Ansi api rp 2geo 2011 (2014) (american petroleum institute)

4.2 Symbols for stability of shallow foundation A actual foundation area A ′ effective foundation area of the foundation depending on the load eccentricity Ao actual foundation area

General

The article outlines commonly used symbols, with additional symbols defined in the text accompanying the relevant formulas It's important to recognize that symbols may carry different meanings across various formulas.

Symbols for stability of shallow foundation

A′ effective foundation area of the foundation depending on the load eccentricity

A o actual foundation area per unit length, of an infinitely long footing

A h embedded vertical cross-sectional area of foundation

A p end area of skirt tip

A s side surface area of foundation skirt embedded at a particular penetration depth (including both sides)

A idealized idealized rectangular foundation area, for irregular foundation shapes b c ,b q ,b γ individual correction factors related to foundation base inclination

B minimum lateral foundation dimension (also foundation width)

B′ minimum effective lateral foundation dimension (also foundation effective width)

C compression index of the soil over the load range considered

Provided by IHS under license with API Licensee=Texas A&M University/5912186001

```,`,,``,,,```,`,,,,,,,```,`,-`-`,,`,,`,`,,` - d c , d q , d γ individual correction factors related to foundation embedment depth

The depth below the seabed to the base level is denoted as $D_b$, while $e$ represents the load eccentricity The initial void ratio of the soil is indicated by $e_o$, with $e_1$ and $e_2$ referring to the load eccentricities along the foundation's length and width, respectively Additionally, $f$ signifies the unit shaft friction resistance along the foundation skirts during installation.

F correction factor g c , g q , g γ individual correction factors related to foundation seafloor surface inclination

G elastic shear modulus of the soil h soil layer thickness

H acting horizontal loads, for relevant loading condition

H d maximum total horizontal load applied to the base of the foundation at failure under undrained conditions

H d ′ maximum total horizontal load applied to the base of the foundation at failure under drained conditions

H ult ultimate horizontal capacity in yield surface design method

∆H horizontal soil resistance due to active and passive earth pressures on foundation skirts i c , i q , i γ individual correction factors related to foundation load inclination

K c , K q , K γ correction factors, which account for load inclination, footing shape, depth of embedment, inclination of base, and inclination of the seafloor

K p coefficient of passive earth pressure

K rd drained horizontal soil reaction coefficient

K ru undrained horizontal soil reaction coefficient

L maximum lateral foundation dimension (also foundation length)

L′ maximum effective lateral foundation dimension (also foundation effective length)

M ult ultimate moment capacity in yield surface design method

N q , N γ dimensionless functions of φ ′ p′ o vertical effective overburden stress at base level (skirt tip level when skirts are used) q o initial effective vertical stress at level of a given soil layer

The effective vertical stress ($\Delta q$) at a specific soil layer is influenced by the unit end bearing pressure ($q$) at the foundation skirt tip during penetration This is measured by the cone tip resistance ($q_c$) from the Cone Penetration Test (CPT), which is essential for calculating the skirt penetration resistance.

Q acting vertical load, for relevant loading condition

Q d maximum total vertical load applied to the base of the footing at failure (excluding weight of soil plug inside skirts) under undrained conditions

Q d ′ maximum total vertical load applied to the base of the footing at failure (excluding weight of soil plug inside skirts) under drained conditions

Q f shaft friction resistance along foundation skirts during skirt penetration

Q o maximum vertical load, per unit length, of an infinitely long footing

Q p end bearing resistance at foundation skirt tip during skirt penetration

Q r total soil resistance during skirt penetration

Q ult ultimate vertical capacity in yield surface design method

The radius $ R $ of the base of a circular foundation is crucial for determining the undrained shear strength of soil, denoted as $ s_u $ and $ s_{uo} $ at the foundation base level The average soil strength from the seabed to the base level is represented as $ s_{u \, ave} $, while $ s_{u2} $ indicates the equivalent shear strength below the base level Additionally, individual correction factors related to the foundation shape are represented by $ s_c $, $ s_q $, and $ s_\gamma $.

The torsional moment $ T $ is influenced by the vertical and horizontal short-term elastic displacements $ u_v $ at the foundation base, while $ u_v $ also accounts for the vertical long-term settlement of a soil layer The ground inclination angle $ \beta $ is expressed in radians and is essential for calculating inclination factors Additionally, the interface friction angle $ \delta $ at the soil-footing interface, as outlined in Clause 7.15, along with the angle of internal friction $ \phi' $ of sand under drained triaxial conditions, are critical parameters in foundation design.

The effective unit weight of soil, denoted as γ´, plays a crucial role in geotechnical engineering The rate of increase of undrained shear strength with depth, represented by κ, is essential for understanding linear shear strength profiles Additionally, Poisson’s ratio of the soil, υ, and the base inclination angle in radians, ν, are important parameters in calculating inclination factors These factors are vital for assessing overturning and torsional short-term undrained rotations of the foundation base.

Symbols for pile foundation design

A p gross end area of the pile, 2 p 4D

A w cross sectional steel area of pile at pile tip, A w = ⋅ π 4 ( D 2 − D i 2 )

A s side surface area of pile

C 1 , C 2 , C 3 Coefficients determined as a function of φ´

D 50 mean effective soil particle diameter

D CPT diameter of the CPT tool, D CPT = 36 mm for a standard cone with a base area of 10 cm 2

D r relative density of a sand; For CPT-based Method 1, 0 ≤ D r≤ 1.0; for CPT-based Method 4, D r > 1.0 should be accepted and used

The initial modulus of subgrade reaction, denoted as $ E_S $, is crucial for understanding the unit shaft friction in various conditions The unit shaft friction in stress units is represented as $ f(z) $, while $ f_c(z) $ indicates the unit shaft friction in compression Additionally, $ f_p(z) $ refers to the unit shaft friction between the sand soil plug and the inner pile wall, specifically for the CPT-based Method 4 The unit shaft friction in tension is denoted as $ f_t(z) $ The distance above the pile tip is calculated as $ h = L - z $, and the rate of increase with depth of the initial modulus of subgrade reaction is essential for determining lateral soil resistance in p-y curves for sand.

K o coefficient of lateral earth pressure at rest

L embedded length of the pile below the original seafloor

L s length of the soil plug in the sand layers

The dimensionless bearing capacity factor, denoted as $N_q$, is influenced by atmospheric pressure $p_a$ measured in stress units, such as $p_a = 100 \, \text{kPa}$ At a specific depth $z$, the effective vertical stress is represented as $p'_{o}(z)$, while the effective vertical stress at the pile tip is indicated as $p'_{o,\text{tip}}$ Additionally, the effective mean stress at depth $z$ is expressed as $p'_{m}(z)$, and the effective horizontal stress at the same depth is denoted as $p'_{oh}(z)$.

The outer perimeter of a pile is calculated using the formula $ P_o = \pi D $ The unit end bearing at the pile tip is denoted as $ q $, measured in stress units The CPT cone-tip resistance at a specific depth $ z $ is represented as $ q_c(z) $, also in stress units To account for general scour, the reduced CPT cone-tip resistance at depth $ z $ is expressed as $ q_{c,f}(z) $ The average value of $ q_c(z) $ between 1.5D above and 1.5D below the pile tip is referred to as $ q_{c,av,1.5D} $ Finally, the cone tip resistance at the pile tip is indicated as $ q_{c,tip} $.

Q mobilized end bearing capacity in Q-z curves, in force unit

Q c axial pile ultimate capacity in compression, in force units

Q f,c shaft friction capacity in compression, in force units

Q f,t shaft friction capacity in tension, in force units

Q f,i,clay cumulative shaft friction capacity of the clay layers within the soil plug, for CPT method 3

Q p end bearing capacity, in force units

Q t axial pile ultimate capacity in tension, in force units s u undrained shear strength of the soil at the point in question, in stress units

The thickness of the WT pile wall, denoted as $ t $, influences the mobilized soil-pile adhesion, which is crucial for axial shear transfer The maximum soil-pile adhesion or unit shaft friction at a specific depth $ z $ is represented by $ t_{\text{max}} f(z) $ Additionally, the residual soil-pile adhesion or unit shaft friction is referred to as $ t_{\text{res}} $ The depth $ z $ is measured below the original seafloor, while $ z $ also indicates the local pile axial deflection relevant to the axial shear transfer Furthermore, $ z $ represents the axial pile tip displacement in relation to the Q-z curves.

The final depth below the seafloor, denoted as \$z'\$, is influenced by general scour, while the axial pile displacement \$z\$ indicates the point at which the residual soil-pile adhesion, \$t_{res}\$, is achieved The dimensionless shaft friction factors for cohesive and cohesionless soils are represented by \$\alpha\$ and \$\beta\$, respectively The submerged or effective soil unit weight is denoted as \$\gamma'\$, and the strain at half the maximum deviator stress for lateral soil resistance-displacement p-y curves in soft clay is represented by \$\epsilon_c\$ The constant volume friction angle at the interface between sand and the pile wall is indicated by \$\delta_{cv}\$, while the angle of internal friction of sand under drained triaxial conditions is represented by \$\phi'\$ The general scour depth is denoted as \$\Delta z_{GS}\$, and the local scour depth is represented by \$\Delta z_{LS}\$ The base of natural logarithms is approximately \$e \approx 2.718\$, and the natural logarithm (base \$e\$) is denoted as \$\ln\$.

General

The foundation must be engineered to support both static and dynamic loads while minimizing deformation and vibrations in the structure It is crucial to evaluate the impact of repetitive and transient actions on the structural response and the strength of the underlying soils Consideration should also be given to potential seabed movements and their effects on foundation components Additionally, the design must assess the potential disturbance to foundation soils caused by conductor installation or shallow well drilling This guidance may not be applicable to "problem" soils, including carbonate materials, volcanic sands, or highly sensitive clays.

Testing and instrumentation

Where there is uncertainty regarding the behavior of foundations, testing or instrumentation should be undertaken Possible methods include the following

Load testing or large-scale field testing should be performed where there is particular uncertainty in the foundation capacity and where safety and/or economy are of particular importance

Model tests should be performed where

1) the foundation configuration differs significantly from earlier configurations where operational experience exists,

2) the soil conditions differ significantly from those where operational experience exists,

3) new methods of installation or removal are envisaged, or

4) a high degree of uncertainty exists as to how the structure or its foundation will behave

Structures should be fitted with temporary instrumentation where

5) the installation method presupposes the existence of measured data for control of the operation, or

6) an installation method is to be applied with which little or no experience has been gained

Structures should be fitted with permanent instrumentation where

7) the safety or behavior of the foundation is dependent on active operation,

8) the foundation configuration, the soil conditions, or the actions differ substantially from those with which experience has been gained,

9) there is a need for monitoring of the whole foundation with regard to penetration, settlement, tilt, or other behavior, or

10) the method of removal presupposes the existence of measured data for control of the operation.

Conductor installation and shallow well drilling

When planning conductor installation and shallow well drilling, it is essential to consider the potential disturbance to foundation soils, as this may lead to a decrease in the stability of the structure or nearby conductors.

Soil disturbances during drilling operations can arise from hydraulic fracture, washout, or shallow gas pockets Hydraulic fracture happens when drilling fluid pressure exceeds safe limits, leading to fluid loss and potential softening of surrounding soil Washout, often seen in granular soils, can be triggered by high drilling fluid circulation rates or drilling without mud, resulting in large voids and stress relief in the soil structure These disturbances may cause loss of drilling fluid circulation, unintended fluid return to the seafloor, or the formation of craters, ultimately compromising foundation stability and increasing displacements Such adverse effects can occur both during and after the installation of structures, whether through a pre-installed template or during exploration drilling.

The designer of the structure must have access to records of conductor installation and shallow well drilling It is essential to evaluate the implications for foundation soils arising from issues such as inadequate grouting, excessive loss of circulation, unintended return of drilling fluids to the seafloor, or the formation of seafloor craters.

The cuttings from the well drilling operation, if allowed to accumulate on the seafloor, should be taken into account in the foundation design, installation procedure and structure removal

6 Geotechnical data acquisition and integrated geoscience studies

Geotechnical assessment

An integrated study combining geophysics, geology, and geotechnical engineering is essential for determining geotechnical parameters and assessing geological hazards Geophysical data is crucial for developing a geological model that enhances the understanding of depositional processes and site features This data aids in interpreting stratigraphy from geotechnical boreholes, defining lateral variability, and optimizing facility locations By incorporating geotechnical data into the geological model, we gain valuable insights into how geological conditions may affect man-made structures, pipelines, anchors, and wellheads.

Shallow geophysical investigation

Shallow geophysical investigations reveal crucial insights into soil stratigraphy and geological features, including slumps, scarps, and irregular topography These studies can identify mud volcanoes, collapse features, sand waves, and faults, as well as erosional surfaces and gas bubbles within sediments By correlating soil boring and in situ test data with seabed survey results, the areal extent of shallow soil layers can often be effectively mapped.

When conducting shallow geophysical investigations, it is essential to consider various types of equipment Echo sounders and swathe bathymetric systems are crucial for determining water depths and seafloor morphology, offering higher data density and improved definition of complex topographies Additionally, seismic three-dimensional data collected for exploration can significantly enhance the development of bathymetry maps.

These data should only be used for preliminary evaluations because the resolution could be of the order of a few meters depending on the variability of the topography

Sub-bottom profilers (tuned transducers) define structural features within the near-surface sediments

NOTE These systems can also provide data to develop water-bottom maps

Side-scan sonar defines seafloor features and seafloor reflectivity

NOTE Backscatter measurements from some swathe systems can also provide morphological information

Seismic sources, such as boomers or minisparkers, can define the structure to deeper depths up to approximately

At depths of 100 meters below the seafloor, various seismic sources such as sparkers, air guns, water guns, or sleeve-exploders can effectively delineate subsurface structures and complement deep seismic data from reservoir studies The seismic signals are captured using either single-channel analogue or multi-channel hydrophones Digital processing of these recorded signals significantly improves image quality by eliminating unwanted noise and multiples.

Seabed refraction equipment provides information on the stratification of the top few meters of the seabed

Shallow sampling techniques, such as drop, piston, or grab sampling, along with vibrocoring and cone penetrometer tests, are effective for calibrating results and enhancing the understanding of shallow geological formations.

Direct observation of the seafloor using a remotely operated vehicle (ROV) or manned submersible can also provide important confirmation or characterization of geological conditions.

Geological modelling and identification of hazards

General

Evaluating the nature, magnitude, and return intervals of active geological processes is essential through site investigation techniques Analytical modeling plays a crucial role in assessing the impact of these processes on structures and foundations Given the uncertainties in defining these geological processes, employing a parametric approach is beneficial for developing effective design criteria.

A geological model is developed by proposing a depositional process, with geophysical data mapped according to these hypotheses Features from the same geological period are grouped together, while those unrelated to a specific process are mapped separately The mapping strategy may be modified as needed to ensure alignment between the data and the model.

The results of the geological modelling phase should ideally allow the interpreter to discuss in a report how

```,`,,``,,,```,`,,,,,,,```,`,-`-`,,`,,`,`,,` - features have developed over time, in order to allow assessment of how the features can affect future man-made developments

Some of the more familiar geological processes, events and conditions are discussed in 6.3.2 to 6.3.7.

Earthquakes

Seismic actions shall be considered in design of structures for areas that are determined to be seismically active

Seismically active areas are identified based on historical earthquake activity, which includes both the frequency of occurrences and their magnitudes, as well as through a tectonic review of the region.

Seismic assessments for specific areas must involve analyzing subsurface soils for potential liquefaction and evaluating the risk of submarine slides caused by earthquakes It is essential to consider the site's proximity to seismogenic faults, the expected ground motion characteristics throughout the structure's lifespan, and the acceptable seismic risk based on the intended operations Additionally, structures located in shallow water that may face tsunami impacts require thorough investigation to understand the consequences of such events.

Fault planes

In offshore regions, fault planes may reach the seafloor, allowing for both vertical and horizontal movement due to tectonic activity, fluid extraction from deep reservoirs, or long-term creep from sedimentation and erosion It is advisable to avoid locating facilities near these fault planes to minimize risks.

When placing structures near potentially active faults, it is crucial to evaluate the impact of future fault movements on the foundation If these movements are found to be harmful, a geological study should be conducted to estimate the magnitude and time scale of expected movements, which will inform the design of the structures.

See Annex A for more guidance.

Seafloor instability

Seafloor movements can result from various factors, including ocean wave pressures, earthquakes, and geological processes Areas with weak, underconsolidated sediments are particularly vulnerable to wave-induced movements, even at minimal slope angles Additionally, earthquakes can trigger failures in seafloor slopes that would typically remain stable under normal soil self-weight and wave loads.

Rapid sedimentation, particularly in actively growing deltas, along with low soil strength, soil self-weight, and wave-induced pressures, significantly influence geological processes that drive sediment movement downslope Key design considerations in these environments include the impact of large-scale sediment movements, such as mudslides and slumps, in regions exposed to strong wave pressures, as well as downslope creep movements in areas not directly influenced by wave or seafloor interactions Additionally, the effects of sediment erosion and deposition on structural performance must be carefully evaluated.

Site investigations in potentially unstable areas should prioritize identifying metastable geological features around the site and defining the soil engineering properties necessary for modeling and estimating seafloor movements.

Geotechnical analyses provide estimates of soil movement with depth beneath the seafloor, which can help predict the impact on structural members Additionally, geological studies that utilize historical bathymetric data are valuable for estimating deposition rates throughout the facility's design life.

Scour and sediment mobility

Scour refers to the erosion of seabed soils caused by currents and waves This process can occur naturally due to geological factors or may be induced by structural elements that disrupt the natural flow patterns above the seafloor.

From observations, seafloor variations can usually be characterized as some combination of the following a) Local scour

Steep-sided scour pits around foundation components such as piles and pile groups, as seen in flume models

Shallow scoured basins of large extent around a structure, possibly due to overall structure effects, multiple structure interaction, or wave-soil-structure interaction

Overall seabed movement of sand waves, ridges, and shoals that would also occur in the absence of a structure

Seafloor movements can lead to either lowering or rising of the seabed, often occurring in cycles The introduction of man-made structures can significantly alter local sediment transport, potentially exacerbating erosion, causing sediment accumulation, or resulting in no significant change.

Scour can lead to the loss of vertical and lateral support for foundations, resulting in unwanted settlements of shallow foundations and excessive stress on foundation components Therefore, it is essential to consider the potential for scour in the design process and explore mitigation strategies.

Shallow gas

The presence of biogenic or petrogenic gas in the pore water of shallow soils is crucial for foundation engineering Natural gas can exist in situ as either a gas or in a solid form when bound with water.

Shallow gas, also referred to as hydrate, poses significant risks during site investigation soil borings and oil well drilling Its impact is crucial for foundation engineering, as the dissolution and expansion of gas in recovered soil samples must be considered when establishing geotechnical parameters for design.

Seabed subsidence

Investigating soil conditions and reservoir extraction processes is essential to determine the potential for seabed subsidence during the field's operational life If subsidence is a possibility, it must be considered in the design phase.

When assessing seabed subsidence from reservoir compaction, it is crucial to evaluate the extent of surface settlements, which are influenced by the reservoir's size, the compressibility of the surrounding rocks, and the expected pressure drop In cases where subsidence predictions are uncertain, it is advisable to increase the air gap to mitigate potential impacts.

Geotechnical investigation

General

Understanding the soil conditions at a construction site is essential for creating a safe and cost-effective design Conducting site investigations helps identify different soil layers and their physical and engineering characteristics Previous geoscience studies and site experience can facilitate the design and installation of new structures with little to no further geotechnical investigation required.

The first step in a geotechnical investigation involves reviewing existing geological, geophysical, and prior soil investigation data This review aims to identify potential constraints and assist in planning the next phases of data acquisition for the site investigation.

Geophysical surveys should be performed before the geotechnical investigation Geotechnical surveys and geotechnical investigation data should be combined in an engineering geological model of the region so as to

On-site studies will be conducted to determine the necessary design parameters, focusing on the depth and area of soils that may influence or be influenced by the foundation installation.

Soil investigation and testing

The soil investigation program must be established following an analysis of the geophysical results and the site's geology Typically, an on-site geotechnical investigation involves two key components: a) sampling for soil classification and testing of engineering properties, and b) in situ soil profiling along with strength testing.

The field investigation and laboratory testing program are influenced by soil variability, environmental design conditions such as earthquake actions, the type and geometry of the structure, as well as the requirements for conductors, risers, and pipelines Additionally, the presence of geohazards like slope instability can significantly impact the entire construction site.

Soil samples can be effectively collected from geotechnical boreholes, freefall piston corers, or vibrocorers, depending on the desired investigation depth and sample quality Additionally, continuous piezocone penetration tests (PCPT) and geophysical borehole logging provide detailed assessments of variations in the vertical soil profile.

The PCPT can be performed in a geotechnical borehole or from the seafloor, depending upon the required investigation depth

In situ strength testing is essential for investigations where sampling disturbance or poor recovery may occur, particularly in silica sands, carbonate materials, and soft soils The quality of samples is influenced by the drilling and sampling process, soil type, and gas presence in pore fluids Vane shear test results are utilized alongside shear strengths from retrieved samples to evaluate soil strength in soft to firm clays Additionally, combining PCPT results with these data allows for the establishment of a continuous shear strength profile in clays, while PCPT data in sands aids in estimating in situ relative density, pile and skirt friction, and end bearing values.

Laboratory testing aims to evaluate the strength, deformation, and consolidation characteristics of soil deposits It is crucial to test samples promptly after collection To effectively assess potential impacts from transportation, storage, or aging, a combination of shipboard and land-based laboratory testing is advisable.

The sophistication of soil sampling, preservation techniques, in situ testing, and laboratory testing programs is determined by the design requirements of the structure and the need to evaluate geohazards For innovative structural designs, deepwater applications, and areas prone to slope instability, enhanced geotechnical programs are essential to gather data for comprehensive analyses Additionally, specialized geological testing methods, such as X-ray radiography and age dating, may be necessary to evaluate geological processes, with X-ray radiography also helping to assess sample quality before laboratory testing.

Geotechnical investigations in seismically active areas should include tests to determine dynamic soil properties and liquefaction potential

For small structures, the influence depth beneath the foundation is limited, making the investigation of near seafloor soil conditions, particularly in soft clay or loose sands and silts, challenging and often overlooked Essential site investigation tools for shallow assessments include in situ vane tests, cone penetration tests, plate load tests, box core samplers, and seabed seismic refraction equipment.

If practical, the soil sampling and testing program should be defined after review of the geophysical results

On-site soil investigation is essential and should involve multiple soil borings and/or corings to obtain samples for engineering property testing and potential in-situ testing The quantity and depth of these borings depend on the soil variability at the site and the platform configuration Additionally, the complexity of soil sampling, preservation methods, required laboratory tests, and the necessity for in-situ property testing are influenced by the platform design requirements and the chosen design philosophy.

For pile-supported structures, a foundation investigation must deliver essential soil engineering property data to assess key parameters, including the axial capacity of piles under tension and compression, the load-deflection behavior of axially and laterally loaded piles, the drivability characteristics of piles, and the bearing capacity of the mudmat.

The extent of soil sampling, in-situ testing, and laboratory testing programs is determined by the design requirements of the platform and the necessity to understand active geological processes that could impact the facility.

For innovative platform designs in deepwater settings, particularly in regions prone to slope instability and gravity-based structures, it is essential to customize the geotechnical program This program must deliver critical data for effective soil-structure interaction and pile capacity assessments.

Identification and classification of soils and rocks

Soils and rocks shall be identified and classified in accordance with a recognized published standard (Annex A).

Carbonate soils

When conducting site investigations in frontier areas or regions with potential carbonate materials, it is essential to employ diagnostic methods to identify carbonate soils These deposits can vary significantly in their cementation, from lightly cemented with notable voids to extremely well cemented Therefore, a site investigation program should be flexible enough to adapt between soil sampling, rotary coring, and in situ testing as needed Additionally, tests must be conducted to determine the carbonate content, especially in sands and silts with more than 15% carbonate.

20 % carbonate material, foundation behavior can be adversely affected In these soils, a carefully developed field and laboratory testing program can be warranted (Annex B)

General

Recommendations pertaining to the aspects of shallow foundation design described in API 2A-WSD are given in

These recommendations focus on the design of temporary foundations, like jacket mudmat foundations with shallow skirts, which provide support during installation under ideal conditions The methods address various load combinations, including dead load, variable live load, environmental loads (such as wind, wave, and current), and thermal loads from pipelines, treating transient or cyclic actions as quasi-static loads For more complex dynamic analyses, particularly those involving structural or foundation soil inertia, including seismic loading, it is essential to seek specialist advice.

For permanent foundations, these recommendations are applicable under specific conditions, such as simple loading and favorable soil conditions They are also relevant in scenarios where foundation failure leads to minimal environmental, safety, and economic impacts It is essential to consult specialist geotechnical engineers when applying these recommendations to permanent foundations.

Alternative design methods are essential for shallow foundations in complex and critical scenarios, particularly in challenging seabed conditions or when facing multi-directional cyclic loading, including situations where cyclic uplift loads significantly counteract the foundation's dead weight One effective strategy may involve implementing a partial factor design approach.

ISO 19901-4 emphasizes the use of advanced analysis techniques, including finite element modeling, to ensure that design requirements are satisfied in complex scenarios Further details can be found in section 7.3.

Principles

Bearing failure refers to any failure mode that leads to significant vertical displacement, lateral displacement, or overturning rotation of the foundation In contrast, pure sliding or torsional failure involves the foundation moving or twisting solely in a horizontal plane.

When assessing the stability of shallow foundations, it is essential to analyze ultimate foundation stability using limit equilibrium methods to ensure a balance between applied loads and foundation resistance Adopting appropriate factors of safety, as outlined in relevant guidelines, is also crucial for a comprehensive evaluation.

When designing foundations, it is crucial to consider the potential consequences of excessive displacement and deformation of the foundation soil For temporary foundations, design may prioritize displacement criteria, allowing for additional movement due to environmental actions, while differential settlement must also be taken into account The suitability of this approach depends on the structure type and installation, necessitating a risk assessment If alternative calculation methods are employed, any discrepancies between calculated foundation capacities and those derived from limit equilibrium methods must be clarified For embedded foundations, loads at the base level, particularly at the skirt tip for skirted foundations, should be utilized, factoring in additional loads from water pressure at the seafloor Undrained calculations are generally used when there is no drainage during loading, while drained calculations apply when excess pore pressures do not develop.

The methods discussed in sections 7.4 to 7.6 utilize the effective area concept; however, they may not be suitable for highly compressible or layered soils, as well as skirted foundations on soft soils experiencing significant overturning moments In such cases, it is essential to seek specialist advice, and further guidance is available below.

Acceptance criteria

General

Incorporating displacement and deformation considerations into foundation design is essential, especially when these factors are critical In such cases, utilizing more advanced analysis methods may be necessary to ensure structural integrity.

Foundations constructed using the methods outlined in sections 7.4, 7.5, 7.6, 7.15, and 7.16 must ensure a sufficient safety margin to prevent failure under specified design loads It is essential to assess design loads while taking into account the intended lifespan of the foundation.

API 2A-WSD outlines the minimum factors of safety that are recommended for the specific failure modes.

Variations in safety factor

In situations where geotechnical data is limited or site conditions are highly uncertain, it may be necessary to increase safety factors due to the significant uncertainty surrounding potential failure mechanisms and analysis methods.

The required minimum safety factor varies between bearing failure and sliding or torsional failure to reflect the differing consequences of each failure mode In certain situations, it may be necessary to apply higher safety factors.

Use in design

The minimum recommended safety factors are crucial for ensuring reliable shallow foundation design in typical offshore platforms These safety margins are established by applying relevant safety factors to the calculated capacity However, it is important to note that in certain situations, such as drained loading, reducing vertical load may inadvertently decrease reliability by increasing the risk of sliding Therefore, careful consideration of a comprehensive range of loading, including the lowest possible vertical load, is essential when selecting design loads.

To determine the ultimate capacity of a foundation under various loading conditions, it is essential to use equations that derive envelopes, which are then adjusted with safety factors to establish allowable load envelopes Figure 1 illustrates examples for both undrained and drained conditions, demonstrating the application of these safety factors Specifically, for undrained loading, the ultimate capacity envelope is factored by 1.5 for both vertical load, Q, and horizontal load.

H, axes (not just the H-axis) This is to ensure a minimum 1.5 factor for all load applications and results in a marginal reduction in the allowable load envelope for combinations of high Q and H

NOTE Since the WSD method is adopted, the maximum storm and operating environmental conditions with no additional load factors should be used to calculate the foundation reaction loading

After establishing an envelope of allowable load, design loads can be applied to this envelope to verify compliance with minimum safety factors As discussed in sections 7.4, 7.5, and 7.6, the recommended approach for calculating the maximum total vertical load at failure for skirted foundations assumes uniform soil depth both inside and outside the skirts.

⎯ in some cases the soil height above skirt tip may be higher inside the skirt than outside the skirt, such as where significant scour has occurred, or

In certain situations, the soil height above the skirt tip can be lower on the inside than on the outside, particularly when the foundation extends deeper than the skirt's depth.

To address any existing differences, adjustments can be made to the design vertical load This can be accomplished by modifying the design vertical load accordingly.

The change in design vertical load, denoted as ∆Q, is necessary to address variations in vertical effective stress at the skirt tip level This involves considering the in situ vertical effective stress, represented as p′ in, at the skirt tip level within the skirts, as well as p′ out, which refers to the in situ vertical effective stress at the skirt tip level outside the skirts.

A is the actual foundation area

A similar method may be used for embedded shallow foundations that are designed without skirts Care should be taken to ensure the design loads are adjusted appropriately in these cases

Figure 1—Typical envelopes for undrained and drained conditions

Envelope of bearing / sliding capacity for Safety Factor = 1

Envelope of bearing capacity for Safety Factor = 1

Envelope of sliding capacity ( δ < φ ') for Safety Factor = 1

These safety factors should be used after the effects of cyclic loading have been taken into account Discussion of derivation of cyclic soil strength is provided in 7.7

The conditions described in 7.3.3.2.1 through 7.3.3.2.6 may require further consideration

Tensile stress beneath skirtless foundations, relative to ambient water pressure, should be avoided to prevent disturbances to the seabed caused by pumping scour, which can undermine the foundation A global stability check is essential to ensure that no tensile stress is present under these conditions.

⎯ a minimum safety factor of 1.5 against average soil tension is recommended for individual foundations;

⎯ a minimum factor of safety of 1.0 against localized soil tension anywhere under the foundation is recommended, accounting for flexibility of the foundation

Tensile stresses in soil can be permissible for skirted foundations that resist tension by generating negative excess pore pressures, necessitating specialist design advice Key factors to consider include soil permeability, drainage paths, action duration, and foundation geometry Additionally, uplift capacity should be evaluated as a reverse bearing capacity problem, with a minimum recommended safety factor of 2.0.

7.3.3.2.2 Non-standard soils or soil profiles

The analysis methods discussed are mainly designed for uniform seabed conditions, specifically all sand or all clay profiles When applied to other soil types, such as silts and carbonate sediments, these methods may need additional scrutiny It is advisable to conduct specialized in situ and laboratory testing to accurately assess the properties of these materials for design purposes Furthermore, careful consideration is essential for foundation design in complex soil profiles, particularly where there is a risk of 'punch through' into underlying soils.

Potential influence of adjacent structures, such as jack-up spudcans or conductors, should be considered

In structures with multiple interconnected foundations, it is possible to redistribute loads among the individual foundations, as long as the structure can handle the new load distribution and the soil exhibits adequate ductility.

7.3.3.2.5 Consideration of surrounding seabed conditions

Foundation design must consider ground conditions beyond the base area, as these can affect the foundation's capacity This is crucial for all types of foundations, especially those at risk of deep-seated failure surfaces.

Carbonate soils, primarily biogenic in nature and formed from the accumulated skeletal remains of marine life, cover a significant portion of the ocean floor These soils are more compressible and susceptible to crushing compared to terrigenous silica deposits, which significantly influences their mechanical behavior.

Shallow foundations are generally effective on carbonate sediments, but their evaluation must consider the significant differences from silica sands and normal clays Carbonate sands and silts typically exhibit higher friction angles yet are more compressible, affecting bearing capacity in contrasting ways Additionally, they are less permeable than silica materials, resulting in longer drainage times for foundations The potential for bearing failure due to pore pressure generation from cyclic loading is heightened by the volume reduction on shearing and extended drainage times Notably, the undrained cyclic strength of carbonate sands is often lower than that of silica sands, leading to substantial consolidation settlements and potential large settlements from cyclic actions Shallow foundations are particularly beneficial for cemented carbonate sediments, offering high bearing capacities, strong resistance to cyclic actions, and minimal settlement risks However, caution is advised for layered profiles of variably cemented and uncemented sediments due to the risks of punch-through failures.

Alternative method of design based on yield surfaces

The effective area method is often viewed as conservative, particularly when significant lateral loads and overturning moments consistently act in one direction An alternative design approach utilizes explicit yield functions to directly derive comprehensive yield surfaces in vertical, horizontal, and overturning moment spaces Further details can be found in Annex A.

Undrained bearing capacity — constant shear strength with depth

When the undrained shear strength remains approximately constant to a depth of at least two-thirds (2/3) of the foundation width below the foundation base, it is permissible to simplify the soil strength to a constant value.

However, the impact of lower soil strength below this depth on foundation capacity shall also be considered

The maximum total vertical load (Q d ) which a footing can support at its base under undrained conditions is

The maximum total vertical load, denoted as \$Q_d\$, applied to the base of the footing at failure, excluding the weight of the soil plug within the skirts, occurs under undrained conditions Additionally, \$s_u\$ represents the undrained shear strength of the soil, as referenced in section 7.7.

N c is a dimensionless constant equal to 5.14;

A´ is the effective area of the foundation depending on the load eccentricity;

K c is the correction factor which accounts for load inclination, footing shape, depth of is the embedment, inclination of base, and inclination of the seafloor

This method evaluates the bearing capacity of surface or skirted foundations, ensuring that the weight of the soil plug is counterbalanced by the weight of the surrounding soil If this balance is not achieved, the design load must be adjusted as specified in section 7.3.3.

A method for determining the correction factor and the effective area is given in Annex A Two special cases of

Equation 2 is commonly used for a vertical central load applied to a foundation at seafloor level, where both the foundation base and seafloor are horizontal This scenario simplifies Equation 2 to the form presented in Equation 3.

Equation 4 for two foundation shapes a) Infinitely long strip footing:

Q o is the maximum vertical load per unit length of footing;

A o is the actual foundation area per unit length b) Circular or square footing:

A is the actual foundation area.

Undrained bearing capacity — linearly increasing shear strength

Seabed sediments exhibit an undrained strength that typically increases with depth This analysis method allows for the evaluation of bearing capacity by assuming a linear increase in strength with depth, rather than a uniform strength, which would be inappropriate.

The maximum total vertical load, Q d , which a footing can support at its base under undrained conditions is d uo c 4 c

Q d is the maximum total vertical load applied to the base of the footing at failure (excluding weight of soil plug inside skirts) under undrained conditions;

The correction factor $ F $ is defined as a function of the ratio $ \frac{қB'}{s_{uo}} $, where $ қ $ represents the rate of increase of undrained shear strength with depth, and $ s_{uo} $ denotes the undrained shear strength of the soil at the foundation base level.

N c is a dimensionless constant equal to 5.14;

B′ is the minimum effective lateral foundation dimension;

A′ is the effective area of the foundation depending on the load eccentricity;

K c is the correction factor which accounts for load inclination, footing shape, depth of embedment, inclination of base, and inclination of the seafloor surface

This method evaluates the bearing capacity of surface or skirted foundations, ensuring that the weight of the soil plug is counterbalanced by the weight of the surrounding soil overburden If this balance is not achieved, the design load must be adjusted accordingly, as specified in section 7.3.3.

A method for determining the correction factors and the effective area is given in Annex A.

Drained bearing capacity

The maximum total vertical load, Q d ′, which a footing can support at its base under drained conditions is

Q d ′ is the maximum total vertical load applied to the base of the footing at failure (excluding weight of soil plug inside skirts) under drained conditions;

N q is (exp [π tan φ ′]) (tan 2 (45° + φ′/2)), a dimensionless function of φ ′;

The empirical dimensionless function $ N_\gamma $ can be approximated by the formula $ 1.5(N_q - 1) \tan \phi' $, where $ \phi' $ represents the effective friction angle of the Mohr envelope Additionally, $ \gamma' $ denotes the effective unit weight of the soil, and $ p'_o $ indicates the vertical effective stress at the base level, specifically at the skirt tip level when skirts are utilized.

B′ is the minimum effective lateral foundation dimension;

A′ is the effective area of the foundation depending on the load eccentricity;

The correction factors $ K_q $ and $ K_\gamma $ are essential for adjusting calculations based on various parameters, including load inclination, footing shape, depth of embedment, base inclination, and seafloor inclination The subscripts $ q $ and $ \gamma $ specifically denote the respective terms in the equation.

This method evaluates the bearing capacity of surface or skirted foundations, ensuring that the weight of the soil plug is counterbalanced by the weight of the surrounding soil overburden If this balance is not achieved, the design load must be adjusted accordingly, as specified in section 7.3.3.

Equation 6 for drained bearing capacity excludes the effective cohesion component, c', and its corresponding bearing capacity factor, N c, as their inclusion is rarely justified It is essential to consult specialist geotechnical advice before considering any adjustments related to effective cohesion Additional guidance can be found in Annex A.

A complete description of the K factors, as well as curves showing the numerical values of N q and N γ as a function of φ′ are given in Annex A

Two notable scenarios of Equation 6 are commonly observed When a vertical central load is applied to a foundation at seafloor level, with both the foundation base and seafloor being horizontal, Equation 6 simplifies for two specific foundation shapes The first case involves an infinitely long strip footing.

Q o is the maximum vertical load, per unit length;

B is the minimum lateral foundation dimension b) Circular or square footing:

Shear strength used in bearing capacity calculations

The effectiveness of shallow foundation design relies heavily on the quality of site investigations and the methods employed to assess characteristic strength and deformation properties, both in situ and in the laboratory Notably, significant uncertainty in determining characteristic shear strength can hinder optimization efforts and lead to reduced safety margins.

Such sources of uncertainty are:

⎯ imprecise definition of the soil strength parameters used in the analysis methods;

⎯ variability in strength measurements (which depends on the scope and content of the soil investigation, sampling disturbance, methods of testing, etc.);

⎯ strategies, methods, and procedures used for assessment of the characteristic strength, which vary from one designer or design environment to another;

⎯ amount of testing forming the basis for proposed characteristic shear strengths, statistical variability, and bias

Both drained and undrained shear strengths are affected by uncertainties, but it is particularly important to exercise caution when using the undrained shear strength of sand in design calculations.

For effective design involving strongly dilatant soils, such as dense sand or hard clays, it is crucial to explicitly consider the potential loss of dilatancy on shear surfaces when utilizing high undrained shear strengths Additionally, caution should be exercised when applying results from unconsolidated undrained triaxial tests for very soft and soft clays.

Unconfined compression tests should not be used alone without additional strength test data, especially in very soft and soft silty clays, where their reliability is questionable More dependable methods for determining undrained shear strength in these soils include consolidated undrained triaxial tests with pore pressure measurement, simple shear tests, in situ vane tests, and penetrometer tests with known correlations It is important to recognize that soils exhibit undrained shear strength anisotropy, leading to variations in triaxial compression, triaxial extension, and simple shear strengths When calculating drained bearing capacity for sands, the friction angle (\$φ' \$) should be based on triaxial test conditions and appropriate stress levels Foundation stability under cyclic loading can be evaluated using pseudo-static analysis with correctly derived cyclic shear strengths Additionally, the cyclic performance of non-cohesive soils can be assessed similarly to cohesive soils, considering the potential dissipation of excess pore pressure during cyclic loading Rate effects must also be taken into account for foundation responses to rapid loading events, and the impact of soil consolidation on strength should be included in design considerations, as it typically enhances overall foundation capacity.

Response of shallow foundations to static and pseudo-static loading

Short-term displacement (undrained loading)

For isotropic and homogeneous foundation materials, the deformations of a circular, rigid structure base resting on the soil surface can be estimated under various elastic load conditions.

Torsion: 3 3 t 16 T θ = G R  (12) where u v, is the vertical displacement; u h is the horizontal displacement; θ r is the overturning rotation; θ t is the torsional rotation;

G is the elastic shear modulus of the soil; ν is Poisson’s ratio of the soil;

R is the radius of the base

These solutions can also be used for approximating the response of a square base of equal area

Equations for rigid, embedded circular foundations are provided in Reference [67] and [68]

Solutions are available for addressing non-uniform soil profiles, such as those with linearly increasing soil strength, as well as for general embedded and flexible foundations, and varying base geometries Additionally, it is important to consider numerical analysis methods for more complex scenarios.

The parameter G is not unique to soil and varies with the strain level applied to each soil element It is crucial to choose a suitable representative value for design purposes, utilizing Equations 9 to 12.

Any assumptions made in this regard shall be clearly documented.

Long-term displacement (primary settlement)

An estimate of the vertical settlement of a soil layer under an imposed vertical load can be determined by the following equation: log10

 +  (13) where u v is the vertical settlement; h is the layer thickness; e o is the initial void ratio of the soil;

C is the compression index of the soil over the load range considered; q o is the initial effective vertical stress;

∆q is the added effective vertical stress

In cases where vertical stress decreases with depth within a thin layer, estimates can be made using the stress at the midpoint of that layer For thick homogeneous layers, it is essential to subdivide them for accurate analysis When multiple layers are present, the total settlement estimate is the sum of the settlements of each layer The compression characteristics of the soil are assessed through relevant consolidation tests.

Long-term displacement (secondary settlement)

Depending on the duration of loading, additional displacement due to secondary compression (creep) may also need to be assessed.

Long-term displacement (regional)

Long-term additional settlement may arise from the global subsidence of the seafloor caused by oil and gas extraction This settlement is measured in relation to sea level rather than the seafloor and is not a significant concern for temporary foundations.

Response of shallow foundations to environmental loading

Offshore foundations experience various environmental loads, including currents, waves, ice, wind, and seismic activity, along with thermal loading It is essential to evaluate both the foundation's impact on the structural response and its own integrity.

In some instances environmental loads may be considered as pseudo-static loads, and assessed using the calculations outlined in 7.8 Examples of where this may be appropriate include current loading

Cyclic loading types necessitate advanced analytical methods, particularly for offshore structures, where they can lead to significant average and cyclic foundation displacements, along with volumetric strain post-cyclic loading It is essential to seek expert guidance for foundation design in these cases.

Hydraulic stability

Scour

Positive measures should be taken to avoid erosion and scour of the soil beneath or near the structure base

Examples of such measures are

⎯ scour skirts penetrating through erodible layers into scour resistant materials or deep enough to eliminate the scour hazard, or

⎯ scour protection placed around the edges of the foundation

Sediment transport studies may be carried out to assess the scour potential of the seabed material around the foundation.

Piping

The foundation should be designed to prevent excessive hydraulic gradients (piping conditions) in the soil due to environmental loadings or operations performed during or subsequent to structure installation

To facilitate the penetration of foundation skirts into the seabed, it is beneficial to maintain an under-pressure within the skirt compartments relative to the ambient hydrostatic pressure Installation procedures must be carefully planned to prevent soil damage, such as plug uplift, erosion, and piping Additionally, if removal of the foundation is expected, a thorough analysis of the forces involved during the removal process should be conducted to ensure that it can be executed with the available resources.

7.12 Shallow foundations equipped with seabed penetrating skirts

Skirts around the periphery of shallow foundations enhance their performance by penetrating the seabed For larger foundation areas, incorporating interior skirts creates compartments beneath the plate foundation These skirts significantly increase the foundation's resistance to overturning moments, bearing loads, sliding loads, and torsion loads, while also reducing vertical and horizontal displacements and rotations Additionally, they improve erosion resistance beneath the foundation.

To ensure the stability of foundations, it is crucial to conduct installation studies that verify the skirts penetrate to the desired depth below the seafloor When evaluating bearing capacity, the foundation level and the depth of embedment should correspond to the skirts' penetration depth, assuming that no critical failure modes are present within the skirt compartments.

To assess sliding capacity, it is important to consider that the soil strength at the skirt tip level ($s_{uo}$) may exceed that at the seafloor level, providing additional capacity under pure sliding conditions Lateral resistance can also be enhanced above the skirt tip through embedded members, which contribute to both active and passive resistance as well as side shear It is crucial to ensure that internal mechanisms within the soil plug of skirted foundations do not compromise overall capacity Additionally, attention must be given to installation disturbances or soil conditions that could reduce resistance above the skirt tip, particularly in scenarios where soil tension cracking may occur on the active side of the skirt.

Skirts can enhance the capacity of shallow foundations to endure short-term tensile stresses relative to ambient water pressure, supported by negative excess pore pressures in the soil Design considerations often accept cyclic tensile stresses from waves lasting a few seconds, while longer-duration tensile stresses may be manageable for skirted foundations on low-permeability clays It is essential for specialist geotechnical engineers to verify the sustainability of tensile stresses for specific designs on a case-by-case basis Further discussion on the soil's ability to resist tensile stresses is available in section 7.3.

When foundation loads are not specified at the skirt tip level, it is crucial to ensure proper load transfer to the skirt tip during stability analysis Additional guidance is available for this process.

Shallow foundations without seabed penetrating skirts

Foundations without skirts, which remain at the seafloor, can require special consideration In particular, the consequences of loss of contact between the foundation and the seafloor shall be assessed.

Installation effects

Shallow foundations are typically installed on the seafloor from a vessel, where vertical heave motions from the vessel's movement and environmental conditions lead to an impact during touchdown This impact can be managed by adhering to specific weather criteria and executing well-planned installation operations However, many small structures still experience foundation failures during installation, particularly in soft soil conditions To mitigate these incidents, it is recommended to use a heave compensator and maintain a low descent rate (less than 0.2 m/s) for controlled installations, as this eliminates the need for additional safety margins Conversely, uncontrolled descent rates can result in excessive penetration beyond the failure displacement, necessitating further investigation into the consequences of such penetration, as detailed in Annex A.

Sliding stability

General

When assessing sliding stability, it is crucial to consider the potential presence of discrete layers of low-strength soil during site investigations and their interpretation, as these layers may create preferential failure surfaces.

Surface foundations

Once the vertical load capacity is determined using equations 7.4 to 7.6, the maximum horizontal load must be restricted to the capacity defined for the extreme condition of pure sliding, as outlined in the following equations for the undrained case.

H d is the maximum total horizontal load applied to the base of the foundation at failure under undrained conditions; s uo is the shear strength at base level

H d ′ is the maximum total horizontal load applied to the base of the foundation at failure under drained conditions;

Q is the actual vertical load acting during the relevant loading condition

Equations 14 and 15 assume that complete soil resistance can be activated at the interface between the foundation and the soil, indicating a full soil-soil contact However, this assumption should be evaluated individually for each case.

In drained conditions, it is advisable to utilize a distinct interface friction angle (δ) between the foundation soil and the structure Furthermore, it is essential to evaluate the potential sliding along a thin, weak layer of low permeability located at shallow depths beneath the foundation base within the sand mass.

In undrained conditions, applying a soil adhesion coefficient can effectively lower the undrained strength at the foundation level Additionally, when an undrained response is expected throughout the soil mass, it may still be beneficial to consider a drained interface between the foundation base plate and the soil Furthermore, it is important to evaluate the potential for sliding along a sand seam within a stable clay layer.

Torsional stability

Torsional stability requires consideration, and additional analysis shall be performed if torsion loads are significant

Torsional loads significantly diminish the bearing capacity and sliding resistance of shallow foundations Currently, there are no correction factors for torsional loads applicable to the bearing capacity methods outlined in sections 7.4 to 7.6 or for assessing pure sliding in section 7.15 Therefore, it is essential to seek specialist advice when these factors need to be considered.

When evaluating torsional stability, it is essential to consider the potential presence of discrete layers of low strength during site investigations and interpretations, as these layers may facilitate preferential displacements.

Recommended design criteria for pile foundations can be found in API 2A-WSD.

Pile capacity for axial compression

General

The axial capacity of a pile under compression, detailed in sections 8.1.2 to 8.1.5, refers to its resistance when compressive loads are applied along its axis Additionally, the capacity for axial tension is covered in section 8.2.

Pile capacities are typically assessed using a simplified calculation model outlined in section 8.1.2, with parameters defined in sections 8.1.3 to 8.1.5 This model, developed through years of offshore practice, is the current industry standard However, it lacks information on axial pile displacements, which are crucial for serviceability, particularly under non-extreme conditions from permanent, variable, and operational environmental loads that are usually below design loads Axial pile behavior, essential for meeting service requirements, is referred to as axial pile performance and is further discussed in section 8.3, with methods for determining this performance detailed in C.8.6.2 and C.8.6.3.

The simplified model for pile capacity outlined in section 8.1.2 relies on a (quasi-)static and monotonic application of axial loads, failing to capture the complex interactions between the pile and soil under real field conditions To better understand the model's limitations and effectively apply engineering judgment to its results, it is beneficial to investigate actual pile performance, as discussed in section 8.3.

The relationships between the mobilized axial shear transfer between the pile and soil, as well as the mobilized end bearing resistance and pile tip displacement, can be analyzed using equation 8.4.

Ultimate axial pile capacity

The ultimate axial capacity of piles in compression, including belled piles, Q c , should be determined by the equation:

Q f,c is the shaft friction capacity in compression, in force units;

Q p is the end bearing capacity, in force units; f(z) is the unit shaft friction, in stress units;

A s is the side surface area of pile; q is the unit end bearing at the pile tip, in stress units;

A p is the gross end area of the pile; z is the depth below the original seafloor

For open-ended pipe piles, the total end bearing capacity, $ Q_p $, must not surpass the combined end bearing capacity of the internal plug and the end bearing on the pile tip wall annulus When calculating the design loads in compression on the pile, it is essential to include the weight of the pile.

When assessing pile capacity, it is essential to consider the relative deformations between the soil and the pile, along with the compressibility of the soil-pile system In certain situations, a detailed analysis of axial pile performance effects on capacity is necessary, with further insights provided in sections 8.3 and C.8.3.

Foundation configurations should be selected based on proven methods that can be reliably, practically, and economically installed under comparable conditions, taking into account the size of the piles and the installation equipment utilized.

Alternatives for possible remedial action in the event that design objectives cannot be obtained during installation should be investigated and defined prior to construction

For belled piles, the shaft friction values must adhere to the specifications outlined in sections 8.1 and 8.2 When calculating the shaft friction resistance, \$Q_{f,c}\$, it is essential to exclude the shaft friction on the upper bell surface and potentially on the pile section above the bell Additionally, if a pilot hole is drilled, the end bearing area should also be excluded from the total bearing area of the bell.

Shaft friction and end bearing in cohesive soils

Several methods exist for calculating shaft friction and end bearing in cohesive soils, with the one outlined below being the current industry standard developed over many years However, it is important to exercise caution in its application, as numerous variables can influence pile capacity.

In cohesive soils, the unit shaft friction, denoted as $ f(z) $, at a depth $ z $ for pipe piles can be determined using the equation $ f(z) = \alpha s_u $, where $ \alpha $ represents the dimensionless shaft friction factor specific to clays, and $ s_u $ is the undrained shear strength of the soil at that depth, measured in stress units This topic is further elaborated in section C.8.1.3.

The factor α can be computed by Equation 18:

0.5ψ 0.25 α= − for ψ > 1.0 with the constraint that α ≤ 1,0 where ψ= ( ) u o s p z′ at depth, z; (19) p′o(z) = effective vertical stress at depth z

This article discusses effective methods for assessing undrained shear strength (\$s_u\$) and effective overburden stress (\$p'_o(z)\$), highlighting the impact of different sampling and testing procedures as outlined in section C.8.1.3 In the case of underconsolidated clays, which experience excess pore pressures during active consolidation, the parameter \$\alpha\$ is typically considered to be 1.0.

When dealing with soils that have s u /p′ o (z) ratios exceeding three, it is crucial to apply Equation 18 with caution This same level of scrutiny should be exercised for deep penetrating piles in soils characterized by high undrained shear strength Additionally, special care must be taken when working with low plasticity clays.

For very long piles some reduction in capacity may be warranted, particularly where the shaft friction degrades on continued displacement This effect is discussed in more detail in C.8.1.3

Where the pile tip is in cohesive soils, the unit end bearing, q, in stress units, may be computed using

Shaft friction, denoted as $ f(z) $, influences both the interior and exterior of a pile The total axial resistance during pile compression is derived from the combination of external shaft friction, end bearing on the pile wall annulus, and the lesser of total internal shaft friction or end bearing of the plug For plugged piles, the bearing pressure is assumed to act across the entire cross-section, while for unplugged piles, it is limited to the pile wall annulus The classification of a pile as plugged or unplugged is determined through static calculations, and although a pile may be driven in an unplugged state, it can perform as if it were plugged under static loads.

Shaft friction resistance and end bearing capacity calculated based on the specified requirements indicate long-term capacities However, the axial capacity right after installation tends to be lower, particularly in underconsolidated to slightly overconsolidated clays This variation is influenced by the generation of excess pore pressure in the soil during installation and its gradual dissipation over time When design loads are applied to a pile foundation, these factors play a crucial role in performance.

Shortly after installation, the immediate capacity of a pile and its subsequent increase over time are crucial factors in design considerations For a more detailed discussion on the soil-pile setup behavior, refer to section C.8.1.3.

When selecting shaft friction values for piles driven in undersized drilled holes, jetted piles, or drilled and grouted piles, it is essential to consider the soil disturbance caused by the installation process Typically, the friction values, denoted as f(z), should not exceed those for driven piles; however, in certain situations involving drilled and grouted piles in overconsolidated clay, f(z) may surpass these limits Additionally, when determining f(z) for drilled and grouted piles, it is crucial to evaluate the strength of the soil-grout interface, taking into account the potential impact of drilling mud A further assessment of the allowable bond stress between the pile steel and the grout, as outlined in API 2A-WSD, Section 10.4.4, is also necessary.

In layered soils, shaft friction values, f(z), in the cohesive layers shall be as given by Equation 17 through

Equation 19 End bearing values for piles tipped in cohesive layers with adjacent weaker layers may be taken as given in Equation 20 provided that a) the pile achieves a penetration of two to three diameters or more into the layer in question, and c) the tip is approximately three diameters or more above the bottom of the layer to preclude punch through

When the required distances are not met, modifications to the end bearing are often needed If the adjacent layers possess similar strength to the layer in question, the distance of the pile tip from the interface becomes less critical.

Shaft friction and end bearing in cohesionless soils

This clause outlines a straightforward approach for evaluating pile capacity in cohesionless soils, while Clause C.8.1.4 introduces more recent and reliable methods that utilize direct correlations between pile unit friction, end bearing data, and cone penetration test (CPT) results Compared to the Main Text method, these CPT-based techniques are deemed superior, offering statistically closer predictions of pile load test outcomes and covering a broader spectrum of cohesionless soils However, due to limited offshore experience with these methods, further validation is necessary before they can be routinely recommended over the Main Text method It is essential that CPT-based methods are employed solely by qualified engineers who possess expertise in interpreting CPT data and are aware of the associated limitations and reliability.

Following installation, pile driving (instrumentation) data may be used to give more confidence in predicted capacities

In cohesionless soils, the unit shaft friction at a specific depth, denoted as f(z), can be determined using the formula f(z) = β p′ o (z), where β represents the dimensionless shaft friction factor applicable to sands, and p′ o (z) signifies the effective vertical stress at that depth.

In the absence of specific data, β values for open-ended pipe piles that are driven unplugged may be taken from

For full displacement piles, including closed-ended or fully plugged open-ended types, the values of β can be considered 25% higher than those listed in Table 1 Additionally, for long piles, the function f(z) does not always increase linearly with overburden stress, as suggested by Equation 21 Therefore, it may be advisable to restrict f to the values provided in Table 1.

Table 1—Design parameters for cohesionless siliceous soil

Limiting Shaft Friction Values kPa (kips/ft 2 )

Limiting Unit End Bearing Values MPa (kips/ft 2 )

Sand Sand Sand-silt c Silt Silt

Not applicable d Not applicable d Not applicable d Not applicable d

The parameters in this table serve as general guidelines However, if detailed information such as CPT records, strength tests on high-quality samples, model tests, or pile driving performance is available, alternative values may be justified Additionally, the definitions for the relative density percentage description are provided.

The shaft friction factor β, which replaces the “K tan δ” term from earlier editions of API 2A-WSD, is introduced to clarify its distinction from the δ parameter in the Annex Soils classified as sand-silt contain notable amounts of both sand and silt, with strength values typically increasing as the sand fraction rises and decreasing with higher silt fractions Previous design parameters for these soil and relative density combinations may lack conservativeness; therefore, it is advisable to utilize CPT-based methods outlined in the annex for these soil types.

For end bearing of piles in cohesionless soils, the unit end bearing, q, in stress units, may be computed using

Equation 22 q = N q p′ o, tip (22) where p′ o, tip is the effective vertical stress at the pile tip;

N q is the dimensionless bearing capacity factor

Table 1 presents the recommended N q values For long piles, the relationship between q and overburden stress is not always linear, as suggested by Equation 22 Therefore, it is advisable to restrict q to the specified values.

Table 1 For plugged piles, the bearing pressure may be assumed to act over the entire cross-section of the pile

In unplugged piles, the bearing pressure is applied solely to the pile annulus, with additional resistance stemming from friction between the soil plug and the inner wall of the pile The classification of a pile as plugged or unplugged relies on static calculations, where the unit shaft friction on the soil plug is equivalent to the outer shaft friction It's important to note that while a pile may be driven in an unplugged state, it can exhibit plugged behavior when subjected to static loads.

Load test data for piles in cohesionless soils reveal that capacity predictions using the described method can show greater variability than those for piles in clay This method is conservative for short offshore piles (less than 45 m or 150 ft) in dense to very dense sands under compression, but may be unconservative in other scenarios Designers should consider this uncertainty by choosing conservative design parameters and/or higher safety factors, particularly in situations where force redistribution occurs after maximum resistance is reached, which can result in abrupt (brittle) failures, especially for short piles in tension.

For soils outside the relative density and description ranges in Table 1, or those with weak grains or compressible structures, alternative methods for selecting design parameters may be necessary Special laboratory or field tests may be required for very loose soils or those with significant mica or volcanic grain content Notably, sands with calcium carbonate, prevalent in many oceanic regions, are particularly important in this context.

When installing piles in undersized drilled or jetted holes within cohesionless soils, it is essential to determine the values of \$f(z)\$ and \$q\$ using a reliable method that considers the soil disturbance caused by the installation process However, these values must not surpass those established for driven piles.

In layered soils, the calculation of shaft friction values, f(z), in cohesionless layers should follow the guidelines outlined in Table 1 For piles embedded in cohesionless layers adjacent to softer layers, end bearing values can also be derived from Table 1, given that the pile penetrates two to three diameters or more into the cohesionless layer and that the tip is positioned at least three diameters above the bottom of the layer to avoid punch-through.

Where these pile tip penetrations are not achieved, some modification in the tabulated values may be necessary

Where adjacent layers are of comparable strength to the layer of interest, the proximity of the pile tip to the layer interface is not a concern.

Shaft friction and end bearing of grouted piles in rock

The unit shaft friction of grouted piles in jetted or drilled rock holes should not exceed half the uniaxial compressive strength of the rock or grout, and is typically much lower This reduction is influenced by construction factors, like the roughness of the hole's side, and rock mass factors, such as discontinuities Additionally, a layer of slaked mud or clay may form on the hole's sidewall, which will not achieve the strength of the rock It is essential to verify the bond stress between the pile and the grout in accordance with API 2A-WSD.

The end bearing capacity of rock must not exceed the uniaxial compressive strength of the rock or grout, adjusted by a suitable bearing capacity factor for the rock type Typically, this capacity should be significantly lower or disregarded in design, influenced by pile construction factors like the removal of drill cuttings and rock mass characteristics, including discontinuities Ultimately, the limiting end bearing capacity for such piles is determined by the stresses in the grout or pile steel.

Design values for (static) unit shaft friction and end bearing can be found in various publications (see References

Most studies on this topic focus on "stubby" stiff piles, commonly used in onshore applications like bored piles However, the design values provided in these publications may be overly conservative for long flexible piles utilized in offshore settings due to the brittle response of unit shaft friction Additionally, it is important to consider that cyclic loads can negatively impact the axial capacity of these piles.

Axial pile performance

Soil reaction for piles under axial compression

Soil reaction for piles under lateral loads

Pile group behavior

Site characterization

Steel catenary risers

Top tension riser

Riser tower foundations

Tiêu đề	Geotechnical And Foundation Design Considerations
Trường học	Texas A&M University
Chuyên ngành	Geotechnical Engineering
Thể loại	Recommended Practice
Năm xuất bản	2011
Thành phố	Washington, DC

Định dạng
Số trang	138
Dung lượng	1,85 MB