.1, 0, 0.1, 0.25, 0.5, 1, 2, 3, 4, and 6 inches. The complete Q-δ curves of all Antioch Bridge and slab bridge piers developed using these parameters are presented in Appendix C. These Q-δ curves represent the pile behavior along the pile axis regardless of the plumb pile or battered pile. The following pile properties were used in conducting the axial load versus deformation analyses:

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Pile AE = 8.62×109 lb.

Pile AE = 4.47×109 lb.

Pile AE = 3.77×109 lb.

Pile AE = 8.1×108 lb.

Pile AE = 2.44×109 lb.

Pile AE = 5.19×108 lb.

4.3.3 Pile Capacity Evaluation

Design Load: As summarized in Tables 4.1 and 4.2, five types of piles are used: 54-inch diameter concrete hollow pile, 30-inch diameter steel pile, 14-inch square concrete pile, 24-inch square concrete pile, and 12-inch square concrete pile. The design loads of these piles as documented on the as-built drawings are 500 tons, 250 tons, 100 tons, 250 tons, and 70 tons, respectively. The prevailing pile design practice in the U.S. requires a minimum static factor of safety of 2.0 and therefore these piles should have ultimate geotechnical capacities of 1000 tons, 500 tons, 200 tons, 500 tons, and 140 tons, respectively, as minimum values.

During construction of the bridge, a pile load testing program was undertaken to verify the ultimate pile capacities. The load testing was conducted on production piles at the following locations:

South Approach: 24-inch square piles at Pier 5 Main Channel: 54-inch diameter piles at Pier 19 North Approach: 24-inch square piles at Piers 28 and 37

Ultimate Pile Capacity: To estimate long term ultimate capacities of the piles, conventional pile capacity evaluation was made which generally involves summing of the skin friction resistance and end bearing resistance. While summation of tmax (peak value of t-z curves) multiplied by its tributary length along the pile plus qmax (peak value of q-u curves) at the tip yields some measures of the static ultimate bearing capacity of a single pile, we elected to use the load resistance at a pile-head displacement of 3 inches from the Q-δ curve as the ultimate pile capacity. This explicitly considered displacement compatibility between skin friction and end bearing. The estimated ultimate pile capacity along with the design load for each pile is presented in Figure 4-5. The ultimate pile capacities estimated from the Q-δ curve have been compared with results from a computer program, APILE, and the comparison is found to be in agreement (the solution from APILE are not included in this report). In addition, following the discussions with the Peer Review Panel members, CPT data were used directly to estimate the pile capacities for comparison with the conventional pile design practice. In the following, a brief description of the CPT-based pile capacity calculation method is provided.

As depicted in Figure 2-2, the Antioch Bridge has one CPT probing conducted at every pier for most cases. The CPT sounding provides soil properties on a continuous basis, which has greater

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Geotechnical & Earthquake Engineering advantage over conventional soil borings using SPT samplings with a 5-foot interval. When foundation soils are stratified with thin beds of different soil types, the CPT-based pile capacity method can capture the variations within short distances. For this purpose, the computer program CPeT-IT was used, which was recently developed by GeoLogismiki (http://www.geologismiki.gr) in collaboration with Peter Robertson of Gregg Drilling & Testing Inc.

The program CPeT-IT is coded to follow a LCPC method (Bustamante and Gianeselli, 1982), which is based on the analysis of 197 pile load tests with a wide range of foundation and soil types.

This partly explains the reportedly good results with the LCPC method. The program also provides simple guidance to account for different pile installations. In this method, the pile unit end bearing, qp, is calculated from the equivalent average cone resistance, qca, multiplied by an end bearing coefficient, kc, whereas the pile unit side friction, fp, is calculated from measured qc values divided by a friction coefficient, α, as shown in the following equations:

/αqfqkq cpcacp == ;

Selection of these coefficients (kc,α) and the limiting value of unit side friction (fp) depends upon the soil and pile type, and their recommended values are listed in Table 4-4, which was developed on the basis of calibration with the pile load test results with variety of pile types and soil conditions. To evaluate the pile unit end bearing, equivalent average cone resistance (qca) is taken as the mean value of the cone tip resistance within one pile diameter (D) zone around the pile tip (0.5D above and 0.5D below the pile tip). Only the measured qc is used for the estimation of both side friction and pile end bearing resistance. This is considered an advantage by many due to the difficulties associated in interpreting sleeve friction (fs) in CPT data. However, both sleeve friction and tip resistance are used for interpretation of soil behavior which proves to be an important parameter for selection of the friction and end bearing coefficients. Figure 4-6 shows the illustration of sample pile capacity calculation at Pier 04 using the CPT data (S03). The ultimate pile capacities estimated using CPT data for all piers are also shown on Figure 4-5 for comparison.

4.4 Lateral Loading Conditions

During an earthquake, lateral loading of a deep foundation is resisted by flexural properties of the pile and lateral soil supports along the pile. The lateral soil supports to the pile is mobilized when there is a relative displacement between the pile and the surrounding soil according to the deflection profile of the pile. This lateral load-deflection relation between the pile and soil is generally known as p-y curve. In this section, the lateral soil support (p-y) curves of all Antioch Bridge and slab bridge piers are developed, and the response results of the piles subjected to lateral push-over loading are presented.

4.4.1 p-y Curves

Determination of the ultimate lateral bearing capacity (pu) and the lateral soil support (p-y) curves of a pile in soils is mainly based on the API Recommended Practice 2A-WSD (1993). The

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Geotechnical & Earthquake Engineering developed p-y curves are used in the soil-structure interaction analysis for forming 6×6 condensed stiffness matrices and kinematic motions (also see Section 5-3), and in the finite element analysis of the bridge for simulating the nonlinear soil springs attached to the piles. The following briefly describes the elements of soil support behaviors for clayey and sandy soils. For the static loads, the ultimate lateral bearing capacity (pu) for piles in soft clay at a certain depth below soil surface (X), increases from 3c to 9c as X increases from 0 to XR, according to:

R

R u XXcD

XXJcXXDcD p for 9 for 3 γ where pu is ultimate lateral bearing capacity (in unit of force per pile length), c is the undrained shear strength, D is the pile diameter, γ is the effective soil unit weight, J is the dimensionless empirical constant varying from 0.25 to 0.5 (usually taken as 0.5), and XR is the critical depth equal to 6D/(J+γD/c). Note that consistent units should be used for the parameters in the above equation.

The lateral soil resistance-deflection relationships for piles in soft clay are generally non-linear. The normalized p-y curves of soft clay for the short-term static load case can be represented by the following table:

p/pu y/yu

0.000 0.000

0.250 0.016

0.500 0.125

0.720 0.375

1.000 1.000

1.000 ∞ where p is the actual lateral resistance, y is the actual lateral deflection, and yu is the ultimate lateral deflection when pu takes place (which equals to 20 times ε50, the strain occurring at 50% the maximum stress on laboratory undrained compression tests of undisturbed soil samples). On the other hand, the ultimate lateral bearing capacity (pu) for piles in sand may be assigned as the smaller one of the following two equations:

),min( ;)( 321 udusu udus ppp HDCpXDCXCp

=+= γγ where (γ, D, X) are defined as above, and (C1, C2, C3) are the empirical coefficients as function of soil internal friction angle (φ'), as shown in Figure 4-7. The lateral soil resistance-deflection relationships for sand are also non-linear and in the absence of more defining information may be approximated by the following expression:

uuu u y yf Ap py Ap kXApp or tanh

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Geotechnical & Earthquake Engineering where (p, y) are defined as above, and A is the loading factor which is 0.9 for cyclic loading and 3.0-0.8X/D for static loading, k is the initial modulus of subgrade reaction as function of φ' (also see Figure 4-7), f represents the corresponding normalized function, and yu is the ultimate lateral deflection approximated by 3Apu/(kX). The normalized p-y curves of sand can be represented by the following table:

p/pu y/yu

0.00 0.00

0.10 0.03

0.46 0.17

0.76 0.33

0.91 0.50

1.00 1.00

1.00 ∞

Figure 4-2 also depicts the normalized p-y curves of soft clay and sand used in the project. In order to compute the p-y curves along an in-situ pile, the following parameters are required, namely, pile diameter D, a series of selected depth X values from pile top to tip, (γ, J, c, ε50) of soft clay, and (γ, φ', k) of sand. All these values can be found in Table 2-1 and in the generalized soil profiles provided in Appendix A. A p-multiplier of 0.5 was applied for pu to collectively account for potential soil cyclic softening and pile group effect for the main bridge and approach piers. For the slab bridge, a p-multiplier of 1.0 may be used for larger pile spacing. The coordinates of p-y curves of all Antioch Bridge and slab bridge piers developed using these parameters are listed in Appendix D. No differentiation on the p-y curves is made between the vertical pile and battered pile since the p-y curves describe the soil behavior perpendicular to the pile axis. The same sets of p-y curves should be attached normal to the pile axis for the plumbed pile and battered pile.

4.4.2 Lateral Push-Over Analysis

In this project, the LPILEplus 5.0 program developed by Ensoft, Inc. (2004) was used to perform the lateral push-over analyses of the piles of Antioch Bridge and slab bridge piers. The input data included the pile flexural properties, soil properties, and a series of desired prescribed boundary conditions at pile top. Fixed-head condition at the pile top (y=prescribed,θ=0) is used, and the prescribed y's are 1, 2, 3, 4, 5 and 6 inches for all the Antioch piles (the lateral displacements are prescribed perpendicular to the pile axis). The resultant depth-varying deflection, moment, and shear diagrams along the pile as well as pile top moment and shear versus pile top deflection curves are included in Appendix E. The following flexural properties were used for the single pile lateral push-over analyses:

Effective pile EI = 8.47×1011 lb-in2.

Effective pile EI = 6.44×1011 lb-in2.

Effective pile EI = 2.35×1011 lb-in2.

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Effective pile EI = 6.95×109 lb-in2.

Effective pile EI = 6.07×1010 lb-in2.

Effective pile EI = 3.11×109 lb-in2.

4.5 Nonlinear Soil Springs for Pile Cap

The pile caps for much of the approach foundations are buried in the soils. For these piers, in addition to the piles, the pile caps would also offer additional resistance against lateral movement derived from passive pressure in the soil. The recommendations for pile cap springs are presented in this section. The estimated values of passive soil resistance depend largely on the undrained shear strength of the soil, and to some extent on the pile cap configuration, i.e., the contact dimension for longitudinal and transverse loading directions. The reaction of soil passive resistance can be modeled as two soil springs attached to the pile cap; one in the longitudinal direction, and one in the transverse direction. For this purpose, tri-linear soil springs were developed, and their coordinates are tabulated in Table 4-5.

4.6 Liquefaction-induced Settlement

The results of liquefaction assessment discussed in Section 4.1 indicate the existence of fairly thick liquefiable zones beneath a large portion of southern segments of the bridge span and the northern half of the slab bridge span. In order to investigate the effect on foundation performance, evaluation of liquefaction-induced ground settlement as well as pile settlement was made. Prediction of liquefaction-induced ground settlement was mainly based on the empirical work of Tokimatsu and Seed (1987), and Ishihara and Yoshimine (1992), in which post-liquefaction volumetric strain was estimated from cyclic shear strain, standard penetration resistance, or safety factor against liquefaction. The computed values of ground settlement are presented in the last column of Table 4- 3, which represents ground surface settlement of a free-field condition (without pile). Depending on the thickness of the liquefied soil and the portion of pile length in the liquefied soil, the pile settlement is expected to be much smaller than the free-field soil settlement.

To estimate the pile settlement resulting from the liquefaction-induced free-field ground settlement, a down-drag analysis was conducted at selected locations (Piers 10, 11, 17, 18, 19, 64, and 69). The down drag behavior was performed for two cases; one without the down drag mechanism and one with the down drag mechanism. Comparison between the two cases enables determination of additional settlement due to the down-drag loading. The BMCOL program with the axial mode was used to compute the Q-δ curves for the two cases. In the case without the down drag mechanism, one end of the t-z curves is fixed before the pile is loaded axially resulting in a load-deformation (Q-δ) curve that is normally observed. A separate analysis with the down drag mechanism is simulated by pulling down the t-z curves, according to applicable ground settlement profile, followed by gradually increasing axial loads on the pile top.

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Geotechnical & Earthquake Engineering

The difference in pile settlements with and without the down drag mechanism at the service load level yields the liquefaction induced foundation settlement. Foundation settlements on the order of

0.2 to 0.4 inches were estimated from the analyses; the results are provided in Appendix F.

However, since the mechanism used to study the pile settlement is an extremely ideal case, these foundation settlements computed from the down-drag analysis should be regarded as qualitative assessment.

The performance criterion adopted for the Antioch Bridge is based on a no-collapse scenario for the Safety Evaluation Earthquake representing a 1,000-year return period ground motion. Judging from the down-drag analysis results and the project-specific design criteria, the performance of foundation for liquefaction-induced settlement is acceptable.

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TABLE 4-1: SUMMARY OF FOUNDATION INFORMATION FOR BRIDGE PIERS

Pier Pile Top Pile Tip ML Pile Group Number Pile Pile Design Number Elevation Elevation Elevation Layout of Piles Type Dimension Load

(ft) (ft) (ft) (ton) Abut 1 15.00 -30.00 20.00 5+6bN

1 11 Square Concrete 14"×14" 100.00 2 0.50 -40.00 9.00 3b×4b

2 12 Square Concrete 24"×24" 250.00 3 -1.00 -45.00 10(8) 3b×4b 12 Square Concrete 24"×24" 250.00 4 -2.00 -50.00 10.00 5b×4b 20 Square Concrete 24"×24" 250.00 5 -2.00 -45.00 9.00 3b×5b 15 Square Concrete 24"×24" 250.00 6 -1.00 -55.00 8.00 3b×4b 12 Square Concrete 24"×24" 250.00 7 5.00 -55.00 -6.00 3b×4b 12 Square Concrete 24"×24" 250.00 8 5.00 -60.00 -16.00 3b×4b 12 Square Concrete 24"×24" 250.00 9 4.00 -60.00 -18.00 5b×5b 25 Square Concrete 24"×24" 250.00 10 4.00 -63.00 -16.00 5b×5b 25 Square Concrete 24"×24" 250.00 11 4.00 -63.00 -19.00 5b×4b 20 Square Concrete 24"×24" 250.00 12 4.00 -60.00 -20(-19) 5b×4b 20 Square Concrete 24"×24" 250.00 13 4.00 -66.00 -23(-22) 5b×4b 20 Square Concrete 24"×24" 250.00 14 4.00 -60.00 -25(-20) 3b×6b 18 Square Concrete 24"×24" 250.00 15 4.00 -65.00 -25(-24) 3b×6b 18 Square Concrete 24"×24" 250.00 16 4.00 -70.00 -27(-26) 3b×6b 18 Square Concrete 24"×24" 250.00 17 2.00 -92.00 -34.00 5b×5b 25 Prestr. concrete hollow 54"φOD,40"φID 500.00 18 2.00 -92.00 -34.00 5b×5b 25 Prestr. concrete hollow 54"φOD,40"φID 500.00 19 2.00 -98.00 -40.00 5b×6b 30 Prestr. concrete hollow 54"φOD,40"φID 500.00 20 2.00 -100.00 -46(-44) 5b×6b 30 Prestr. concrete hollow 54"φOD,40"φID 500.00 21 2.00 -98.00 -19(-20) 5b×5b 25 Prestr. concrete hollow 54"φOD,40"φID 500.00 22 -14.00 -98.00 -9.00 7b×7b 49 Square Concrete 24"×24" 250.00 23 -16.00 -103.00 -12.00 5b×4b 20 Square Concrete 24"×24" 250.00 24 -17.00 -105.00 -13.00 5b×4b 20 Square Concrete 24"×24" 250.00 25 -18.00 -103.00 -13.00 5b×4b 20 Square Concrete 24"×24" 250.00 26 -18.50 -105.00 -13.00 5b×6b 30 Square Concrete 24"×24" 250.00 27 -19.50 -105.00 -14.00 5b×6b 30 Square Concrete 24"×24" 250.00 28 -20.00 -103.00 -14.00 4b×6b 24 Square Concrete 24"×24" 250.00 29 -21.00 -105.00 -15.00 4b×6b 24 Square Concrete 24"×24" 250.00 30 -21.00 -112.00 -16.00 4b×6b 24 Square Concrete 24"×24" 250.00 31 -19.00 -112.00 -16.00 3b×6b 18 Square Concrete 24"×24" 250.00 32 -19.00 -112.00 -17.00 3b×6b 18 Square Concrete 24"×24" 250.00 33 -19.00 -112.00 -17.00 3b×6b 18 Square Concrete 24"×24" 250.00 34 -18.00 -112.00 -17.00 3b×5b 15 Square Concrete 24"×24" 250.00 35 -18.00 -112.00 -17.00 3b×5b 15 Square Concrete 24"×24" 250.00 36 -18.00 -106.00 -17.00 3b×5b 15 Square Concrete 24"×24" 250.00 37 -18.50 -111.00 -16.00 3b×6b 18 Square Concrete 24"×24" 250.00 38 -19.00 -111.00 -15.00 5b×4b 20 Square Concrete 24"×24" 250.00 39 2.00 -103.00 -7(-10) 3b×4b 12 Steel Pipe 30"φ 250.00 40 2.50 -103.00 -12.00 3b×4b 12 Steel Pipe 30"φ 250.00 41 -13.00 -95.00 -7.00 2×6 14 Square Concrete 14"×14" 100.00

Note: 1 two rows of piles with 5 piles in the south row and 6 battered piles in the north row;

2 3 piles in the longitudinal direction and 4 piles in the transverse direction with subscript b for the exterior piles battered at 1/3 slope.

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TABLE 4-2: SUMMARY OF FOUNDATION INFORMATION FOR SLAB BRIDGE PIERS

Pier Pile Top Pile Tip ML Pile Group Number Pile Pile Design Number Elevation Elevation Elevation Layout of Piles Type Dimension Load

(ft) (ft) (ft) (ton) 42 -12.00 -90.00 -13.00 1×41 4 Square concrete 12"×12" 70.00 43 -12.00 -90.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 44 -12.00 -90.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 45 -12.00 -90.00 -12.00 1×4 4 Square concrete 12"×12" 70.00 46 -12.00 -90.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 47 -12.00 -90.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 48 -12.00 -90.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 49 -12.00 -90.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 50 -12.00 -90.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 51 -12.00 -90.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 52 -12.00 -85.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 53 -12.00 -85.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 54 -13.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 55 -13.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 56 -13.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 57 -13.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 58 -13.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 59 -13.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 60 -13.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 61 -13.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 62 -13.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 63 -15.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 64 -15.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 65 -15.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 66 -15.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 67 -15.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 68 -15.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 69 -15.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00 70 -15.00 -80.00 -13.00 1×4 4 Square concrete 12"×12" 70.00

Abut 71 -13.00 -80.00 -7.00 1×4 4 Square concrete 12"×12" 70.00 Note: 1 1 pile in the longitudinal direction and 4 piles in the transverse direction.

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TABLE 4-3: SUMMARY OF LIQUEFACTION ANALYSES

Location Sounding Mudline Elevation (ft)

Tip Elevation (ft) amax (g) Potential Liquefaction Zones

Elevations (ft) Seismic

Settlement (in)

Abut 1 B-06-01 28.7 -30.0 0.417 Not Significant in 50 feet depth 0.1 Pier 2 06-CPT-1 9.6 -40.0 0.430 -17.1 to -19.8, -34.2 to -36.2 2.2 Pier 3 06-CPT-2 10.4 -45.0 0.399 Not Significant in 50 feet depth 0.5 Pier 4 06-CPT-3 10.5 -50.0 0.394 -9.4 to -10.2, -11.3 to -14.1 1.4 Pier 5 06-CPT-4 9.5 -45.0 0.442 -17.9 to -42.2 6.2 Pier 6 B-06-02 8.7 -55.0 0.393 -13.0 to -40.0 5.6 Pier 7 06-CPT-5 -2.5 -55.0 0.426 -5.7 to -12.9, -14.6 to -15.9, -34.9 to -44.4 5.2 Pier 8 06-CPT-6 -12.0 -60.0 0.432 -16.2 to 19.8, -34.9 to -49.0 4.8 Pier 9 06-CPT-7 -15.0 -60.0 0.474 -22.1 to -29, -44.8 to -52.0, -54.9 to -56.3 8.5 Pier 10 06-CPT-8 -8.5 -63.0 0.507 -14.0 to -36.0, -41.6 to -50.7, -55.7 to -60.3 8.1

Pier 11 06-CPT-9 -10.5 -63.0 0.522 -14.4 to -37.0, -39.6 to -41.3, -42.9 to -47.8, -51.4 to -54.4 10.0

Pier 12 06-CPT-10 -15.0 -60.0 0.428 -22.1 to -38.8, -43.8 to -46.4 6.8 Pier 13 B-06-03 -13.1 -66.0 0.500 -30.0 to -55.0, -57.5 to -62.5 8.8 Pier 14 06-CPT-11 -18.0 -60.0 0.483 -22.5 to -42.8 5.9 Pier 15 06-CPT-12 -20.0 -65.0 0.473 -26.2 to -40.6, -43.5 to -44.5 5.0 Pier 16 06-CPT-13 -21.0 -70.0 0.488 -25.8 to -40.3 5.1 Pier 17 06-CPT-14 -22.0 -92.0 0.474 -27.2 to -72.4 11.9 Pier 18 B-06-04 -19.6 -92.0 0.387 -52 to -69.6 16.2 Pier 19 06-CPT-15 -39.0 -98.0 0.504 -43.5 to -80.2 9.7 Pier 49 06-CPT-34 -8.0 -90.0 0.357 -14.6 to -23.1, -34.1 to -45.9 3.8 Pier 57 B-06-09 -11.3 -80.0 0.366 -28.0 to -64.0 7.1 Pier 64 06-CPT-35 -8.0 -80.0 0.378 -19.7 to -58.0 10.3 Pier 69 B-06-10 -11.8 -80.0 0.384 -29.0 to -64.0 9.6

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TABLE 4-4: END BEARING AND FRICTIONAL FACTORS (KC,α) USED IN THE LCPC METHOD

Factor, kc Nature of soil qc (MPa) Group I…