.. _capacity-methods: ######################## Capacity of Single Piles ######################## ``edafos`` implements the pile capacity methods presented below. .. _api-method: ********** API Method ********** American Petroleum Institute (API). .. admonition:: Required Properties :Pile: - :math:`\alpha` or :math:`d`: side length or diameter for surface area, :math:`A_s` (shaft resistance) - :math:`\alpha` or :math:`d` (:math:`t`): side length or diameter (with thickness for open ended) for toe area, :math:`A_p, A_{pp}` (toe resistance) - pile type: open-ended or closed-ended for :math:`K` selection (cohesionless soils) :Soil: - type: cohesive/cohesionless classification - :math:`\gamma`: total unit weight for effective stress calculations - :math:`s_u`: undrained shear strength (cohesive soils) - :math:`N_{cor}`: SPT-N corrected to select :math:`\delta`, :math:`f_{s.lim}`, :math:`N_q`, :math:`q_{s.lim}` (cohesionless soils) **Note**: ``edafos`` runs a pre-check to verify that all required properties have been defined prior to running the capacity calculations. Refer to the :meth:`~edafos.deepfoundations.capacity_base.CapacityMethod._pre_check` method for more information. Cohesive Soils ============== The revised API method was included in RP-2A (1993) and has been widely used in the offshore industry. Shaft Resistance ---------------- The general equation for shaft resistance is given by: .. math:: R_s = \sum{f_s A_s} :label: R_s-api where: - :math:`f_s`: unit shaft resistance (adhesion) - :math:`A_s`: side surface area of pile and, .. math:: f_s = \alpha s_u :label: f_s-api-clay where: - :math:`\alpha`: coefficient as per revised API (1987) - :math:`s_u`: undrained shear strength of soil The :math:`\alpha` factor is calculated based on the conditional in equation :eq:`a-rev-api-clay`. .. math:: :label: a-rev-api-clay \alpha = \begin{cases} 0.5\psi^{-0.5} & \textrm{if} \quad \psi \leq 1.0 \\ 0.5\psi^{-0.25} & \textrm{if} \quad \psi > 1.0 \end{cases} \quad \leq 1.0 where: - :math:`\psi`: :math:`s_u/\bar{\sigma'}` at a depth, :math:`z` - :math:`\bar{\sigma'}`: average effective stress (at midpoint) - :math:`s_u`: undrained shear strength of soil Toe Resistance -------------- The toe resistance is equal to: .. math:: R_p = q_p A_p :label: R_p-api where: - :math:`q_p`: unit toe resistance - :math:`A_p`: pile toe cross-sectional area **Important:** Toe resistance must always be checked against :math:`R_p = q_p A_{pp}` where :math:`A_{pp}` is the cross sectional area of soil plug in open end pipe or H-piles at pile toe. The unit toe resistance, :math:`q_p`, is given by: .. math:: q_p = 9 s_u :label: q_p-api-clay where: - :math:`s_u`: Undrained shear strength at the tip of the pile, usually taken as the **average over a distance of two diameters** below the tip of the pile. | Cohesionless Soils ================== Following API RP2A (1987) recommendations. Shaft Resistance ---------------- Shaft resistance is given by the general form in equation :eq:`R_s-api`. Unit shaft resistance for piles in cohesionless soils is calculated by: .. math:: f_s = K \sigma' \tan{\delta} :label: f_s-api-sand where: - :math:`K`: coefficient of lateral earth (ratio of horizontal to vertical normal effective stress) - :math:`\bar{\sigma'}`: average effective stress (at midpoint) - :math:`\delta`: friction angle between the soil and the pile wall :numref:`API_K_table` offers recommended values for the coefficient of lateral earth, :math:`K`. .. _API_K_table: .. table:: Values for coefficient of lateral earth, :math:`K` +------------------------------------------------+-----+ | Condition | K | +================================================+=====+ | unplugged, open-ended pipe piles (tens & comp) | 0.8 | +------------------------------------------------+-----+ | full-displacement piles | 1.0 | +------------------------------------------------+-----+ :numref:`API_d_table` offers guidelines for :math:`\delta`, the friction angle between the soil and the pile wall as well as limiting, :math:`f_s`. .. _API_d_table: .. table:: Guidelines for Side Friction in Siliceous Soil +----------------------------------------+----------------+-----------------------+ | Soil | :math:`\delta` | Limiting, :math:`f_s` | + + , degrees +-----------------------+ | | | kips/ft2 | kPa | +========================================+================+==========+============+ | Very loose to medium, sand to silt | 15 | 1.0 | 47.8 | +----------------------------------------+----------------+----------+------------+ | Loose to dense, sand to silt | 20 | 1.4 | 67.0 | +----------------------------------------+----------------+----------+------------+ | Medium to dense, sand to sand-silt | 25 | 1.7 | 81.4 | +----------------------------------------+----------------+----------+------------+ | Dense to very dense, sand to sand-silt | 30 | 2.0 | 95.8 | +----------------------------------------+----------------+----------+------------+ | Dense to very dense, gravel to sand | 35 | 2.4 | 114.9 | +----------------------------------------+----------------+----------+------------+ Toe Resistance -------------- Toe resistance is given by the general form in equation :eq:`R_p-api`. Unit toe resistance for piles in cohesionless soils is calculated by: .. math:: q_p = \sigma' N_q :label: q_p-api-sand where: - :math:`\sigma'`: effective stress at pile tip (not average) - :math:`N_q`: bearing capacity factor :numref:`API_q_table` offers guidelines for :math:`N_q`, bearing capacity factor as well as limiting, :math:`q_p`. .. _API_q_table: .. table:: Guidelines for Toe Resistance in Siliceous Soil +----------------------------------------+-------------+--------------------------+ | Soil | :math:`N_q` | Limiting, :math:`q_p` | + + +--------------------------+ | | | kips/ft\ :sup:`2` | MPa | +========================================+=============+===================+======+ | Very loose to medium, sand to silt | 8 | 40 | 1.9 | +----------------------------------------+-------------+-------------------+------+ | Loose to dense, sand to silt | 12 | 60 | 2.9 | +----------------------------------------+-------------+-------------------+------+ | Medium to dense, sand to sand-silt | 20 | 100 | 4.8 | +----------------------------------------+-------------+-------------------+------+ | Dense to very dense, sand to sand-silt | 40 | 200 | 9.6 | +----------------------------------------+-------------+-------------------+------+ | Dense to very dense, gravel to sand | 50 | 250 | 12.0 | +----------------------------------------+-------------+-------------------+------+ In order to interpret :numref:`API_d_table` and :numref:`API_q_table` algorithmically, the correlation in :numref:`API_SPT_corr_table` is employed in ``edafos``. .. _API_SPT_corr_table: .. table:: SPT-N corrected Correlations +--------------+-----------------------+--------------------+ | Density | :math:`N_{cor}` (bpf) | :math:`\phi` (deg) | +==============+=======================+====================+ | Very loose | 0 - 4 | < 28 | +--------------+-----------------------+--------------------+ | Loose | 5 - 10 | 28 - 30 | +--------------+-----------------------+--------------------+ | Medium dense | 11 - 30 | 30 - 36 | +--------------+-----------------------+--------------------+ | Dense | 31 - 50 | 36 - 41 | +--------------+-----------------------+--------------------+ | Very Dense | over 50 | > 41 | +--------------+-----------------------+--------------------+ In which case :numref:`API_d_table`, :numref:`API_q_table` and :numref:`API_SPT_corr_table` can be consolidated as in :numref:`API_d_q_SPT_table`. .. _API_d_q_SPT_table: .. table:: Guidelines for Shaft and Toe Resistance in Siliceous Soil with SPT-N values +----------------------------------------+-----------------------+----------------------+-------------------------+-------------+-------------------------+ | Soil | :math:`N_{cor}` (bpf) | :math:`\delta` (deg) | :math:`f_{s.lim}` (ksf) | :math:`N_q` | :math:`q_{p.lim}` (ksf) | +========================================+=======================+======================+=========================+=============+=========================+ | Very loose to medium, sand to silt | 0 - 4 | 15 | 1.0 | 8 | 40 | +----------------------------------------+-----------------------+----------------------+-------------------------+-------------+-------------------------+ | Loose to dense, sand to silt | 5 - 10 | 20 | 1.4 | 12 | 60 | +----------------------------------------+-----------------------+----------------------+-------------------------+-------------+-------------------------+ | Medium to dense, sand to sand-silt | 11 - 30 | 25 | 1.7 | 20 | 100 | +----------------------------------------+-----------------------+----------------------+-------------------------+-------------+-------------------------+ | Dense to very dense, sand to sand-silt | 31 - 50 | 30 | 2.0 | 40 | 200 | +----------------------------------------+-----------------------+----------------------+-------------------------+-------------+-------------------------+ | Dense to very dense, gravel to sand | over 50 | 35 | 2.4 | 50 | 250 | +----------------------------------------+-----------------------+----------------------+-------------------------+-------------+-------------------------+ | .. _olson90-method: *************** Olson 90 Method *************** The Olson 90 method is for cohesionless soils only. It was created from a database of 31 load tests on steel pipe piles. .. admonition:: Required Properties :Pile: - :math:`\alpha` or :math:`d`: side length or diameter for surface area, :math:`A_s` (shaft resistance) - :math:`\alpha` or :math:`d` (:math:`t`): side length or diameter (with thickness for open ended) for toe area, :math:`A_p, A_{pp}` (toe resistance) - pile type: open-ended or closed-ended for :math:`K` selection (cohesionless soils) :Soil: - type: cohesive/cohesionless classification - :math:`\gamma`: total unit weight for effective stress calculations - :math:`s_u`: undrained shear strength (cohesive soils) - desc, :math:`N_{cor}`: soil description and SPT-N corrected to select :math:`\delta`, :math:`f_{s.lim}`, :math:`N_q`, :math:`q_{s.lim}` (cohesionless soils) **Note**: ``edafos`` runs a pre-check to verify that all required properties have been defined prior to running the capacity calculations. Refer to the :meth:`~edafos.deepfoundations.capacity_base.CapacityMethod._pre_check` method for more information. Cohesionless Soils ================== Olson 90 is similar to the Revised API method with two main differences. First, the coefficient of lateral earth, :math:`K`, is calculated rather than taken from :numref:`API_K_table`. In Olson 90, :math:`K` is: .. math:: :label: olson90-K K = \begin{cases} 0.16 + 0.015 \, N_{cor} & \textrm{non-displacement piles}\\ 0.70 + 0.015 \, N_{cor} & \textrm{full displacement piles} \end{cases} where: - :math:`N_{cor}`: SPT-N values corrected for overburden pressure Next, Olson 90 provides revised guidelines for shaft and tow resistances which are offered in :numref:`Olson90_table`. .. _Olson90_table: .. table:: Olson 90 guidelines for Shaft and Toe Resistance +---------------+-----------------------+----------------------+-------------------------+-------------+-------------------------+ | Soil | :math:`N_{cor}` (bpf) | :math:`\delta` (deg) | :math:`f_{s.lim}` (ksf) | :math:`N_q` | :math:`q_{p.lim}` (ksf) | +===============+=======================+======================+=========================+=============+=========================+ | Gravel | 0 - 4 | [20] | [1.4] | [12] | [60] | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 5 - 10 | [25] | [1.7] | [20] | [100] | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 11 - 30 | [30] | [2.0] | [40] | [200] | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | over 30 | [35] | [2.4] | [60] | [250] | +---------------+-----------------------+----------------------+-------------------------+-------------+-------------------------+ | Sand / Gravel | 0 - 4 | [20] | [1.4] | [12] | [60] | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 5 - 10 | [25] | [1.7] | [20] | [100] | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 11 - 30 | [30] | [2.0] | [40] | [200] | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | over 30 | [35] | [2.4] | [60] | [250] | +---------------+-----------------------+----------------------+-------------------------+-------------+-------------------------+ | Sand | 0 - 4 | [20] | [1.0] | [50] | [40] | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 5 - 10 | 30 | 1.1 | 120 | 120 | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 11 - 30 | 35 | 1.9 | 120 | 190 | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 31 - 50 | 40 | 2.6 | 120 | 190 | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 51 - 100 | 40 | 3.7 | 130 | 200 | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | over 100 | 40 | 3.8 | 220 | 530 | +---------------+-----------------------+----------------------+-------------------------+-------------+-------------------------+ | Sand / Silt | 0 - 4 | 10 | [1.0] | [10] | [10] | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 5 - 10 | 10 | [1.0] | [20] | [40] | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 11 - 30 | 15 | [1.4] | 50 | 110 | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 31 - 50 | 20 | 2.0 | 100 | 160 | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 51 - 100 | [30] | [2.0] | [100] | [200] | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 101 - 200 | [34] | [20] | [100] | [200] | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | over 200 | 40 | 20 | [100] | [200] | +---------------+-----------------------+----------------------+-------------------------+-------------+-------------------------+ | Silt | 0 - 4 | [10] | [1.0] | [10] | [40] | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 5 - 10 | 15 | [1.0] | [10] | [40] | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 11 - 30 | 20 | [1.4] | [10] | [40] | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | 31 - 50 | 20 | [1.4] | [12] | [60] | + +-----------------------+----------------------+-------------------------+-------------+-------------------------+ | | over 50 | [25] | [1.4] | [12] | [60] | +---------------+-----------------------+----------------------+-------------------------+-------------+-------------------------+ **Note:** - Must not interpolate. In using values in :numref:`Olson90_table`, use the line corresponding to N = 4 for any layer with N less than or equal to 4, the line corresponding to 10 for N = 5 - 10, and so on. - Number in brackets were extrapolated, no supporting data.