英文紙質(zhì)習(xí)題集電子版課件

1、Groundwater DynamicsProblem SetsWeimin Ye Professor, Ph.D.Department of Geotechnical EngineeringSchool of Civil EngineeringTongji University1239 Siping Road, Shanghai, China P.R.Groundwater Dynamics Problem SetsFirst EditionWeimin YE Qian Zhao Yonggui Chen Bin Ye Long Xu PrefaceGroundwater hydrology

2、 is the science that treats the occurrence, distribution and movement of water below the surface of the earth. Groundwater Dynamics addresses the principles that govern the groundwater movement in the pores, fissures and solution cracksAs a compulsory course for bachelor students majoring in geologi

3、cal engineering, Groundnwater Dynamcis has been taught in bilingual classes at Tongji University for more than ten years. It was awarded as one of the National Bilingual Demonstration Courses by the Ministry of Education of China in 2009.This book is intended for a supplementary textbook of the cour

4、se Groundwater Dynamics taught in English. It also can be used as a reference book for graduate students, engineers who study and work in relevant fields. Problems are reorganized in 7 chapters according to the syllabus of Groundwater Dynamics. Some of them are adapted and edited from other textbook

5、s, which are listed in the reference of this book. Many thanks should be given to the authors of these books. In each chapter, problems are presented in “Words and phrases explanation”, “Fill in the blanks”, “True-false questions”, “Construction problems” and “Analysis and calculation”, in order to

6、help readers to understand the fundamental principles, problems and methods in the field.The authors are grateful to the Project National Bilingual Demonstration Courses : “Groundwater Dynamics” for the financial support. Thanks are also given to some of our former students, Mr. Zhang Wenxiang and M

7、r. Zhang Xingya, who once help us to read the manuscript and provided constructive feedback. Senior editor Ms. Yang Ningxia at Tongji University Press is also appreciated for her contributions to the preparation and editing of this book. WeiminYEShanghai, China P. R.ContentsPrefaceChapter 1. Fundame

8、ntals of seepage theoryChapter 2. Base flow to streamsChapter 3. Steady radial flow to a fully penetrating wellChapter 4. Transient radial flow to a fully penetrating wellChapter 5. Well flow near aquifer boundariesChapter 6. Groundwater flow to partially penetrating wellsChapter 7. Special problems

9、References Appendix A: Values of W(u) for Values of u (From Wenzel, 1942)Appendix B: Values of W(u, r/B) or W(u, a) for Values of u or u and r/B and a (From Hantush) Appendix C: Values of K0(r/B) for Values of r/B (From Hantush, 1956)Appendix D: AnswersChapter 1. Fundamentals of seepage theoryWords

10、and phrases explanation Porous mediaSeepageDarcy velocityLaminar flowTurbulent flowHydraulic gradientCritical hydraulic gradientHydraulic conductivityStorativity / Storage coefficientSpecific storagePermeabilityCoefficient of transmissivityUniformity coefficient Effective grain size PorosityEffectiv

11、e porosityPendular waterSpecific yield (Sy) Specific retention (Sr) Specific dischargeIntrinsic permeabilityAquiferAquitard AquifugeAquiclude Unconfined aquifer Confined, or artesian aquiferReynolds numberThe law of mass conservationFill in the blanks1. Groundwater hydrology can be defined as a scie

12、nce of _, distribution and _ of water below the surface of the earth. While groundwater dynamics is a discipline that deals with the principles of the groundwater movement in _, _and _. 2. Secondary interstices developed after the rock was_; examples include joints, _, _ and openings formed by plant

13、s and animals. 3. The major forms of existence of groundwater in porous media are_, _, _and_.4. In porous media, _ are the pores that do not interconnected, they have _contribution to the groundwater movement and however, they are _for the water storage. _ refers to those interconnected pores that a

14、re not occupied by bound water, consequently, they are available for fluid flow.5. An aquifer may be defined as a _ that contains sufficient permeable materials to yield significant quantity of water to wells or springs. 6. According to Darcys law, the flow rate through porous media is proportional

15、to _ and inversely proportional to _. 7. The cross-sectional area of flow for a porous medium is actually much _ than the dimensions of the aquifer. The actual velocity (interstitial velocity) is a velocity of _; in contrary, the Darcian velocity is the average velocity of _.8. In Darcys law, the fa

16、ctor q=Q/A is called the _, which has the dimensions of _. It is also sometimes called the _ velocity, which is not a true velocity as the _ is partially blocked with soil materials.9. The intrinsic permeability of geomaterial is considered to be independent of the pore fluid but only a function of

17、_, the units of the intrinsic permeability can be _or cm2.10. When the hydraulic head in a saturated aquifer or confining formation changes, water will be _ or _. The storage coefficient, or _, is the volume of water that a permeable unit will absorb or _ from the storage per unit _ per unit change

18、in _. 11. Based on the relationship between properties and locations, aquifers can be divided into_ and_ formations; Based on the relationship between properties and directions, they also can be considered as _ or _. 12. A homogeneous formation is one that has the same properties at all _, while in

19、a heterogeneous unit, hydraulic properties changes _. 13. The continuity equation of seepage flow represents _ and _ of groundwater movement.14. Water passes from one aquifer to another aquifer with different hydraulic conductivity, the direction of the flow path will _ . 15. Adjacent flow lines wil

20、l be _ to an impervious boundary and equipotential lines will _ it at _.16. The larger value of the leakage factor B indicates that the _ thickness of the aquitard, _ hydraulic conductivity, _ amount of leakage. 17. Groundwater models can be classified in several ways, steady state or _; confined, _

21、 or a combination of _; one-dimensional, _, _, or _.18. In Figure 1-1, based on the shape of groundwater depression cone, we can conclude that: for case (a), K0 K; for case (b), K0 K. Figure 11True - false questions1. The uniformity coefficient of a sediment is the ratio of the grain size that is 50

22、% finer by weight to the grain size that is 10% finer by weight, that is, Cu=d50/d10.2. An aquifer should have ability to store and transmit significant water. 3. Storativity is a concept that also can be applied to an unconfined aquifer.4. For an unconfined aquifer, specific yield and coefficient o

23、f storage are same concepts. 5. Practically, hydraulic head can be recognized as the driving impetus behind groundwater flow.6. Darcys equation is valid only when conditions are such that the resistive forces of viscosity predominate, which corresponds to a Reynolds number less than 1 to 10. 7. Gene

24、rally, the constant-permeameter can be employed for measuring hydraulic conductivity of geo-materials with low permeability. 8. The intrinsic hydraulic conductivity of an aquifer remains constant no matter how much the salinity of the fluid changes.9. Transmissivity is the amount of water that can b

25、e transmitted horizontally through a unit width of an aquifer under a hydraulic gradient equals to 1.10. A homogeneous and anisotropic aquifer has constant hydraulic conductivity everywhere. 11. When flow refraction occurs, larger difference of the hydraulic conductivities of the two mediums results

26、 in larger difference of incident angle and refraction angle. 12. For an aquifer formed by horizontal sub-layers, the equivalent hydraulic conductivity in the horizontal direction is always larger than that in the vertical direction.13. Groundwater cannot pass a no-flow boundary, while equipotential

27、 lines will intersect it at angles. 14. In deriving the equations for groundwater flow, the laws of mass conservation and energy conservation should be employed. 15. According to the law of mass conservation, any change in mass flowing into a small volume of the aquifer must be balanced by a corresp

28、onding change in mass flux out of the volume, or change in the mass stored in the volume, or both.16. In seepage domain, intersection of flow lines could happen at certain places. 17. In a water-table aquifer, if there is recharge or discharge across the water-table, flow lines will be at an angle t

29、o the water table. If not, the flow lines can be parallel to it. 18. In flow domain, streamline is considered as impervious boundary and equipotential line is considered as drainage boundary.19. In a homogeneous aquifer, flow lines and equipotential lines are always orthogonal.20. In an isotropic me

30、dium, the flow lines are parallel to grad h, while in an anisotropic medium they are not. 21. Continuity equation and fundamental differential equation for groundwater flow are based on the law of mass conservation.22. Leakage factor B and leakage coefficient are parameters that indicate the leakage

31、 capacity.23. Neumann boundary can be stream surface or equipotential plane. In some cases, it is also treated as Dirichlet boundary.24. Practically, the boundary with known flow rate and hydraulic head can be treated as either Neumann boundary or Dirichlet boundary.25. Surface water, such as stream

32、s or lakes, can be treated as Dirichlet boundary.Construction problem1. For each case in Figure 1-2, draw the hydraulic head profile for flow passes through aquifer.(a) (b) nFigure 1-22. Draw the streamlines of the flow systems in Figure 1-3 (a) and (b), respectively. Also indicate the flow directio

33、ns at points A & B when the flow direction at point R is given in Figure 1-4 (c)(K2=5K1). Figure 133. An unconfined aquifer locates between two streams, which have same water heads, as shown in Figure 1-4. Draw, 1) The water table of the aquifer in Figure 1-4 (a) and (b), respectively2) The sche

34、matic flow net. (a) (b)Figure 14Calculation1. A sand sample has a median pore radius of 0.12 mm. The fluid density is 1.02×103 kg/m3 and the fluid viscosity is 1.16×10-3 N.s/m2. If the flow rate is 0.006 m/s, is Darcys law valid in the sample? 2. A confined aquifer with a thickness of 30m

35、has specific storage of 2.51×10-5 m-1. Determine how much water can be released when the piezometric surface is lowered by 1 m over an area of 0.8 km2.3. A confined aquifer has a specific storage of 5.4×10-4 m-1 and a thickness of 25 m. How much water would it yield if the water declined a

36、n average of 4.0 m over a circular area with a radius of 150 m.4. According to the falling-head permeameter in the Figure 1-5. 1) Derive the equation of calculation of the hydraulic conductivity of the geo-materials (sample) tested. 2) This method generally employed for measuring hydraulic conductiv

37、ity of geo-materials with lower or higher values? Figure 1-55. Consider groundwater flows through a confined aquifer with uniform thickness of 40 m, the discharge per unit width is 42 m2/h, find the specific discharge (Darcy velocity) and the actual velocity of the flow when the effective porosity o

38、f the aquifer is given as 0.24.6. The hydraulic conductivity of a confined aquifer is 30m/d. There are two cross-sections A and B 4200m apart, the thickness of the aquifer linearly changes from 110m in cross-section A to 70m in B. When given HA=123.8m，HB=150m: Calculate the unit discharge q and the

39、hydraulic head midway between A and B.7. A confined aquifer locates on top of horizontal impervious bedrock; it has a varying thickness as shown in the Fig1-5. Assuming the hydraulic conductivity of the aquifer K changes along x axis: K=10+0.004x (m/d), where x=0 at section (A). If the piezometric h

40、eads at section (A) and (B) are 125m and 118m, respectively. 1) Determine the flow rate per unit width2) Plot the piezometeric head between points A and B. 70m30m900m(A)(B)Fig 1-58. A falling head permeameter has a 10-cm diameter cylinder. The specimen tested is 30-cm-long and the diameter of the tu

41、be is 12 mm. The initial water level in the tube is 25cm above the outlet level and drops to 20 cm after 3 hours of operation. Determine the hydraulic conductivity of the specimen.9. A confined aquifer has a thickness of 50 m and coefficient of storage 4.4×10-4. The porosity of the aquifer is 0

42、.24. Determine 1) The fractions of the expansibility of water and compressibility the aquifer skeleton in making up the storage coefficient of the aquifer. 2) The compressibility of the aquifer skeleton, assuming that the compressibility of water is 4.2×10-10 m2/N. 10. An unconfined aquifer has

43、 a porosity of 0.25 and a specific retention of 0.13. When groundwater level drops an average of 4.0m over an area of 1.5 km2, find the specific yield of the aquifer and the volume change of pore water.11. A homogeneous and isotropic confined aquifer has a hydraulic conductivity of 18.5m/d and a por

44、osity of 0.24. The elevations of the piezometric head at two observation wells 800m apart are 25.8 m and 22.5m, respectively. Determine the specific discharge and actual velocity of the one dimensional steady flow.12. An aquifer consists of three horizontal, homogeneous and isotropic layers, from to

45、p to bottom are labled as A, B and C, with hydraulic conductivity equals to KA; KB; KC, respectively. Given KA=2KB，KC=2KA, if flow approaches the boundary of layer A and B with an incident angle of 400, calculate the refraction angle in layer C. 13. A confined aquifer has three different horizontal

46、formations. Formation 1 has a thickness of 6.0m and a hydraulic conductivity of 5m/d. Formation 2 has a thickness of 1.5m and a hydraulic conductivity of 30m/d. Formation 3 has a thickness of 8.0 m and a hydraulic conductivity of 8m/d. Assume that each formation is isotropic and homogeneous. 1) Dete

47、rmine both the overall (equivalent) horizontal and vertical hydraulic conductivities. 2) If a hydraulic gradient of 5 is applied, find the flow rate. 14.An unconfined aquifer consists of four horizontal layers, each individually homogeneous and isotropic. From top to bottom, the four layers have the

48、ir thickness and hydraulic conductivity of 10m and 10.3 m/d; 8 m and 7.8 m/d; 4.5 m and 5.0 m/d, as well as 12 m 3.0 m/d, respectively. 1）Determine the equivalent horizontal and vertical hydraulic conductivities. 2）Compare the equivalent hydraulic conductivities in 1).15. A well penetrates a homogen

49、eous, isotropic, infinitely extended unconfined aquifer. The initial groundwater table is at H0(x, y) above the impermeable bedrock. Derive the mathematical expression that describes the transient flow towards the well for each of the following conditions:1) The well pumps water at constant rate Qw.

50、2) The water table Hw remains constant in the well16. An aquifer is composed of n layers of identical strata, as shown in Figure 1-6. Each stratum has two alternating sub-layers with thickness of M1 and M2 and hydraulic conductivities of K1 and K2, respectively. (1) Find the equivalent hydraulic con

51、ductivity: Kh in horizontal direction and Kv in vertical direction.(2) Prove KhKv.Figure 1617. Based on the refraction of flow lines described in Figure 1-7, find out the relationship between K1 and K2. Figure 1-718. There is a leaky confined aquifer has a horizontal hydraulic conductivity of 0.8 m/

52、h, which is overlain by an aquitard with a vertical hydraulic conductivity of 2.4×10-3 m/d. Given the flow in the aquitard is in the downward direction with an angle of 60 with the vertical (the incident angle), determine the refraction angle. 19. A confined aquifer has a constant thickness of

53、30 m and is stratified between two observation boreholes as shown in the following Figure 1-8.1) Derive the equation for calculation of the equivalent horizontal hydraulic conductivity of that section of the confined aquifer between the observation boreholes. If K1=12m/d, K2=9m/d, K3=35m/d; L1=80m/d

54、, L2=120m/d, L3=240m/d. Determine the equivalent horizontal hydraulic conductivity.2) Given the piezometric surface elevations as indicates in the Figure, determine the flow per unit width of the aquifer. Plot the potentiometric surface between the two observation boreholes.Figure 1-820. Figure 1-9

55、is a profile of a uniform, horizontal confined aquifer. There are two observation boreholes A and B, with elevations of the piezometric head readings of HA=50.2 m and HB=45.8 m. The thickness of the aquifer is 45 m, along the flow direction there are 3 sub-layers with the length of L1=300m，L2=600m a

56、nd L3=100m, corresponding hydraulic conductivities are given as K1=35m/d，K2=15m/d and K3=20m/d, respectively. a) Calculate the equivalent horizontal hydraulic conductivity and the discharge per unit width b) Plot the profile of piezometric headc) Rework on (a) and (b) if HB=43.8m.Figure 1921. Figure 1-10 is a horizontal homogeneous and isotropic unconfined aquifer with an