Helper Functions

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pcf psf ft / :

Helper Functions

z# γ.e# γ.b# K# K.c# c# ELF.min# q.sur# z.exc# fFHAbove t# 1 time : Determine soil forces for each soil layer below the dredge line F.hsi# 01 matrix : F.hqi# 01 matrix : Depth to force resultant for soil and for surcharge from dredge line y.s# 01 matrix : y.q# 01 matrix : 61 line n 1 z# rows range z# n el z.exc# < y.1# z# n el : y.2# z# n 1 + el : d.s# y.2# y.1# - : P.h1# y.1# γ.e# n el * K# n el * K.c# n el c# n el * - 0.1 psf * ELF.min# y.1# * Max eval : P.h2# y.2# γ.e# n el * K# n el * K.c# n el c# n el * - 0.1 psf * ELF.min# y.1# * Max eval : F.temp# P.h1# P.h2# + (d.s# 2 / * : F.hsi# F.hsi# F.temp# stack eval : Distance to force from dredge line y.temp# z.exc# d.s# 2 P.h2# * P.h1# + (* 3 P.h2# P.h1# + (* / y.1# + (- eval : y.s# y.s# y.temp# stack eval : Find Equivalent ka considering cohesion. Use base soil weights (not submerged) P.h1# y.1# γ.b# n el * K# n el * K.c# n el c# n el * - 0.1 psf * ELF.min# y.1# * Max eval : P.h2# y.2# γ.b# n el * K# n el * K.c# n el c# n el * - 0.1 psf * ELF.min# y.1# * Max eval : F.heq# P.h1# P.h2# + (d.s# 2 / * : K.qeq 2 F.heq# * γ.b# n el d.s# 2^* / eval : F.temp# q.sur# K.qeq * d.s# * eval : F.hqi# F.hqi# F.temp# stack eval : Distance to force from dredge line y.temp# z.exc# d.s# 2 P.h2# * P.h1# + (* 3 P.h2# P.h1# + (* / y.1# + (- eval : y.q# y.q# y.temp# stack eval : 201 line 011 line if 11 line for F.hsi# F.hqi# y.s# y.q# 1 time t# - 51 sys 41 line :

z# γ.e# γ.b# K# K.c# c# ELF.min# q.sur# z.exc# fFHbelow t# 1 time : Determine soil forces for each soil layer below the dredge line F.hsi# 01 matrix : F.hqi# 01 matrix : Depth to force resultant for soil and for surcharge from dredge line y.s# 01 matrix : y.q# 01 matrix : 61 line n 1 z# rows range z# n el z.exc# ≥ (z# n el H.tot# < (& y.1# z# n el : y.2# z# n 1 + el : d.s# y.2# y.1# - : P.h1# y.1# γ.e# n el * K# n el * K.c# n el c# n el * - 0 psf * ELF.min# y.1# * Max eval : P.h2# y.2# γ.e# n el * K# n el * K.c# n el c# n el * - 0 psf * ELF.min# y.1# * Max eval : F.temp# P.h1# P.h2# + (d.s# 2 / * : F.hsi# F.hsi# F.temp# stack eval : Distance to force from dredge line y.temp# d.s# 2 P.h2# * P.h1# + (* 3 P.h2# P.h1# + (* / y.1# z.exc# - (+ : y.s# y.s# y.temp# stack eval : Find Equivalent ka considering cohesion. Use base soil weights (not submerged) P.h1# y.1# γ.b# n el * K# n el * K.c# n el c# n el * - 0 psf * ELF.min# y.1# * Max eval : P.h2# y.2# γ.b# n el * K# n el * K.c# n el c# n el * - 0 psf * ELF.min# y.1# * Max eval : F.heq# P.h1# P.h2# + (d.s# 2 / * : K.qeq 2 F.heq# * γ.b# n el d.s# 2^* / eval : F.temp# q.sur# K.qeq * d.s# * eval : F.hqi# F.hqi# F.temp# stack eval : Distance to force from dredge line y.temp# d.s# 2 P.h2# * P.h1# + (* 3 P.h2# P.h1# + (* / y.1# z.exc# - (+ : y.q# y.q# y.temp# stack eval : 201 line 011 line if 11 line for F.hsi# F.hqi# y.s# y.q# 1 time t# - 51 sys 41 line :

M.soil# z.find# fSS# This finds the soil stratum that z.find lands in Set initial value as the deepest layer soil.row# M.soil# M.soil# rows row eval : soil.row# 11 el z.find# : n 2 M.soil# rows range z.soil# M.soil# n 1 el : z.soil# z.find# ≤ continue soil.row# M.soil# n 1 - row eval : soil.row# 11 el z.find# : break 31 line if 21 line for soil.row# 61 line :

MK'.a# d.wata# d.watp# h.exc# H.tot# fSoilGeom Redfine MK.a#, with no text MK.a# 06 matrix : n 2 MK'.a# rows range temp_row# MK'.a# n row : MK.a# MK.a# temp_row# stack eval : 21 line for 31 line Find the soil stratum for water elevations and dredge line Place holder for fSS() Water on Active side Soil 1 el MK.a# d.wata# fSS# : Water on Passive side Soil 2 el MK.a# d.watp# fSS# : At dredge line Soil 3 el MK.a# h.exc# fSS# : At bottom of pile Soil 4 el MK.a# H.tot# fSS# : n 1 Soil rows range MK.a# MK.a# Soil n el stack eval : 11 line for 111 line Delete repeated elevations and sort MKsort# MK.a# 1 csort : MSP# 06 matrix : MSP# MKsort# 1 row eval : n 2 MKsort# rows range MKsort# n 1 el MKsort# n 1 - 1 el ≠ k k 1 + : M.row# MKsort# n row : MSP# MSP# M.row# stack eval : 31 line continue if 11 line for MSP# MSP# 1 csort : 61 line MSP# 11 sys 41 line :

h.exc# ω# β'.a# β'.p# X.βa# X.βp# h.effβa# h.effβp# K.toe# fKsoils Determine Active Force for each Soil stratum n 1 z# rows range β# β'.a# X.βa# β'.a# tan * 2 h.effβa# * / atan Min eval : If the backslope is steeper than the friction angle use equivlement surcharge method β# ϕ# n el ≥ K.s# n el 145 deg * ϕ# n el 2 / - tan 1 β# tan / / + : β# 0 deg * : 21 line K.s# n el 1 : if K.ai# n 1 el ϕ# n el ω# + cos (2^ω# cos (2^ω# δ# n el - cos * 1 ϕ# n el δ# n el + sin ϕ# n el β# - sin * ω# δ# n el - cos ω# β# + cos * / sqrt + (2^* / K.s# n el * eval : K.ahi# n 1 el K.ai# n 1 el δ# n el ω# - cos * eval : K.ahci# n 1 el 2 K.ahi# n 1 el sqrt * eval : 61 line for Determine Passive Pressure coeff for each soil stratum n 1 z# rows range X.βp# K.toe# h.effβp# * < β# X.βp# β'.p# tan * 2 h.effβp# * / atan eval : β# β'.p# : if If the backslope is steeper than the friction angle use equivlement surcharge method β# ϕ# n el ≥ K.sp# n el 1 β# tan / 1 β# n el tan / 45 deg * ϕ# n el 2 / + tan + / eval : β# 0 deg * : 21 line K.sp# n el 1 : if ω.p# 1 ω# * - : K.pi# n 1 el ϕ# n el ω.p# - cos (2^ω.p# cos (2^ω.p# δ# n el + cos * 1 ϕ# n el δ# n el + sin ϕ# n el β# + sin * ω.p# δ# n el + cos ω.p# β# + cos * / sqrt - (2^* / K.sp# n el * eval : K.phi# n 1 el K.pi# n el δ# n el ω.p# - cos * eval : K.phci# n 1 el 2 K.phi# n 1 el sqrt * eval : 71 line for K.ai# K.ahi# K.ahci# K.pi# K.phi# K.phci# 61 sys 51 line :

F.H# H.T# z.anc# F.Hq# fFHWATrib1 Tributary Method for Single Anchor, refer to FHWA Cir 4 Fig 39 Distance from top of sheeting to top anchor H.anc# 1 el z.anc# 1 el : Destance from top anchor to dredge line H.anc# 2 el H.T# H.anc# 1 el - : Maximum soil pressure p# F.H# 23 / H.T# * / : Maximum surcharge pressure (use average) pq# F.Hq# H.T# / : M.B# 1354 / H.anc# 1 el (2^* p# * pq# H.anc# 1 el (2^* 2 / + : T is returned as Matrix T# 1 el 23 H.T# (2^* 10 H.T# * H.anc# 1 el * - 54 H.anc# 2 el * / p# * H.anc# 1 el H.anc# 2 el 2 / (+ (pq# * + eval : Reaction at dredge line R# 23 / H.T# * p# * H.T# pq# * + (T# 1 el - eval : Point of zero shear (approx) x.zs# 19 / 26 H.T# (2^* 52 H.T# * H.anc# 1 el * - sqrt * H.anc# 2 el 2 / 1 H.anc# 1 el (2^H.anc# 2 el (2^/ - (* + 2 / eval : Moment between top anchor and dredge line M.BC# R# x.zs# * p# x.zs# 3^* 4 H.anc# 2 el * / - pq# x.zs# * 2 H.anc# 2 el * / H.anc# 2 el (2^H.anc# 1 el (2^- x.zs# H.anc# 2 el * - (* + eval : M.BC# trace M.max# M.B# M.BC# Max eval : T# R# M.max# p# pq# 51 sys 211 line :

F.H# H.T# z.anc# F.Hq# fFHWATribM Triburtary Method for multiple anchors, refer to FHWA Cir 4 Fig 39 H# is entered as column matrix Top anchor and bending moment nr# z.anc# rows : Establish height between anchors H.anc# 1 el z.anc# 1 el 0 ft * - : n 2 z.anc# rows range H.anc# n el z.anc# n el z.anc# n 1 - el - : 11 line for H.anc# nr# 1 + el H.T# z.anc# nr# el - : 41 line Max soil pressure p# F.H# H.T# 13 / H.anc# 1 el * - 13 / H.anc# nr# el * - / eval : Maximum surcharge pressure (use average) pq# F.Hq# H.T# / : 41 line Top Anchor T# 1 el 23 / H.anc# 1 el * 12 / H.anc# 2 el * + (p# * H.anc# 1 el H.anc# 2 el 2 / (+ (pq# * + eval : 21 line Bottom Anchor T# nr# el H.anc# nr# 1 - el 2 / 2348 / H.anc# nr# el * + (p# * H.anc# nr# 1 - el 2 / H.anc# nr# el 2 / + (pq# * + eval : 21 line Middle Anchors nr# 2 > n 2 nr# 1 - range T# n el H.anc# n el 2 / H.anc# n 1 + el 2 / + (p# * H.anc# n el 2 / H.anc# n 1 + el 2 / + (pq# * + eval : 11 line for 11 line 0 if 21 line Reaction at dredge line R# 316 / H.anc# nr# el * p# * 12 / H.anc# nr# el * p# * + : 21 line Maximum bending moment above dredge line At top anchor M.maxi# 1 el 1354 / H.anc# 1 el (2^* p# * pq# H.anc# 1 el (2^* 2 / + eval : Other locations n 2 H.anc# rows range M.maxi# n el p# H.anc# n el (2^* 10 / pq# H.anc# n el (2^* 10 / + eval : 11 line for M.max# M.maxi# Max eval : 61 line T# R# M.max# p# pq# 51 sys 121 line :

Main Function

MK.a# d.wata# d.watp# h.exc# H.tot# ω# β'.a# β'.p# X.βa# X.βp# h.effβa# h.effβp# K.toe# ELF.min# q.sur# LF.s# LF.q# d.brc# fER Description place holder Res# MK.a# d.wata# d.watp# h.exc# H.tot# fSoilGeom : z# Res# 1 col eval : ϕ# Res# 2 col eval : c# Res# 3 col eval : δ# Res# 4 col eval : γ.b# Res# 5 col eval : γ'.b# Res# 6 col eval : 81 line Create soil matrix for active and passive depending on water elevation n 1 z# rows range z# n 1 el d.wata# ≤ γ.a# n 1 el γ.b# n el : 11 line γ.a# n 1 el γ'.b# n el : 11 line if z# n 1 el d.watp# ≤ γ.p# n 1 el γ.b# n el : 11 line γ.p# n 1 el γ'.b# n el : 11 line if 21 line for 21 line Find active and passive coeff Res# h.exc# ω# β'.a# β'.p# X.βa# X.βp# h.effβa# h.effβp# K.toe# fKsoils : K.ai# Res# 1 el : K.ahi# Res# 2 el : K.ahci# Res# 3 el : K.pi# Res# 4 el : K.phi# Res# 5 el : K.phci# Res# 6 el : 81 line Determine soil forces for each soil layer above the dredge line Res# z# γ.a# γ.b# K.ahi# K.ahci# c# ELF.min# q.sur# h.exc# fFHAbove : F.hsai# Res# 1 el : F.hqai# Res# 2 el : y.sa# Res# 3 el : y.qa# Res# 4 el : Total Active Soil Pressure F.htots# F.hsai# sum eval : F.Hs# LF.s# F.htots# * : Total Surcharge Pressure F.htotq# F.hqai# sum eval : F.Hq# LF.q# F.htotq# * : 121 line Choose which to use - single or Multiple d.brc# rows 1 ≡ Res# F.Hs# h.exc# d.brc# F.Hq# fFHWATrib1 : 11 line Res# F.Hs# h.exc# d.brc# F.Hq# fFHWATribM : 11 line if T# Res# 1 el : R# Res# 2 el : M.max# Res# 3 el : p.s# Res# 4 el : p.q# Res# 5 el : 71 line Must update to include water ******************* Define a function to determine soil and surcharge forces below the dredge line Place holder for fFHBelow() function Find active soil forces and surcharge Res# z# γ.a# γ.b# K.ahi# K.ahci# c# ELF.min# q.sur# h.exc# fFHbelow : F.hsbi# Res# 1 el : F.hqbi# Res# 2 el : y.sb# Res# 3 el : y.qb# Res# 4 el : Find Passive forces (no surcharge) Res# z# γ.p# γ.b# K.phi# K.phci# c# 0 psf * 0 psf * h.exc# fFHbelow : F.hsbpi# Res# 1 el : F.hqbpi# Res# 2 el : y.sbp# Res# 3 el : y.qbp# Res# 4 el : 121 line 41 line Factor Of Safety at Toe F.htoe# F.hsbi# F.hqbi# sum + R# + sum : F.Rtoe# F.hsbpi# sum : FS.toe# F.Rtoe# F.htoe# / : 41 line Output FS.toe# M.max# p.s# p.q# T# R# K.ahi# K.ahci# K.phi# K.phci# F.hsai# F.hqai# F.htots# F.htotq# F.htoe# F.Rtoe# z# y.sa# y.qa# F.Hs# F.Hq# 211 sys 91 line :

Geometry Parameters

Height of Excavation

h.exc 45 ft * :

Depth of Embedment

d.emb 5 ft * :

H.tot h.exc d.emb + : ft 50

Depth to Water - active

d.wata h.exc : ft 45

Depth to water - passive

d.watp h.exc : ft 45

Wall batter (from vertical)

ω 0 deg * :

Backslope

β'.a 15 deg * :

Distance to broken back slope

X.βa 5 ft * :

Height of wall influenced by slope

h.effβa H.tot : ft 50

Toeslope

β'.p 0 deg * - :

Distance to broken back slope

X.βp 10 ft * :

Height of wall influenced by slope

h.effβp d.emb : ft 5

Factor of height to distance where slope is considered infinite

K.toe 1.5 :

Factor to increase total active soils pressure to trasnform to apparent pressure diagram

LF.s 1.3 :

Factor to increase total active surcharge pressure to trasnform to uniform load

LF.q 1.05 :

Enter Soils info, use H.tot for bottom soil MK.a d ϕ c δ γ γ' 0 ft * 28 deg * 1000 psf * 5 deg * 120 pcf * 65 pcf * 24 ft * 28 deg * 0 psf * 10 deg * 120 pcf * 65 pcf * 35 ft * 32 deg * 0 psf * 20 deg * 130 pcf * 70 pcf * 48 ft * 28 deg * 1000 psf * 0 deg * 130 pcf * 65 pcf * 56 mat :

Soil Parameters

Surcharge

Enter soil strata's in Matrix

q.sur 250 psf * :

Toe Factor of Safety

FS.rtoe 1.5 :

FHWA uses 1.5

Unit weight of water

γ.wat 62.4 psf ft / * :

Minimum EFP (when cohesion is negative)

ELF.min 5 psf ft / * :

Sheeting Info

Depth to Braces

d.brc 10 ft * 11 mat :

Name / Section Mod, MoI, Fy

PZ - 27

S.x 31 in 3^* :

I.x 187.5 in 4^* :

F.y 50 ksi * :

E 29000 ksi * :

Modulus of Elasticity

Allowable Bending Stress /

F.b F.y 0.65 * : ksi 32.5

M.csht S.x F.b * : kip ft * 83.9583

Moment capacity

FBE MK.a d.wata d.watp h.exc H.tot ω β'.a β'.p X.βa X.βp h.effβa h.effβp K.toe ELF.min q.sur LF.s LF.q d.brc fER :

FS.toe FBE 1 el : 2.4719

F.ptot FBE 15 el : kip ft / 51.9172

FS of embedment

w.wal FBE 5 el : kip ft / 32.0182 11 mat

Line load on wales

Moment on sheeting

M.rwall FBE 2 el : kip ft * ft / 214.0205

Max pressure (soil and surcharge no water)

p.a FBE 4 el : psf 235.7791

R.bs FBE 6 el : kip ft / 13.0017

Reaction at base of EXC

K.ah FBE 7 el : 0.3464 0.3309 0.2612 0.2612 0.364 0.364 61 mat

K.ph FBE 9 el : 3.2027 3.7125 6.4708 6.4708 2.7698 2.7698 61 mat

Active/passive pressure coefficents

K.ach FBE 8 el : 1.1771 1.1505 1.0221 1.0221 1.2066 1.2066 61 mat

Active/passive pressure coefficents for Cohesion

K.pch FBE 10 el : 3.5792 3.8536 5.0876 5.0876 3.3286 3.3286 61 mat

F.ai FBE 11 el : kip ft / 0.0024 12.8859 13.5808 31 mat

Soil forces from classical earth pressure diagram (above dredge line)

Y.sa FBE 18 el : ft 33 15.1582 4.7917 31 mat

Surcharge forces from classical earth pressure diagram (above dredge line)

F.qi FBE 12 el : kip ft / 0.0004 4.881 5.2234 31 mat

Y.qa FBE 19 el : ft 33 15.1582 4.7917 31 mat

Total froce from classical earth pressure diagram

F.atot FBE 13 el : kip ft / 26.4691

F.qtot FBE 14 el : kip ft / 10.1048

F.app FBE 20 el : kip ft / 34.4098

F.qapp FBE 21 el : kip ft / 10.6101

Total Used for Apparent Press