--- title: "Critical gradient; quick condition in sand" subject: "Soil Mechanics" chapter: 6 key: "semester_4/soil_mechanics:critical-hydraulic-gradient-quick" source: https://www.bctengineer.com/q/semester_4/soil_mechanics/critical-hydraulic-gradient-quick site: BCT Engineering --- # Critical gradient; quick condition in sand Soil Mechanics · Chapter 6: Principle of Effective Stress, Capillarity and Permeability - Asked in: 2073 Magh, 4+1 marks - Video: [Geotechnical Engineering !! Basic Soil Mechanics !! Critical Hydraulic Gradient](https://www.youtube.com/watch?v=hSD-p3Ibomw) — Geotechnic Gurujee: GATE & IES - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/critical-hydraulic-gradient-quick - Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-6 ## Question Obtain the expression for the critical hydraulic gradient necessary for quick condition to develop. Why is there more likelihood of quick conditions in sand than in clay? ## Short answer Critical hydraulic gradient for quick condition is ic = gamma'/gamma_w = (G-1)/(1+e), obtained by setting effective stress zero. Sand is more likely than clay because it is cohesionless and permeable, allowing large upward gradients and grain lifting; clay has cohesion and low permeability. ## Answer #### Expression for critical hydraulic gradient Take a sand layer of thickness $L$ and saturated unit weight $\gamma_{sat}$ in a tank. Water flows upward under a net head $h$ (head loss over the sample). ```text h ↑ head causing upward flow --------------- water ======= sand L --------------- filter ↑ ↑ ↑ inflow ``` At the base of the sand layer: $$ \sigma = \gamma_{sat}L \quad (\text{ignoring water above the soil, it cancels in } \sigma') $$ $$ u = \gamma_w (L + h) $$ $$ \sigma' = \sigma - u = \gamma_{sat}L - \gamma_w L - \gamma_w h = \gamma' L - \gamma_w h $$ Quick condition begins when $\sigma' = 0$: $$ \gamma' L = \gamma_w h_c \quad \Rightarrow \quad i_c = \frac{h_c}{L} = \frac{\gamma'}{\gamma_w} $$ Using $\gamma' = \dfrac{(G-1)\gamma_w}{1+e}$: $$ i_c = \frac{G-1}{1+e} $$ For $G = 2.65$ and $e = 0.65$, $i_c = 1.0$. #### Why sand more than clay - Sand is cohesionless: once $\sigma' = 0$ the grains have no strength at all. Clay has cohesion, so it keeps some strength even when $\sigma'$ is zero. - Sand is highly permeable, so a large hydraulic gradient can easily be developed and a large flow of water occurs at the exit surface. In clay, low permeability makes the flow very small, so the critical gradient is rarely reached. - Clay particles are bound by electrochemical forces, which resist being lifted by seepage. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Quick condition in upward seepage begins when: A. Total stress becomes zero B. Effective stress becomes zero C. Pore pressure becomes zero D. Seepage velocity equals discharge velocity Answer: B. Upward flow raises u until sigma' = sigma - u = 0; the grains then have no contact stress and lose all strength. (Key point: Condition for quick) 2. The critical hydraulic gradient is given by: A. i_c = gamma_sat/gamma_w B. i_c = (1+e)/(G-1) C. i_c = gamma'/gamma_w = (G-1)/(1+e) D. i_c = G/(1+e) Answer: C. Setting gamma'L = gamma_w h_c gives i_c = gamma'/gamma_w, which with gamma' = (G-1)gamma_w/(1+e) becomes (G-1)/(1+e). (Key point: Critical gradient expression) 3. For G = 2.65 and e = 0.65, the critical gradient is about: A. 0.5 B. 1.65 C. 2.0 D. 1.0 Answer: D. i_c = (2.65-1)/(1+0.65) = 1.65/1.65 = 1.0. (Key point: Numerical value) 4. Why is quick condition more likely in sand than in clay? A. Sand is cohesionless and highly permeable, so a large gradient and flow can develop B. Sand has a higher critical gradient than clay C. Clay has a larger void ratio D. Sand particles are bound by electrochemical forces Answer: A. Sand has no cohesion once sigma' = 0 and its high permeability allows large gradients and exit flow; clay has cohesion and very low flow. 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