CELE Geotechnical Engineering — Shear Strength of SoilsStudy Notes

The shear strength of soil is most commonly described by the Mohr-Coulomb failure criterion, which states that soil fails in shear when the shear stress on any plane reaches a critical value that depends linearly on the normal stress acting on that plane. **Mohr-Coulomb Equation (Total Stress Form):** τf = c + σ tan φ where: • τf = shear strength (shear stress at failure) in kPa • c = cohesion in kPa (the shear strength intercept when normal stress is zero) • σ = normal stress on the failure plane in kPa • φ = angle of internal friction in degrees (the slope of the failure envelope) **Mohr-Coulomb Equation (Effective Stress Form):** τf = c' + σ' tan φ' where: • c' = effective cohesion in kPa • σ' = effective normal stress on the failure plane in kPa (σ' = σ − u, where u is pore water pressure) • φ' = angle of internal friction (effective stress basis) in degrees The distinction between total stress and effective stress forms is crucial. For **drained conditions** (where pore pressures have dissipated), use the effective stress form with c' and φ'. For **undrained conditions** (rapid loading with no drainage), use the total stress form with c and φ, where φ ≈ 0 for saturated clay. **Physical Interpretation:** • The angle φ represents frictional resistance. Higher φ means particles interlock better and slide less easily. Typical ranges: sand φ = 30–45°, clay φ = 15–30°, silt φ = 20–35°. • Cohesion c represents bonding and attraction between particles. Pure sand has c ≈ 0 (frictional soil); dry clay has c > 0 due to capillary suction; normally consolidated saturated clay has c' ≈ 0 (frictional behavior governs the effective stress). • The Mohr-Coulomb envelope is the locus of all failure points plotted on a Mohr stress circle diagram (τ vs σ). **Relationship Between Principal Stresses and Mohr-Coulomb Parameters:** At failure, the relationship between the major principal stress σ1 (axial stress) and minor principal stress σ3 (confining pressure) can be derived from the Mohr circle and Coulomb criterion: For cohesionless soil (c = 0): sin φ = (σ1 − σ3) / (σ1 + σ3) For soil with cohesion: σ1 = σ3 tan²(45° + φ/2) + 2c tan(45° + φ/2) These relationships are essential for triaxial test interpretation and PRC exam problem-solving.

Three primary laboratory tests are used to determine shear strength parameters and to understand soil behavior under different drainage conditions. Each test has specific advantages and limitations, and the choice of test depends on the type of analysis required (short-term vs. long-term) and the soil type. **2.1 Direct Shear Test (DST)** The direct shear test is one of the oldest and simplest methods for determining shear strength. A soil sample is placed in a square or rectangular box (typically 60 mm × 60 mm or 100 mm × 100 mm), which is split horizontally into two halves. A vertical (normal) load is applied, and the upper half is then sheared horizontally at a constant rate of displacement while the lower half is held fixed. Procedure: 1. Place soil sample in shear box 2. Apply vertical normal load (constant throughout test) 3. Apply horizontal shear force and record displacement until failure 4. Repeat test at different normal loads (typically 3–5 different loads per soil sample) 5. Plot shear stress (τ = V/A, where V is shear force and A is box area) vs. normal stress (σ = P/A, where P is normal load) 6. Draw best-fit line through data points; intercept = c, slope = tan φ Advantages: • Simple, economical, portable • Can test unsaturated soils easily • Provides direct measurement of failure parameters • Can measure residual shear strength (long-term friction after large displacement) Limitations: • Failure is forced to occur on a predetermined horizontal plane (not necessarily the weakest plane) • Difficulty controlling drainage (partially drained conditions may occur unintentionally) • Limited stress levels achievable • Large soil samples required for coarse-grained soils • Results can vary with shear box stiffness and operator technique **2.2 Triaxial Compression Test (TCT)** The triaxial test is the most versatile and widely used laboratory method. A cylindrical soil sample (typically 50 mm diameter × 100 mm height) is enclosed in a rubber membrane and placed inside a pressure chamber (triaxial cell). The sample experiences three principal stresses: the confining pressure σ3 (same in all horizontal directions) and the axial stress σ1 (vertical). The axial stress is increased until the sample fails. **Three Types of Triaxial Tests (Drainage Conditions):** **a) Unconsolidated-Undrained (UU) Test:** • Confining pressure applied, then axial load applied without allowing drainage • Pore pressures develop but are not measured • Represents rapid construction or sudden loading (e.g., clay immediately after excavation) • For saturated clay, failure occurs at constant volume with φ ≈ 0 and constant c_u (undrained cohesion) • Results in total stress parameters: c_u and φ_u (typically φ_u ≈ 0 for saturated clay, so c_u is the main parameter) • Controls **short-term stability** of clay structures **b) Consolidated-Undrained (CU) Test:** • Confining pressure applied and allowed to consolidate fully (drainage allowed) • Then axial load applied without drainage (pore pressures develop and are typically measured with a pore pressure transducer) • Represents intermediate time periods; combines consolidation effects with undrained loading • Yields both total stress parameters and effective stress parameters • The pore pressure parameter A and B are measured: Δu = B[Δσ3 + A(Δσ1 − Δσ3)] • More realistic for many field conditions in the Philippines (e.g., embankments partially consolidating during construction) **c) Consolidated-Drained (CD) Test:** • Confining pressure applied and allowed to consolidate • Axial load applied very slowly (or drained) to allow pore pressures to remain zero (or dissipate as they form) • Shearing is at an extremely slow rate to maintain drained conditions • Yields effective stress parameters: c' and φ' (long-term values) • Controls **long-term stability** after all consolidation has occurred • Most appropriate for granular soils (sand, gravel) which drain readily **Triaxial Test Interpretation:** • Plot stress-strain curve (deviatoric stress q = (σ1 − σ3)/2 vs. strain ε) to observe peak and residual strengths • Plot Mohr circles at failure for different confining pressures • Fit Mohr-Coulomb envelope to determine c and φ Advantages of Triaxial Test: • Precise control of drainage conditions • Can apply three different principal stresses (more realistic stress state than direct shear) • Can measure pore pressures (CU test) • Wide range of stress levels achievable • Applicable to all soil types • Provides stress-strain relationship and modulus information Limitations: • More complex and expensive than direct shear • Time-consuming, especially for CD tests on low-permeability clays (can take weeks) • Requires skilled technician and good equipment • Potential for membrane penetration by coarse particles **2.3 Unconfined Compression (UC) Test** The unconfined compression test is a special case of the UU triaxial test where the confining pressure σ3 = 0. A cylindrical clay sample is placed vertically in a testing machine, and an axial load is applied at constant strain rate until failure occurs. Only one principal stress (σ1) is applied; the lateral stress is atmospheric (zero gauge pressure). Test Procedure: 1. Trim clay sample to cylinder (typically 38 mm diameter × 76 mm height) 2. Place sample in UC apparatus 3. Apply vertical compressive load at constant strain rate (~1%/min) 4. Record load and displacement 5. Plot stress-strain curve 6. Identify peak stress as unconfined compressive strength qu **Critical Relationship for UC Test:** For a saturated clay under undrained conditions (φ_u ≈ 0): c_u = qu / 2 where: • c_u = undrained shear strength in kPa • qu = unconfined compressive strength in kPa (the peak axial stress) This relationship comes from the Mohr-Coulomb criterion. At failure with σ3 = 0 and φ = 0: τf = c_u = (σ1 − 0) / 2 = σ1 / 2 = qu / 2 **Example UC Calculation:** If a clay sample fails at qu = 120 kPa, then: c_u = 120 / 2 = 60 kPa (undrained shear strength) Advantages of UC Test: • Very rapid and economical • No confining pressure cell needed (simple apparatus) • Excellent for routine quality control and site investigation • Gives immediate estimate of bearing capacity for foundation design Limitations: • Only applicable to cohesive soils that can stand unsupported • Cannot be performed on sands or very soft clays • Only gives undrained strength (short-term parameter) • Does not provide friction angle directly • Lateral strain uncontrolled (may differ from field conditions) • Less reliable for very sensitive clays **Applicability Summary for Philippine Projects:** • **UC Test**: Rapid site assessment for clay deposits during initial investigation (common in Metro Manila Quaternary clays) • **UU Test**: Short-term stability analysis for new clay embankments, cuts, and excavations • **CU Test**: Intermediate-term analysis during construction of dams, embankments (especially in rainy season) • **CD Test**: Long-term slope stability, foundation design after consolidation is complete

One of the most critical concepts in geotechnical engineering is understanding when soil behaves in a drained manner versus an undrained manner. This distinction directly affects whether you use effective stress parameters (c', φ') or total stress parameters (c_u, φ_u) in design calculations. The time frame for the applied load is the controlling factor. **3.1 Undrained Behavior (Short-Term, Rapid Loading)** Undrained conditions occur when stress is applied to saturated soil faster than water can drain from the soil pores. Water is incompressible, so excess pore pressures develop (positive pore pressure greater than hydrostatic pressure). These excess pore pressures reduce the effective stress and shear strength. **When Undrained Conditions Occur:** • Immediate response of clay to construction loading (day 1 of excavation, immediately after filling) • Sudden live loads or impact loads (train loads, seismic shaking, pile driving) • Soils with very low permeability (intact clay with k < 10⁻⁷ cm/s) • Fast construction: embankment filling in one season, rapid excavation **Undrained Behavior Characteristics for Saturated Clay:** • Pore pressure ratio R_u = Δu / Δσ3 is high (often 0.5–1.0) • Pore pressures developed: Δu ≈ Δσ3 (approximately equal to the change in confining pressure) • Shear strength is nearly constant regardless of confining pressure (φ_u ≈ 0) • Shear strength is characterized by a single parameter: c_u (undrained cohesion) • Volume remains approximately constant (saturated clay is incompressible in the short term) • Mohr-Coulomb failure envelope is horizontal (φ = 0), and c = c_u **Undrained Shear Strength Parameter c_u:** For saturated clay under undrained loading: • c_u is measured from UU triaxial test, CU triaxial test, or UC (unconfined compression) test • c_u = qu / 2 (from UC test, simplest field method) • Typical values for Philippine clays: 25–150 kPa (depending on depth and consolidation history) • c_u increases with depth due to overburden pressure and consolidation • c_u is higher in preconsolidated clays than in normally consolidated clays at the same depth **Design Applications (Undrained, Short-Term):** • Bearing capacity of foundations on clay (immediate settlement, first few days) • Stability of clay slopes immediately after excavation • Stability of excavations and cuts in soft clay • Lateral pressure on retaining walls during construction • Undrained design uses: τ = c_u, bearing capacity factor Nc ≈ 5.14 (for φ = 0) **3.2 Drained Behavior (Long-Term, Slow or Completed Drainage)** Drained conditions occur when stress is applied slowly enough that pore pressures dissipate, or when sufficient time has passed for water to drain completely from the soil. Excess pore pressures return to hydrostatic values (u = γw × h, where h is depth), and effective stress increases as pore pressure decreases. **When Drained Conditions Occur:** • Long-term response of clay (weeks, months, years after loading) • After initial consolidation is complete (typically estimated by Tv = 0.5 with 50% consolidation) • Granular soils (sand, gravel) almost always behave in a drained manner because of high permeability • Slow loading rates in low-permeability soils • Steady-state seepage conditions (groundwater flow has stabilized) **Drained Behavior Characteristics:** • Pore pressures dissipate to hydrostatic values • Effective stress increases as pore pressure decreases (from undrained to drained condition) • Shear strength depends on both c' and φ', and increases with normal stress • Frictional resistance governs strength • Volume may change during shearing (dilation in dense sand, compression in loose sand) • Mohr-Coulomb failure envelope has positive slope (φ' > 0) **Drained Shear Strength Parameters c' and φ':** • c' is effective cohesion, measured from CD triaxial test or corrected direct shear test • φ' is angle of internal friction (effective stress basis) • For normally consolidated clay: c' ≈ 0, and φ' ≈ 30–35° • For sand: c' ≈ 0, and φ' ≈ 30–45° (depends on grain size, shape, and density) • c' and φ' are relatively constant for a given soil, independent of stress history (unlike c_u) **Design Applications (Drained, Long-Term):** • Long-term bearing capacity (after consolidation, years of service) • Long-term slope stability (embankments, natural slopes after many years) • Retaining wall design (at-rest and active earth pressure after consolidation) • Drained design uses: τ = c' + σ' tan φ', bearing capacity factor Nc is larger (≈ 25–30 for typical φ' ≈ 30°) **3.3 Comparison Table: Undrained vs. Drained** | Aspect | Undrained (Short-Term) | Drained (Long-Term) | |--------|------------------------|---------------------| | **Time Scale** | Hours to days (immediate) | Weeks to years (long-term) | | **Permeability Effect** | Water cannot drain; pores locked | Water freely drains | | **Pore Pressure** | Excess pore pressure develops | Returns to hydrostatic | | **Effective Stress** | Decreases (σ' = σ − Δu) | Increases or stabilizes | | **Shear Strength** | Constant (independent of confining pressure) | Increases with confining pressure | | **Failure Criterion** | τ = c_u (φ ≈ 0) | τ = c' + σ' tan φ' | | **Soil Type** | Saturated clay | Sand; clay after consolidation | | **Typical Strength** | 25–200 kPa (c_u) | Varies with stress; typically larger in sandy soil | | **Critical Condition** | New construction, rapid load | Foundation settlement, long-term slopes | | **Design Examples** | Excavation stability (week 1) | Foundation design (year 10) | **3.4 Transition: From Undrained to Drained** In reality, most saturated clay soils undergo a transition from undrained behavior (immediately after loading) to drained behavior (after consolidation). This process is governed by the coefficient of consolidation (cv) and is quantified by the time factor Tv: Tv = cv × t / H² where: • cv = coefficient of consolidation (from consolidation test) in m²/s • t = elapsed time in seconds • H = drainage path length in meters • Tv = dimensionless time factor Typical milestones: • Tv ≈ 0.2 (50% consolidation) ≈ half excess pore pressure dissipated • Tv ≈ 0.5 (approaching 85% consolidation) ≈ most consolidation complete • Tv ≈ 1.0 (95% consolidation) ≈ essentially drained conditions **For a low-permeability clay with cv ≈ 1 × 10⁻⁷ m²/s and drainage path H ≈ 5 m:** Time to 50% consolidation ≈ 0.2 × (5)² / (1 × 10⁻⁷) ≈ 5 × 10⁷ seconds ≈ 1.6 years This long time scale is why undrained analysis is critical for short-term (< 1–2 year) performance of clay structures in the Philippines, but drained analysis is necessary for long-term foundation design. **3.5 Practical Implications for Philippine Engineering Practice** **For Building Foundations (RA 544, Building Code Requirements):** • Initial bearing capacity analysis (design phase) typically uses drained parameters (long-term) • Short-term settlement (immediate) may use undrained parameters if ground is recently loaded • Foundation depth typically > 1.5 m, so drainage conditions depend on soil permeability and loading rate • Precast pile foundation in clay: upper soil (0–5 m depth with low permeability) may exhibit undrained behavior initially; lower soil (> 10 m) behaves in drained manner over project life **For Slope Stability and Embankments:** • Critical circle analysis often uses two methods: - UU (undrained): Controls short-term stability during and immediately after construction (critical during wet season) - CD (drained): Controls long-term stability after consolidation (critical for design life of 50+ years) • Factor of safety requirements: typically FS ≥ 1.3 (undrained, short-term) and FS ≥ 1.5 (drained, long-term) • Slopes in Metro Manila clays may have low undrained strength (soft clay, c_u ≈ 30–50 kPa), making short-term stability critical **For Excavations:** • Excavations in clay (0–5 m depth) often fail in undrained manner (hours to days) • Bracing must be designed for undrained strength; add surcharge effects from undrained c_u • Maximum stable excavation depth ≈ 4 × c_u (for φ = 0 soil without bracing), e.g., c_u ≈ 50 kPa → max depth ≈ 2 m without support **For Retaining Walls:** • Active earth pressure during construction (undrained): Ka = 1 − 4c_u/(γ × H) (reduced from 0.33 due to cohesion) • At-rest pressure (drained, long-term): K0 = 1 − sin φ' (increases with time as pore pressures dissipate) • Drainage behind wall is critical; if wall allows pore pressure buildup (no drainage), strength decreases and wall pressure increases

This section compiles the essential formulas and relationships you must master for the PRC Civil Engineer Licensure Examination. Each formula is presented with its context, limitations, and typical applications. **4.1 Mohr-Coulomb Failure Criterion** **Total Stress Form:** τf = c + σ tan φ where: • τf = shear strength (shear stress at failure) [kPa] • c = cohesion (total stress) [kPa] • σ = normal stress [kPa] • φ = angle of internal friction [degrees] **Effective Stress Form (Terzaghi's Principle):** τf = c' + σ' tan φ' where: • c' = effective cohesion [kPa] • σ' = effective normal stress = σ − u [kPa] • u = pore water pressure [kPa] • φ' = angle of internal friction (effective) [degrees] **When to Use:** • Total stress (c, φ): Undrained analysis (short-term clay behavior) • Effective stress (c', φ'): Drained analysis (long-term behavior, sand) **4.2 Principal Stress Relationships at Failure** **For Cohesionless Soil (c = 0):** sin φ = (σ1 − σ3) / (σ1 + σ3) Alternatively: σ1 = σ3 tan²(45° + φ/2) **For Soil with Cohesion:** σ1 = σ3 tan²(45° + φ/2) + 2c tan(45° + φ/2) Alternatively (from Mohr circle): c = (σ1 − σ3) sin φ / [2 cos(45° − φ/2)] **Deviator Stress:** q = Δσ = σ1 − σ3 [kPa] **Confining Pressure (Minor Principal Stress):** σ3 = confining pressure [kPa] **When to Use:** • Interpreting triaxial test results • Finding φ from principal stresses at failure • Calculating bearing capacity with φ-dependent terms **4.3 Unconfined Compression Test** **Undrained Shear Strength from UC Test:** c_u = qu / 2 where: • c_u = undrained shear strength [kPa] • qu = unconfined compressive strength (peak axial stress) [kPa] **Note:** This formula applies only to saturated clay under undrained loading (φ_u ≈ 0). For partially saturated clay or silt, c_u may differ from qu/2. **When to Use:** • Quick field assessment of clay strength • Preliminary bearing capacity estimates • Stability analysis for short-term loading • PRC exam: Almost always, an UC test is given with qu, and you must calculate c_u = qu/2 **4.4 Clay Consistency Based on Undrained Strength** | Classification | Undrained Strength c_u | SPT Blows/300 mm | |---|---|---| | Very Soft | < 25 kPa | < 2 | | Soft | 25–50 kPa | 2–4 | | Firm | 50–100 kPa | 4–8 | | Stiff | 100–200 kPa | 8–15 | | Very Stiff | 200–400 kPa | 15–30 | | Hard | > 400 kPa | > 30 | **When to Use:** • Classifying clay for design purposes • Correlating lab tests with field boring data • Preliminary bearing capacity estimates **4.5 Direct Shear Test Analysis** **Shear Stress:** τ = V / A where: • V = applied shear force [N or kN] • A = area of shear box [m²] **Normal Stress:** σ = P / A where: • P = applied normal load [N or kN] **Friction Angle from Slope of τ-σ Plot:** tan φ = Δτ / Δσ (slope of best-fit line through failure points) φ = arctan(Δτ / Δσ) **Cohesion from τ-σ Plot:** c = y-intercept of the failure envelope (extrapolate line to σ = 0) **When to Use:** • Calculating c and φ from direct shear test data • Finding residual friction angle (run test to large displacement) • Sand and gravel testing (easier than triaxial) **4.6 Triaxial Test Parameters** **Deviator Stress at Failure:** q_f = (σ1 − σ3)_f [kPa] **Effective Stress Principal Stresses at Failure:** σ1' = σ1 − u_f σ3' = σ3 − u_f where u_f is pore pressure at failure (measured in CU test). **Friction Angle from Triaxial Test:** sin φ' = (σ1' − σ3') / (σ1' + σ3') φ' = arcsin[(σ1' − σ3') / (σ1' + σ3')] **Pore Pressure Parameters (CU Test):** Δu = B[Δσ3 + A(Δσ1 − Δσ3)] where: • B ≈ 1.0 for saturated soil (usually) • A = pore pressure coefficient (typically 0.5–1.0 at failure) **When to Use:** • Triaxial test interpretation • CU test analysis with pore pressure measurement • Determining both total and effective parameters from one test **4.7 Effective Stress and Pore Pressure Relationships** **Terzaghi's Effective Stress Principle:** σ' = σ − u where: • σ' = effective stress [kPa] • σ = total stress (all-encompassing stress) [kPa] • u = pore water pressure (gauge pressure, positive when above hydrostatic) [kPa] **Undrained Response (φ ≈ 0):** Δσ' = Δσ − Δu = 0 (if Δu = Δσ, all load goes into pore pressure) c_undrained ≈ c_u = constant **Drained Response (φ = φ'):** Δσ' = Δσ − Δu = Δσ (if Δu = 0, load directly increases effective stress) τf = c' + σ' tan φ' (frictional behavior) **When to Use:** • Analyzing consolidated-undrained (CU) tests • Calculating effective stress at any depth • Explaining why undrained strength is constant while drained strength increases with confining pressure **4.8 Consolidation and Drainage Time Factor** **Time Factor (Terzaghi's One-Dimensional Consolidation):** Tv = cv × t / H² where: • Tv = dimensionless time factor [unitless] • cv = coefficient of consolidation [m²/s or cm²/s] • t = time [s] or [day] • H = drainage path length (distance to nearest drainage boundary) [m or cm] **Typical Consolidation Milestones:** • Tv ≈ 0.2 → 50% consolidation (half excess pore pressure dissipated) • Tv ≈ 0.5 → 85% consolidation • Tv ≈ 1.0 → 95% consolidation (approaching drained conditions) **Time to Reach 50% Consolidation:** t_50 = 0.2 × H² / cv **When to Use:** • Estimating when embankment will transition from undrained to drained behavior • Scheduling construction to allow consolidation • Correlating field settlements with test predictions • **Note:** This is NOT always asked directly on the PRC exam, but understanding it is critical for time-dependent analysis. **4.9 Bearing Capacity Factors (Related to φ')** For a **horizontal foundation with φ' = 0 (undrained clay):** Nc ≈ 5.14 (from Terzaghi or Meyerhof) For a **horizontal foundation with φ' > 0:** | φ' [deg] | Nc | Nq | Nγ | |---|---|---|---| | 0 | 5.14 | 1.00 | 0.00 | | 10 | 6.30 | 1.97 | 0.92 | | 15 | 7.55 | 2.97 | 1.93 | | 20 | 9.19 | 4.44 | 3.64 | | 25 | 11.26 | 6.77 | 6.76 | | 30 | 13.80 | 10.94 | 12.53 | | 35 | 17.69 | 18.40 | 22.40 | | 40 | 23.30 | 33.30 | 42.16 | **When to Use:** • Foundation bearing capacity design • Understanding why drained (φ' > 0) foundations have much higher capacity than undrained (φ' = 0) **4.10 Summary Table: Which Formula for Which Condition** | Condition | Use Formula | Parameters | Time Scale | Typical Soil | |---|---|---|---|---| | **Undrained Loading** | τf = c_u | c_u only (φ ≈ 0) | Hours–days | Saturated clay | | **Unconfined Compression** | c_u = qu/2 | qu measured | Quick test | Soft clay | | **Drained Loading** | τf = c' + σ' tan φ' | c', φ' | Weeks–years | Sand; consolidated clay | | **Principal Stress (c=0)** | sin φ = (σ1−σ3)/(σ1+σ3) | σ1, σ3 | Analysis | Granular soil | | **Time-Dependent** | Tv = cv × t / H² | cv, t, H | Consolidation | Any soil | | **Effective Stress** | σ' = σ − u | σ, u | Always (drained/undrained) | All soils | **4.11 Exam Tips and Common Mistakes** 1. **c_u = qu / 2, not qu:** This is the most common error. Half the unconfined compressive strength is the shear strength, not the full strength. 2. **Effective Stress vs. Total Stress:** Always check which parameters you have: - If given c_u, φ_u ≈ 0 → undrained analysis - If given c', φ' → drained analysis 3. **Principal Stresses:** - σ1 = larger principal stress (more compressive) - σ3 = smaller principal stress (confining pressure) - Deviator = σ1 − σ3, NOT σ1 or σ3 alone 4. **Normal Stress on Failure Plane:** - For triaxial test, normal stress on failure plane ≠ σ3 - Mohr circle geometry: normal stress ≈ (σ1 + σ3)/2 at the failure plane 5. **Pore Pressure Dissipation:** - Excess pore pressure Δu develops immediately (undrained) - Returns to hydrostatic slowly (drained) - Plot effective stress vs. total stress on Mohr circles carefully 6. **Test Selection:** - UU → quick, undrained, φ ≈ 0 - CU → intermediate, measures pore pressure - CD → slow, long-term effective parameters - UC → simplest, undrained only, soft clay - Direct shear → simple, both sand and clay, but forced failure plane 7. **Sign Conventions:** - All stresses are compressive (positive in geotechnical convention) - Pore pressure u is positive when above atmospheric (which it always is below water table) - Excess pore pressure Δu is positive (above hydrostatic)