Lateral Soil Methods¶
There are various methods available that can be used to calculate PY curves for further lateral analysis:
Method 
Required Input 
Additional Required Input 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
24 

X 
X 
O 

X 
X 
X 
X 
CLAYAPI Factor, Limit s_{u} 

X 
X 
X 
O 
O 
Reese K Static, Reese K Cyclic 

X 
X 
X 
X 
X 

X 
X 
X 
x0 

X 
X 
X 
Alpha, Eir, Krm, Top depth of rock layer 

X 
X 
X 
X 
O 
O 
O 
O 

X 
X 

X 
X 
X 
X 
X 
O 
O 
Reese K Static 

X 
X 
X 
X 
x0, number of cycles 

X 
X 
X 
Gamma C, number of cycles 

X 
X 
O 

X 
O 

X 
X 
X 
X 
X 

X 
X 
X 

X 
List of soil parameters used in the lateral methods:
No. 
Symbol 
Unit 
Soil Parameter 

1 
\(s_{u,top}\) 
(kPa) 
undrained shear strength at the top of the layer 
2 
\(s_{u,bottom}\) 
(kPa) 
undrained shear strength at the bottom of the layer 
3 
\(J\) 
() 
empirical constant with values ranging from 0.25 to 0.5 having been determined by field testing 
4 
\(e_{50}\) 
() 
strain at one half the maximum deviator stress in laboratory undrained compression tests 
5 
\(\phi\) 
(deg) 
angle of internal friction in sand 
6 
\(K\) 
(kPa/m) 
rate of increase with depth of the modulus of subgrade reaction 
7 
\(p_{lim}\) 
(kPa) 
Limit for the ultimate lateral resistance 
8 
\(q_{c,top}\) 
(kPa) 
CPT cone resistance at the top of the layer 
9 
\(q_{c,bottom}\) 
(kPa) 
CPT cone resistance at the bottom of the layer 
10 
\(Dyson R\) 
() 
R parameter for Dyson method 
11 
\(Dyson N\) 
() 
N parameter for Dyson method 
12 
\(Dyson M\) 
() 
M parameter for Dyson method 
13 
\(Wess R\) 
() 
R parameter for Wesselink method 
14 
\(Wess N\) 
() 
N parameter for Wesselink method 
15 
\(Gamma\) 
() 
gamma parameter for Wesselink method 
16 
\(UCS\) 
(kPa) 
Unconfined compressvie strength 
17 
\(Dunn K_{r}\) 
() 
K_{r} parameter for Dunnavant method 
18 
\(Reese K Static\) 
(kPa/m) 
Static K parameter for Reese method 
19 
\(Reese K Cyclic\) 
(kPa/m) 
Cyclic K parameter for Reese method 
20 
\(Reese \alpha\) 
() 
alpha parameter for Reese method 
21 
\(Reese E_{ir}\) 
(kPa) 
E_{ir} parameter for Reese method 
22 
\(Novello \gamma_{C}\) 
() 
gamma C parameter for Novello method 
23 
\(G_{max,A}\) 
(kPa) 
Small strain shear modulus at reference depth 
24 
\(G_{max,B}\) 
() 
Exponent for Gmax variation as function of depth 
For SANDAPI, ABBS, KALLEHAVE and Sorensen P_{lim} is an optional input.
Note
Where possible the notation used in the explanation of each method is the same as used in the original source paper, rather than translate many different methods and styles of notation to a common one to be used in OPILE. A full list of different notations and descriptions is given within this help file.
Attention
It is always advised to consult the original reference sources of these methods if the user is not familiar with the implementation of a particular method. The references cited within the OPILE documentation are not intended to be exhaustive. Note that easy unit conversions can be made when inputting data such as dimensions and shear strengths, see units convention section for details.
SANDAPI¶
OPILE has one implementation of the SANDAPI formulation even if API2000 and API RP2GEO formulate the methodology using slightly different equations. The equations as presented in API RP2GEO have been implemented:
According to API RP2GEO (2011) the ultimate lateral bearing capacity for sand has been found to vary from a value at shallow depths determined by:
\[p_{us} = (C_{1} \cdot z + C_{2} \cdot D)C_{1} \cdot \gamma' \cdot z\]
To a value at large depths determined by:
\[p_{ud} = C_{3} \cdot D \cdot \gamma' \cdot z\]
At any given depth the smallest value of pu should be used as the ultimate bearing capacity.
Where:
\(\gamma'\)
is the submerged soil unit weight
\(z\)
is the depth below the original seafloor.
\(D\)
is the pile outside diameter
\(C_{1}\)
coefficient calculated as: \(C_{1} = \frac {(\tan{\beta})^2 \cdot \tan{(\alpha)}}{\tan{(\beta\phi')}} \cdot K_{0} \cdot \left[\frac {\tan{(\phi')} \cdot \sin{(\beta)}}{\cos{(\alpha)} \cdot \tan{(\beta  \phi')}} + \tan{\beta} \cdot (\tan{\phi'} \cdot \sin{\beta}\tan{\alpha})\right]\)
\(C_{2}\)
coefficient calculated as: \(C_{2} = \frac {\tan{(\beta)}}{\tan{(\beta  \phi')}}  K_{a}\)
\(C_{3}\)
coefficient calculated as: \(C_{3} = K_{a}((\tan{\beta})^8  1 )+ K_{0} \cdot \tan{\phi'} \cdot (\tan{\beta})^4\)
\(\alpha\)
\(\alpha = \frac {\phi'}{2}\)
\(\beta\)
\(\beta = 45 + \frac {\phi'}{2}\)
\(K_{0}\)
\(0.4\)
\(K_{a}\)
\(\frac {1sin(\phi')}{1+sin(\phi')}\)
The lateral soil resistancedeflection (py) relationships for sand are nonlinear and may be approximate at a specific depth z by the following expression:
\[p = A \cdot p_{u} \cdot \tanh{\left(\frac{kz}{Ap_{u}} \right)}\]
Where:
\(A\)
is a factor to account for cyclic or static loading condition, evaluated by: \(A= (3.00.8\frac{z}{D}) \geq 0.9\) for static loading and \(0.9\) for cyclic loading.
\(k\)
is the rate of increase with depth of initial modulus of subgrade reaction \([kN/m^{3}]\)  see table below
\(p_{u}\)
is the ultimate lateral resistance at depth z
For SANDAPI there is an optional parameter \(P_{lim}\) which limits the lateral pressure, if necessary. If this optional parameter is left blank then it will not be used, otherwise the limit will be applied.
The the rate of increase with depth of initial modulus of subgrade reaction can be derived from the table below as a function of \(\phi'\).
\(\phi'\) 
\(k\) 

\(MN/m^3\) 
\(lb/in^3\) 

25 
5.4 
20 

30 
11 
40 

35 
22 
80 

40 
45 
165 
CLAYAPI¶
According to API (2000) for static lateral loads the ultimate unit lateral bearing capacity pu for a pile embedded in CLAYS is calculated according to:
Where:
\(p_{u}\)
is the ultimate lateral resistance (kPa)
\(c\)
is the undrained shear strength for undisturbed clay soil samples.
\(D\)
is the pile outside diameter
\(\sigma'_{v}\)
is the effective overburden pressure at the depth in question (kPa)
\(J\)
is a dimensionless empirical constant with values ranging from 0.25 to 0.5.
\(X\)
is depth below soil surface
\(X_{R}\)
is depth below soil surface to bottom of reduced resistance zone. Given by: \(X_{R} = \frac {6 \cdot D}{\frac {\gamma' \cdot D}{c}+ J}\)
The curve for STATIC loading is generated from the following coordinate points:
\(p/p_{u}\) 
\(y/y_{c}\) 
0.00 
0 
0.23 
0.1 
0.33 
0.3 
0.50 
1.0 
0.72 
3.0 
1.00 
8 
1.00 
infinity 
where:
\(p\)
is the acutal lateral resistance (kPa)
\(y\)
is the actual lateral deflection [m]
\(y_{c}\)
\(y_{c} = 2.5 \cdot \epsilon_{50} \cdot D\)
\(\epsilon_{50}\)
is the strain which occurs at onehalf the maximum stress on laboratory undrained compression tests of undisturbed samples. Within OPILE it is referred to as “e50”
For the case where equilibrium has been reached under CYCLIC loading the PY curves may be generated from the following table:
\(X > X_{R}\) 
\(X < X_{R}\) 

\(p/p_{u}\) 
\(y/y_{c}\) 
\(p/p_{u}\) 
\(y/y_{c}\) 
0.00 
0 
0.00 
0 
0.23 
0.1 
0.23 
0.1 
0.33 
0.3 
0.33 
0.3 
0.50 
1.0 
0.50 
1.0 
0.72 
3.0 
0.72 
3.0 
0.72 
infinity 
0.72 \(\frac{X}{X_{R}}\) 
15 
0.72 \(\frac{X}{X_{R}}\) 
infinity 
In addition some account of the recommendation within API for the treatment of stiff clays is made. For stiff clay (c > 96 kPa) which might undergo rapid deterioration under cyclic loadings the ultimate resistance will be reduced to something considerably less than that for soft clays. While stiff clays also have nonlinear stressstrain relationships, they are generally more brittle than soft clays. In developing stressstrain curves and subsequent PY curves for cyclic loads, good judgment should reflect the rapid deterioration of load capacity at large deflections for stiff clays (according to API WSD (2000)). This is accounted for in OPILE by the application of a factor to the ultimate resistance, where the undrained shear strength is above a specified shear strength limit (usually 96kPa):
The “Stiff CLAY API Factor” is applied to the calculated ultimate lateral resistance where the shear strength is above the specified limit. The application of this factor is only made if the STATIC/CYCLIC option is set to CYCLIC. The initial points on the PY curve remain the same, after a larger displacement the ultimate pressure is reduced. The single shear strength value (as recommended by API WSD (2000) implements a cutoff rather than a transition. If stiff clays are to be analysed the use of the Dunnavant method could also be considered.
Specifically for CLAYAPI, the parameter Xr can be manually set by the user. When the tickbox ‘Manually define Xr’ is checked, a text box for defining Xr will appear. When checked, OPILE will overwrite Xr by the user inputted value.
A modification to Yc for large diameter piles, according to Stevens and Audibert (1979) can be performed by ticking the tickbox ‘Modify Y for large diameter piles’. The modification performed in OPILE is:
\[Y_{c} = Y_{c} \cdot \left(12.75 \cdot \frac{0.0254}{D} \right)^{0.5}\]
CLAYREESE¶
Reese et al (1975) developed a PY curve suitable for use in stiff clays. The PY curve has a complex shape and can be applied for static and cyclic loading. For both the static and cyclic curves an initial linear section is defined using an initial stiffness which is assumed to vary linearly with depth, from zero at the surface. The linear section is defined by an initial stiffness gradient k. Typical values for k are shown in the table below:
\(k (kPa/m)\) 
undrained shear strength (kPa) 

50  100 
100  200 
200  400 

static loading 
135 000 
270 000 
540 000 
cyclic loading 
55 000 
110 000 
220 000 
The PY curve for STATIC conditions is then calculated using the following logic:
The PY curve for CYCLIC conditions is then calculated using the following logic:
Where:
\(p_{u}\)
\(\textrm{min} \left(b \cdot (2 \cdot s_{uav} + \sigma'_{v} + 2.83 \cdot s_{uav} \cdot \frac{H}{b}), b \cdot 11 \cdot s_{u}\right)\)
\(s_{u}\)
su is the undrained shear strength at the depth in question
\(s_{uav}\)
is the undrained shear strength averaged from the current depth to the seabed (or to the depth of the layer above with a different lateral method).
\(H\)
is the depth
\(b\)
is the pile diameter
\(\sigma'_{v}\)
is the effective overburden pressure
\(y_{c}\)
\(y_{c} = \epsilon_{50} \cdot b\)
\(y_{p}\)
\(y_{p} = 4.1 \cdot A \cdot y_{c}\)
\(\epsilon_{50}\)
is the strain at one half the maximum undrained shear strength in a triaxial test.
\(A\)
is an empirical adjustment factor determined for STATIC loading: \(\textrm{min} \left(0.05 \cdot (\frac{H}{b})^{2} + 0.29 \cdot \frac{H}{b} + 0.2, 0.6\right)\)
\(A\)
is an empirical adjustment factor determined for CYCLIC loading: \(\textrm{min} \left(0.055 \cdot (\frac{H}{b})^{2} + 0.15 \cdot \frac{H}{b} + 0.2, 0.3\right)\)
DYSON¶
The DYSON py curve method is intended for use in calcareous soils and is described by Dyson & Randolph (2001)
\[p = \gamma' \cdot D \cdot R \cdot \left(\frac{q_{c}}{\gamma' \cdot D} \right)^{n} \cdot \left(\frac{y}{D}\right)^{m}\]
where:
\(p\)
lateral resistance (kPa)
\(R\)
is a constant for curve stiffness ()
\(q_{c}\)
is cone tip resistance at the specified depth in [kPa], which in OPILE is interpolated between cone resistances specified for the top and bottom of a layer.
\(n\)
is a constant
\(m\)
is a constant controlling the amount of curvature in the py relation.
\(\gamma'\)
is the soil submerged unit weight (kN/m3)
\(D\)
is the pile diameter (m).
For a calcareous soil near the Goodwyn A platform Dyson and Randolph (2001) found R to be between 2.56 and 2.84, n=0.72 and m is between 0.52 and 0.64.
WESSELINK¶
Wesselink is a PY curve method which is intended for use in calcareous soils and is described by Wesselink et al (1988). The curve is given by:
\[p = R \cdot \left(\frac{x}{x_{0}}\right)^{N} \cdot \left(\frac{y}{D}\right)^{\gamma}\]
where:
\(R\)
is a control variable for curve stiffness [kPa]
\(N\)
constant controlling the rate of increase in p with depth x
\(\gamma\)
is a constant controlling the amount of curvature in the py relation
\(x_{0}\)
is a constant length taken as 1m, input into a text box
Typical values of the input parameters are shown below:
Reference
Soil test and type
R (kPa)
N
gamma
Wesselink et al (1988)
Bass Strait, Kingfish B centrifuge tests
650
0.7
0.65
Wesselink et al (1988)`
Bass Strait, Halibut centrifuge tests
850
0.7
0.65
Williams et al (1988)
Bass Strait, Kingfish B onshore pit test
500
0.5
0.50
Dyson and Randolph (1997)
North West Shelf, Goodwyn A, centrifuge tests
210 to 270
1.5
0.85
ROCKREESE97¶
The ROCKREESE97 method has been taken from Reese, L. & Van Impe, W.F. (2001). The PY curve has a complex shape and can be applied for static and cyclic loading.
The PY curve is calculated using the following logic:
The ultimate lateral resistance of the rock \(p_{ur}\) in kN/m can be calculated using the following logic:
Where:
\(y\)
is the displacement
\(q_{u}\)
is the compressive strength of the rock
\(x_{r}\)
is the depth below the rock surface
\(B\)
is the pile diameter
\(y_{rm}\)
\(y_{rm} = k_{rm} \cdot B\)
\(k_{rm}\)
is a constant ranging from 0.0005 to 0.00005, for more information see Reese, L. & Van Impe, W.F. (2001)
\(K_{ir}\)
\(K_{ir} = k_{ir} \cdot E_{ir}\)
\(k_{ir}\)
\[\begin{split}k_{ir} = \left\ \begin{array} 1100 + 400 \cdot \frac{x_{r}}{3 . B} & \quad \text{if } 0 < x_{r} < 3B \\ 500 & \quad \text{otherwise } \end{array}\right.\end{split}\]\(E_{ir}\)
is the initial reaction modulus of the rock (user input) in kPa
\(\alpha_{r}\)
is a strength reduction factor
EVANS¶
Evans and Duncan (1982) developed PY curves for c\(phi\) soils for the application of shortterm static loading and for cyclic loading. Similar as the CLAYREESE method, for both the static and cyclic curves an initial linear section is defined using an initial stiffness which is assumed to vary linearly with depth, from zero at the surface. The linear section is defined by an initial stiffness gradient k. Typical values for k are shown in the table below:
\(k (kPa/m)\) 
undrained shear strength (kPa) 

50  100 
100  200 
200  400 

static loading 
135 000 
270 000 
540 000 
cyclic loading 
55 000 
110 000 
220 000 
The PY curve for STATIC and CYCLIC conditions is calculated using the following logic:
Where:
\(p_{u}\)
\(p_{u} = A' \cdot p_{u\phi} + p_{uc}\)
\(A'\)
taken from the figure below
\(p_{u\phi}\)
\[\begin{split}p_{u\phi} = Min \left\ \begin{array} \gamma \gamma \cdot X \left(\frac{K_{0} \cdot x \cdot \tan{(\phi)} \cdot \sin{(\beta)}}{\tan{(\beta  \phi)} \cdot \cos{(\alpha)}} + \frac{\tan{(\beta)}}{\tan{(\beta  \phi)}} \cdot (b + x \cdot \tan{(\beta)} \cdot \tan{(\alpha)}) \cdot K_{0} \cdot x \cdot \tan{(\beta)} * (\tan{(\phi)} \cdot \sin{(\beta)}  \tan{(\alpha)})  K_{A} \cdot b \right) \\ K_{A} \cdot b \cdot \gamma \cdot x \cdot \left(\tan{(\beta)}^{8}1 \right) + K_{0} \cdot b \cdot x \cdot \tan{(\alpha)} \cdot \tan{(\beta)}^{4} \end{array}\right.\end{split}\]\(p_{uc}\)
\[\begin{split}p_{uc} = Min \left\ \begin{array} ( \left(3 + \frac{\gamma'}{c} . x + \frac{J}{b} . x \right) . c . b \\ 9 . c . b \end{array}\right.\end{split}\]\(\alpha\)
\(\frac{\phi}{2}\)
\(\beta\)
\(45 + \alpha\)
\(c\)
is the undrained shear strength at the depth in question (cohesion)
\(\phi\)
is the angle of internal friction
\(x\)
is the depth at which the passive resistance is considered
\(b\)
is the pile diameter
\(\gamma\)
is the unit weight of the soil
\(K_{0}\)
taken as 0.4
\(K_{A}\)
\(K_{A} = tan(45  \frac{\phi}{2})^{2}\)
\(m\)
\(m = \frac{p_{u}  p_{m}}{y_{u}  y_{m}}\)
\(n\)
\(n = \frac{p_{m}}{m \cdot y_{m}}\)
\(C\)
\(C = \frac{p_{m}}{y_{m}^{1/n}}\)
\(y_{k}\)
\(y_{k} = (\frac{C}{k \cdot x})^{\frac{n}{n1}}\)
\(A'\)
is an empirical adjustment factor determined for STATIC loading:
Note
Note that it can occur that \(y_{k} > \frac{b}{60}\), in this case the exponential part of the curve is not present.
FRAGIO¶
Fragio et al (1985) developed a PY curve criterion for weak calcareous claystone. It was developed from pile load tests in calcareous claystone with strengths of between 9 and 36MPa. The response is intended to represent brittle failure near the surface. The initial linear response is influenced by the rock mass stiffness and the peak stress is reached at a displacement yu. The peak stress is given by:
Where:
\(s\)
is the rock mass shear strength [kPa]
Fragio et al (1985) found that by fitting the test data a value of s of 10% (which can be changed by the user in OPILE) of the unconfined compressive strength of the intact rock gave a good match with the measured response. After the initial response the curve remains at pu until y exceeds 3yu where it drops to 0.5pu as shown in the figure below.
The reduction only occurs at the surface where it is expected that a brittle failure may occur, the reduction depth is typically 6 pile diameters below mudline and can be varied in OPILE. At some transition depth the curve takes on the shape of the deep failure curve, with no reduction from the peak stress. A linear interpolation is used between the surface and the transition depth to determine the response at displacements where the reduction takes place.
ABBS¶
The ABBS method was designed for application in soft rock and is described by Abbs (1983). It was developed for carbonate rocks having strengths in the range of 0.5 to 5MPa. The first part of the curve is given by the CLAYREESE method for static loading in stiff clay, up until the end of the second parabolic section (i.e. \(y \leq 6Ayc\)). After that the pressure undergoes a rapid change to the residual pressure given by the SANDAPI method for cyclic loading.
The Abbs (1983) method essentially assumes that the behaviour is elastic up to the peak in the parabolic section. Once this point is passed, interparticle bonding is assumed to be destroyed and the resistance is assumed to be represented by the “residual frictional resistance” curve. The slope of the drop from peak resistance to the residual frictional resistance curve is arbitrary. On first loading the slope would probably be more shallow than shown but as the structures are subject to cyclic loading the acutal slope is not critical. On subsequent load cycles the residual frictional curve is assumed to apply. The fall from the peak to the residual curve is therefore assumed to occur during an additional 10% displacement after the point of peak resistance. This slope is convenient from a computational point of view and represents the most dramatic fall that is anticipated from the more brittle materials encountered in the field.
The PY curve is generated using the following logic:
Where:
\(p_{u}\)
\(p_{u} = \textrm{min} \left( b \cdot (2 \cdot s_{uav} + \sigma'_{v} + 2.83 \cdot s_{uav} \cdot \frac{H}{b}), b \cdot 11 \cdot s_{u} \right)\) in kN/m
\(s_{u}\)
is the undrained shear strength at the depth in question
\(s_{uav}\)
is the undrained shear strength averaged from the current depth to the seabed (or to the depth of the layer above with a different lateral method).
\(H\)
is the depth
\(b\)
is the pile diameter
\(\sigma'{v}\)
is the effective overburden depth
\(y_{c}\)
\(y_{c} = \epsilon_{50} \cdot b\)
\(\epsilon_{50}\)
is the strain at one half the maximum undrained shear strength in a triaxial test
\(A\)
\[\begin{split}A = \left\ \begin{eqnarray} 0.6 & \quad \text{if } \frac{H}{b} \gt 3 \\ \textrm{min} \left(0.05 \cdot \frac{H}{b}^{2} + 0.29 \cdot \frac{H}{b} + 0.2 , 0.6 \right) & \quad \text{if } 0 \gt \frac{H}{b} \geq 3 \\ 0.2 & \quad \text{if } \frac{H}{b} \leq 0 \end{eqnarray}\right.\end{split}\]\(Sand_{A}\)
is a factor to account for CYCLIC loading  taken as 0.9.
\(p_{Sand}\)
is the ultimate pressure (i.e. at large displacements) calculated using the SANDAPI method.
\(Sand_{K}\)
is the subgrade modulus
Caution
Note, it is possible that the SANDAPI method returns a higher residual pressure than that calculated by the CLAYREESE method. This results in an unusual and unlikely looking PY curve. OPILE does not automatically check and warn the used this has hapenned. The user therefore remains responsible for checking the input parameters and the PY curves returned.
Typical curves for the ABBS method are shown below:
NOVELLO99¶
NOVELLO99 is a PY curve method which is intended for use in uncemented/very weakly cemented calcareous sediments and is described by Novello (1999).
The STATIC curve is given by:
Where:
\(D\)
is the outer diameter (m)
\(\sigma'_{v}\)
is the effective overburden pressure (kPa)
\(q_{c}\)
is the cone tip resistance (kPa)
\(P_{limit}\)
is the limiting plastic stress
The CYCLIC curve is given by:
Where:
\(U^{*}\)
is the excess pore pressure coefficient
The excess pore pressure coefficient is calculated according to Dobry (1988):
Where:
\(N\)
is the number of cycles
\(\gamma_{c}\)
cyclic shear strain []
\(g(\gamma_{c})\)
\[\begin{split}g(\gamma_{c}) = \left\ \begin{eqnarray} \textrm{Exp}(5.47  \frac{2.08}{\gamma_{c} \cdot 100 + 0.11}) & \quad \text{if } \gamma_{c} \gt 0.01\% \\ 0 & \quad \text{otherwise } \end{eqnarray}\right.\end{split}\]
KALLEHAVE¶
The KALLEHAVE method is presented in Kallehave et. al. (2012) for application on large diameter piles for offshore wind turbines in sand, where the API recommendations for sand resulted in underprediction of soil stiffness. The method is based on the API RP2GEO sand method presented in API RP2GEO (2011), but uses a modification on the subgrade reaction modulus \((k*z)\):
Where:
\(k\)
subgrade reaction modulus (Sand K) [kPa/m]
\(z_{0}\)
Reference depth = 2.5 [m]
\(D_{0}\)
Reference diameter = 0.61 [m]
\(m\)
0.6
Sorensen¶
The SORENSEN method is based on Sorensen et. al. (2010) and provides py curves for monopile foundations with diameters of 4m to 6m in sand. The method uses a similar approach as KALLEHAVE and is calibrated for dense sand with friction angle 40 degrees.
The SORENSEN method is based on the API RP2GEO sand method presented in API RP2GEO (2011), but uses a modification on the SAND subgrade reaction modulus \((k*z)\):
Where:
\(\phi_{d}\)
Friction angle (deg)
\(z_{ref}\)
Reference depth = 1.0 [m]
\(D_{ref}\)
Reference diameter = 1.0 [m]
The parameters a, b, c and d are defined in Table 1 of Sorensen et. al. (2010):
a
b
c
d
[kN/m^2]
[]
[]
[]
50 000
0.6
0.5
3.6
CLAY JEANJEAN¶
The CLAYJEANJEAN method is based on Jeanjean (2009) and provides py curves for soft clays subjected to cyclic loads. The PY curves were derived from Finite Element Analysis of cyclic loaded conductors and are defined by the following equation:
Where:
\(p\)
Soil resistance [kPa]
\(p_{max}\)
Maximum soil resistance [kPa]
\(G_{max}\)
Maximum shear modulus [kPa] defined with parameters A [kPa] and B [] from soil input table
\(z_{0}\)
Depth reference for Gmax [m]
\(N_{p0}\)
Lateral soil resistance factor []
\(N_{pd}\)
Lateral depth dependent soil resistance factor []
\(f_{Su}\)
Clay maximum stiffness to strength ratio []
\(s_{u}\)
Undrained shear strength [kPa]
\(D\)
Pile diameter [m]
\(\xi\)
empirical factor []
The depth reference \(z_{0}\) for the maximum shear modulus can be overwritten by checking the “z0 for Gmax” checbox in the Lateral Soil tab:
The factor \(\xi\) is defined as:
where:
\(\lambda\)
\(\frac{s_{u0}}{s_{u1} \cdot D}\)
\(s_{u0}\)
Shear strength intercept at top of layer [kPa]
\(s_{u1}\)
Rate of increase of shear strength with depth [kPa/m]
The rate of increase of shear strength with depth is defined as:
The parameters \(N_{p0}\), \(N_{pd}\), \(f_{Su}\) and \(d\) are defined in Jeanjean (2009):
\(N_{p0}\)
\(N_{pd}\)
\(f_{Su}\)
[kN/m^2]
[]
[]
12
4
100
CLAYJJ2017¶
The CLAYJJ2017 method is based on Jeanjean et al. (2017). In this approach a normalised PY curve is derived either from site specific DSS stressstrain curves or, in the absence thereof, on the tabulated normalised curves as repeated below. The tabulated values are based on database of DSS test results as evaluted by Jeanjean. OPILE only implements the tabulated normalised PY curves.
\(s_{u} \leq 100kPa\) 
\(s_{u} > 100kPa\) 

\(\frac{p}{p_{u}}\) 
\(\frac{y}{D}\) 
\(\frac{y}{D}\) 
0 
0 
0 
0.05 
0.0003 
0.0004 
0.2 
0.003 
0.0035 
0.3 
0.0053 
0.007 
0.4 
0.009 
0.0125 
0.5 
0.0145 
0.02 
0.6 
0.022 
0.03 
0.7 
0.032 
0.045 
0.8 
0.05 
0.07 
0.9 
0.082 
0.114 
0.975 
0.15 
0.16 
1.0 
0.25 
0.25 
The tabulated normalised PY curves are then denoramlised into a py curve for a given pile diameter, \(D\), and with a value of the ultimate lateral pressure, \(p_{u}\), calculated as:
\[P_{u} = N_{p} \cdot s_{u}\]
Where:
\(N_{p0}\)
\(N_{1}  (1  \alpha)  (N_{1}  N_{2}) \left[1 \left(\frac{z}{dD} \right)^{0.6} \right]^{1.35} \leq N_{pd}\)
\(N_{1}\)
12
\(N_{2}\)
3.22
\(d\)
\(16.8  2.3 \textrm{log_{10}}(\lambda) \geq 14.5\)
\(\lambda\)
\(s_{u0} / (s_{u1}D)\)
\(s_{u}\)
\(s_{u0}+s_{u1}z\) , as determined in DSS testing
\(N_{pd}\)
9 + 3 \(\alpha\)
\(\alpha\)
the soil pile adhesion factor
For gapping conditions, the value of \(N_{p0}\) in the shallow wedge is multiplied by the correction factor \(C\) to account for strength anisotropy.
\[C = 1 + \left(\frac{s_{uTE}}{s_{uDSS}}1\right) \left(\frac{N_{pd}N_{p}}{N_{pd}N_{pz=0}} \right)\]
where \(N_{pz=0}\) is the value of \(N_{p}\) at ground level (z=0). The ratio \(\frac{s_{uTE}}{s_{uDSS}}\) is, in OPILE, taken by default as 0.9, but can be specified by the user. For non gapping conditions, the value of \(p_{u}\) is not modified.
Custom lateral methods¶
The custom lateral methods “CUST_PY” numbers 1 to 3 which are available under the lateral soil input allow the generation of custom PY curve shapes. The custom curves are used in conjunction with the limiting lateral pressure Plim and the Yc normalisation parameter for the lateral displacement. The custom py curves are thus defined normalised in terms of P/Pult (a noramlised lateral pressure) and Y/Yc (a normalised lateral displacement). Both normalisation factors, Yc and Pult, are defined on the lateral soil input.
The normalised PY curves can be defined on the Custom Input tab under the Custom Response Curves tab. The table to be completed will be highlighted yellow as soon as a custom PY curve method is selected on the Lateral Soil input.